Sharp Blue: Relativity, FTL and causality


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A brief note to my recent visitors: If you’ve arrived here from sites with highly misleading blurbs and expect to find a discussion of how faster-than-light travel is possible, I’m afraid you will be disappointed. This article outlines an argument commonly accepted by physicists which demonstrates that in special relativity faster-than-light travel is not possible.

(This article forms a companion piece of sorts to the first half of the section on Special Relativity in my Very Brief History of Time, so it might make more sense if you read that first. If that doesn’t make sense, try reading the earlier parts too!)

One of the most striking aspects of special relativity is that faster than light travel is equivalent to time travel. This is also one of the most widely understood aspects of the theory, and almost every explanation I’ve seen of the effects of superluminal travel on causality has been badly garbled. In this article, I will try to explain it more clearly.

The paths of light rays in a special relativistic spacetime (a so-called Minkowski spacetime) act like a causal grain running through the spacetime. The outgoing light rays from an event form a surface in spacetime called the event’s future light cone. The light rays converging on an event form a surface called the event’s past light cone. For any event P (where P is a label for something happening at a given place at a given time), the events within P’s future light cone make up its absolute future and those within its past light cone make up its absolute past: the former are the events that P can influence and the latter are the events that can influence P. Unlike the situation in classical mechanics, there are also events outside both light cones of P that can neither influence nor be influenced by P (at least in the absence of faster than light travel or communication). These concepts are summarised in figure 1 (where, as usual in such spacetime diagrams, I’ve suppressed two spatial dimensions):

Minkowski spacetime
Figure 1 The causal structure of Minkowski spacetime. The events that occur after P in all frames form the absolute future of P. The events that occur before P in all frames form the absolute past of P. Event Q is in neither P’s absolute future nor P’s absolute past.

To understand this causal structure a little better, we’ll have to look more closely at how different observers see spacetime. In the following, we’ll be exclusively concerned with observers at rest in inertial frames, which are collections of coordinate systems moving at uniform velocity with respect to one another. Special relativity is founded on two postulates (and a lot of experimental evidence supporting its conclusions, of course):

  1. The laws of physics look the same to all observers in inertial reference frames. This is the “Principle of Relativity” that lets us perform calculations relative to any inertial frame we like and be assured that we will get the same values for all physically meaningful quantities. This postulate holds in classical mechanics too.
  2. The speed of light is the same in all directions in all inertial frames. It is this postulate that gives rise to all the strange consequences of special relativity, including those discussed here.

The constancy of the speed of light in all frames means that different observers must slice spacetime into space and time in different ways. This is quite unlike the situation in classical mechanics, in which everyone can agree on what is space and what is time. In particular, from the point of view of a stationary observer, an observer moving at constant velocity has a coordinate frame whose space and time axes are “tilted” towards the light cone. By the relativity postulate, this situation must be symmetric - the second observer will consider herself stationary and the first observer’s frame “tilted”. From this sort of reasoning and a little bit of mathematical sophistication, we can cook up a recipe for translating the coordinates assigned to events between inertial frames. Each such translation is known as a Lorentz transformation. Let’s look at one more closely:

A Lorentz transformation
Figure 2 A Lorentz transformation. The frames are moving at 0.4c relative to each other. The light cones are left invariant by the transformation. Event Q occurs before event P in the white frame but after P in the blue frame.

In this diagram, we can see the seeds of our strategy for violating causality using faster than light signals. Looking at events P and Q, we see that P occurs after Q according to the observer in the white frame, but to the observer in the blue frame P happens first. This situation is enshrined in the lore of relativity under the name “relativity of simultaneity”, because different observers will have different ideas about which events take place simultaneously. For events within the light cones, though, all observers agree on temporal ordering. It’s not possible to tilt the coordinate frame enough to make events in P’s absolute future appear to be in P’s past. That’s why it’s called the absolute future in the first place!

All of the foregoing may be quite odd to those unfamiliar with relativity, but all will be well for causality provided that there are no superluminal causal influences. If we have faster than light effects then it’s rather easy to make paradoxical causality violations. For the sake of concreteness, I’ll consider a pair of “ansibles” - superluminal transmitters whose signals are received simultaneously with their transmission when both the transmitter and receiver share an inertial frame. The same sort of argument applies to faster than light effects that are not instantaneous, and to signals carried by faster than light spacecraft. I’ve just chosen this case because it makes the diagrams easier to draw and easier to understand. Let’s look at a single use of our ansible:

The first transmission
Figure 3 First superluminal transmission. Alice transmits from event P and the signal is instantaneously received by Bob at event Q. Alice and Bob are at rest relative to each other.

By itself, this single use of the ansible doesn’t create a causality violation. If Bob transmits a signal back towards Alice using a conventional light-speed transmitter, she receives it a later time than when she signalled to Bob. Even if Bob re-transmits with his ansible, Alice receives the reply just a little after she sent out her signal. The problems arise when we bring another inertial frame into play. Let’s suppose that we have another pair of inertial observers, Carol and Dave, who are moving with respect to Alice and Bob, and who have a pair of ansibles of their own. As Carol flies past Bob at event Q, Bob gives her the message from Alice and she transmits it to Dave as soon in the diagram (in which I’ve not drawn any coordinate grids to reduce clutter):

The second transmission
Figure 4 Second superluminal transmission. Carol transmits from event Q and the signal is instantaneously received by Dave at event R. Carol and Dave are at rest relative to each other, and moving at constant velocity relative to Alice and Bob. (The coordinate grid is centred on event Q.)

Now causality is in real trouble, as we can see if we consider the pair of transmissions (from Alice to Bob, then from Carol to Dave):

A causality violation
Figure 5 Creating a causality violation using two superluminal transmissions. Notice that Carol and Dave think that it’s the first signal that goes backwards in time, but Alice and Bob think it’s the second one that does.

Notice that we’ve arranged for Dave to receive the signal from Carol as he’s flying past Alice. Notice too that he receives it before Alice has sent her first signal! This means that Alice can transmit information into her own past by way of Bob, Carol, Dave, some spaceships, and two pairs of ansibles. And that’s why faster than light travel or communication, special relativity and causality cannot coexist.

Next in Series: “Time Dilation” >>

My God! What gorgeous diagrams! Sorry... what was the point you were trying to explain again?

Hi, I have never thought that this arguement holds up. The ties between spacetime and light spreading presuppose that faster than light travel is impossible. You are using the theory to prove itself. If you have instantaneous communication or travel, the graph becomes completely even. This is because there is no longer any distance limitation to what can effect any observer.

No, I'm not using the theory to prove itself. In fact, I don't think we can prove physical theories at all - see, for example, "Science and Truth" in this series. If I haven't made it clear enough, my intention was to explain that in the theory of special relativity the existence of faster than light communication necessarily implies causality violations. This doesn't, of course, mean that in the real world FTL implies causality violation, because it's possible that special relativity is wrong. As is sometimes said, you can pick at most two of {special relativity, FTL, causality}. However, special relativity is supported by such a vast mass of experimental data to such a high precision (mostly through its combination with quantum mechanics in quantum field theory) that it's going to be very difficult to make a theory that fits all this data and allows FTL and causality to coexist.

I think this example is seriously messed up, if I may say so with my unscientific mind. You start out with 4 people, who all accelerated to some ungoodly velocity so time passes different in each reference system. But they still have a common framework - the outside universe, or whatever you want to call it. If you have a chain of communication A -> B -> C -> D, and D happens to be stuck in the past relative to A, why should the signal arrive in A's past? The time D is stuck in is not the time A is stuck in. By the time (according to A) that D gets the message, some additional time has passed for A.

These guys either have a common reference system, or they don't. Since in your hypothetical example they can communicate, they necessarily also have a common reference. Maybe the flow of their time is different, okay, but that'd simply be like having 2 computers running at different clock speeds.

The moral of the story, to me, seems to be: Don't pick one theory and try to explain the universe with it.

You might think that the example is seriously messed up but nevertheless it is in accordance with the theory of special relativity. There is more to special relativity than time passing at different speeds for observers in different inertial frames, because it requires more than just this change to classical notions of space and time to render the speed of light invariant. Indeed, the relativity of simultaneity - the fact that there is no absolute ordering of events outside each others' light cones - is in a sense more fundamental than time dilation as it is an immediate consequence of the need to leave light cones invariant.

The fact that they can communicate does not mean they have a common frame any more than the fact I can talk to someone on a train using a cellphone means that the train and I have a common inertial frame. What is happening is that the various observers are giving different coordinates to the same events. In a future article I will describe in more detail how they might do this using standard clocks and rigid measuring rods.

The moral of the story is that you can pick at most two members of the set {special relativity, causality, FTL}. You are explicitly saying that you reject special relativity, but this seems quite unwise to me as, in combination with quantum mechanics as quantum field theory, it is far and away the most stringently tested theory in science. A more reasonable position is to reject either causality or faster-than-light communication, and the standard choice by physicists is to reject FTL. But I sometimes think that perhaps the universe might turn out to be less causal than we expect.

Dear Richard,

i am very-very sorry to tell you that the above, unfortunately, does not constitute the prove of impossibility of FTL.

1: why would causality problem by itself render FTL impossible ? just look at the quantum mechanics.

2: please look at Figure 2. per STR event Q cannot affect event P. that's the whole idea of the minkowski diagram. but if FTL exists, then event Q can affect event P. that means the minkowski diagram is incorrect. thus it cannot be used as tool of proof.

3: you claim that one have to reject STR to accept FTL. why? imagine tomorrow The Nature publishes results of experiment that shows new .. er... nature force. so now we have EM-weak, gravity, strong, ... and "FTL interaction". would that mean that STR becomes "wrong"? no way! it would be the same fine theory for bodies and events when FTL interaction does not happen. like Newton's laws are just fine while v is very small compared to c. that's it.

still i must explicitly state here, for the benefit of readers whose professional interests and/or primary education are not related to physics: >>> there is absolutely no reasons to believe that FTL exists

I never claimed that I was attempting to prove the impossibility of FTL, only that I would show that in special relativity FTL is equivalent to time travel, which it is.

1. The issue with causality in special relativity with FTL is very different to the one in quantum mechanics. In quantum mechanics, the results of measurements are not in general determined by earlier states (only the probabilities of various outcomes are). However, in non-relativistic QM the model of space and time is Newtonian and even though events may cause any of a range of effects, those effects will surely occur after the cause. Indeed, even relatistic quantum field theory respects the causal structure of spacetime, which manifests itself technically as the commutation of field operators associated with events with spacelike separation.

2. But the Minkowski diagram still shows the relationships between coordinates ascribed to events by inertial observers in relative motion. The causality structure is secondary to this - the Lorentz transformations come straight from the postulates of special relativity, and then can be used to classify the orderings of pairs of events into invariant or relative classes.

3. No, I claim that if special relativity holds then we must choose between FTL and causality. Or else we could pick FTL and causality and have to modify special relativity. If we find FTL interactions that cannot be used to generate causality violations then we would have to take the latter option, but given how general the problem is and how successful special relativity has been, it's more likely that we would easily be able to construct causality violations.

But you are entirely right that we have no reason to believe that FTL exists.

I've been thinking more about what I said in section 2 of my previous comment and think it's a bit misleading. It's possible to get the causal structure of spacetime directly from the postulates too. But, of course, judgements about what is more or less fundamental are somewhat subjective anyway. What I was trying to say is that even if superluminal motion or communication exists, the Minkowski diagram will still be useful for showing different inertial coordinate systems. One works from the diagram towards the causal structure not the other way around.

I now see that the structure of my article doesn't reflect a development from the postulates. Instead I describe causality in spacetime in summary and then develop a more detailed picture. This seemed the best way to introduce the material when I wrote it but now I'm not so sure.

Also, I meant to say "in subluminal relative motion".

"if special relativity holds then we must choose between FTL and causality"

couldn't FTL be limited to non-casuality-violation interactions ?

also I am afraid, I have no idea what casuality means in non-QM (ie macro) world.

couldn't STR be a subset of more "general" theory (== our observable world is a subset) - thus what "seems" like FTL and/or casuality violations may be just fine from "bigger" view... somehow...

hey, i got linked to this page from SF site!

or, putting it more simple - most theories have limits in their application. so STR is limited to discribing systems without FTL interaction. in your words - it "holds" in FTL-compatible world. within its own limits. like all other theories. what's the problem ?

Is the causality violation in figure 5 (the red triangle) the same as what is known as a closed timelike curve, or is that something completely other?

No, it isn't a closed timelike curve, as the two sides PQ and QR are spacelike. There are no closed timelike curves in the Minkowskian spacetime of special relativity. In general relativity, however, the light cones at different events in general have different orientations, and then it's possible for some spacetimes to have curves that always remain inside the light cones at each event (and which thus are timelike) and which also are closed. This means that it would be possible for a slower than light to traverse them and thus to travel into its own past.

Thanks for explaining that so well! I never had such a clear picture of it before.

I would only add that you are using "causality" as a shorthand for a particular notion of causality, "causality as we know it". If the events in Figure 5 could actually transpire, it might well be that Alice and friends would find themselves in what we might call "Greek tragedy causality" or "ironic moral lesson causality" -- that is, even if the older Alice of event P sends the younger Alice at event R a message attempting to dissuade her from the course of action that led her to the situation she finds herself in at P, the message will, inevitably, have the opposite effect, causing her to send the message at P. The graph, in other words, will not be "rewritten" by the superluminal transmission -- the graph is inviolate, and the set of events at P-Q-R are a causal loop -- each can be considered a cause of the other two.

This kind of causality is clearly different from how we usually think of the world, but it still seems to merit the name "causality". A very good dramatization of this worldview is the recent book "The Time Traveler's Wife".

One might almost say this notion of causality is implied by the graph, at least by the idea of the graph as a static "record of history".

Another alternative -- featured recently (though not by any means for the first time) in an Orson Scott Card book whose title is something like "Pastwatch: The Redemption of Christopher Columbus" -- is that sending a message back can change the past, erasing the events that caused the message. We could call this "orphaned effects" or "vanished history" causality, in the sense that we could observe effects, in such a world, whose causes "never happened". Alice's message at P, received at R, successfully averts the situation that gave rise to her sending P. Thus, when she arrives at P' -- the replacement for P -- she sends no message, despite her memory of receiving a message at R, which was sent from a P located in "vanished history" (as well as a vanished *future*, from her perspective just before time P').

It's then a philosophical question whether P "was there and went away", or whether P occurred in "a parallel universe". I'm not sure any experiment could be devised to distinguish between these two alternatives.

(To fully describe the "parallel universe" variant, it might be possible to create another time axis orthogonal to t, along which you could layer the "erased pasts" of the universe?)

Also, if there were superlumnal signals and thus time travelling messages, it's interesting to think about what experiments could discover if you were in a "Greek tragedy/fixed past" universe or a "orphaned effects/malleable past" universe. If you observe a lot of failed attempts to change the past, and no successful ones, you have a strong reason to suspect a fixed past. If you can establish any effects whose causes have vanished, you can prove a malleable past. But I suspect that this will always be a "historical science" like cosmology, not a "laboratory science" like particle physics, since the experiment "try and change the past, and see if you vanish" is not possible. Only your inheritor self, in the alternate present created by your intervention, can observe the result of the experiment (which she never initiated).

In any of these cases, though, some kind of "causality" still exists, though it isn't our everyday notion of causality, in which all effects are caused by causes that happened in their pasts, and our decisions can change the future unconstrained by "what is already going to happen".

Also n.b. however, while I don't believe the "orphaned effects" model has ever been historically popular, the "Greek tragedy" model -- which you could also call Kismet or predestination -- has at various historical periods been the dominant one.

Thinking again: actually it's the "P was there and went away" interpretation of the malleable-past alternative that requires a second time axis, so that you can answer the questions "was there when? went away when?"

I would only add that you are using "causality" as a shorthand for a particular notion of causality, "causality as we know it".

Pretty much every word we use could have "as we know it" appended to it.

what we might call "Greek tragedy causality" or "ironic moral lesson causality"

I believe physicists refer to it as Novikov's principle of self-consistency.

while I don't believe the "orphaned effects" model has ever been historically popular

Historically? In historical terms, the idea of time travel is very young. But for as long as there have been time travel stories, there have been plenty of stories which assumed that the past can be changed.

Visser calls the "orphaned effects" version the "radical rewrite conjecture".

As for the consistent histories version, my favourite story along those lines is Egan's "The Hundred Light-Year Diary".

> Pretty much every word we use could have "as we know it" appended to it.

Well, sure. But what I mean is that neither time-travel-allowing scenario requires us to abandon the notion of thing A causing thing B, the way it is abandoned in some kind of surrealist dream logic. It just makes causality a local phenomenon.

> In historical terms, the idea of time travel is very young.

But the idea of messages foretelling the future -- prophecy -- is very old, has the same issues. The ancient Greeks, or medieval Muslim theologians, or Calvin, would have had no problem with Novikov's principle of self-consistency -- it's only we moderns who find it weird.

We find it weird principally because of our own sense of self-importance -- our decisions should MATTER, damn it -- we should be the authors of our destinies, not just from our own relative perspective, but absolutely speaking.

The ancients would have had no problem with calling a Novikovian universe's mode of operation "causality". Believers in predestination often discuss final cause and effect -- though for a predestinationist, a final cause is an absolute mandate rather than a vague wish. For us moderns, proximate causes rule and final causes are metaphorical (a hammer's final cause is nailing whether or not it ever happens to nail any nails). But John Calvin's causality is still causality.

But what I mean is that neither time-travel-allowing scenario requires us to abandon the notion of thing A causing thing B, the way it is abandoned in some kind of surrealist dream logic. It just makes causality a local phenomenon.

That was the conclusion I've come to. I've been wondering if there would be any way to test that, observationally, with current technology -- would we expect to see any evidence of effects without causes at the astronomical scale? (My guess is "no", without also observing over astronomical timescales, but it's just a guess.)

But what I mean is that neither time-travel-allowing scenario requires us to abandon the notion of thing A causing thing B, the way it is abandoned in some kind of surrealist dream logic.

No argument. (Although I have no doubt that if we lived in a universe governed by surrealist dream logic, you'd find a use for the word "causality" there too. :)

But the idea of messages foretelling the future -- prophecy -- is very old, has the same issues.

There are similarities, but prophecy is not the same thing as receiving a message from the future. Note that I didn't say that predestination is a new idea; I said that the "orphaned effects" model is. What would that model look like in the context of prophecy? I doubt the ancient Greeks ever said that an oracle prophesied a future that was erased from existence when people took actions based on the prophecy.

When someone's prediction doesn't come to pass, we don't conclude that a timeline has been erased. At most, we might say that we've heeded his warning. More often, we'd just say his prediction turned out to be wrong. The "orphaned effects" model has very different conceptual underpinnings than prophecy, and those underpinnings are of recent origin, historically speaking.

The ancients would have had no problem with calling a Novikovian universe's mode of operation "causality".

I'm sure they wouldn't. But the original essay is a discussion of modern physics, not ancient philosophy. In modern physics, causality means that an effect must lie in the future light cone of its cause.

To put it another way: Rich noted, "As is sometimes said, you can pick at most two of {special relativity, FTL, causality}." But no one ever said, "pick two out of {special relativity, FTL, predestination}."

(Although I have no doubt that if we lived in a universe governed by surrealist dream logic, you'd find a use for the word "causality" there too. :)

Of course. On Thursdays, for instance, it would mean "what the fishdog says to the ampersand-dune".

Note that I didn't say that predestination is a new idea; I said that the "orphaned effects" model is.

Right, that was my point -- "Novikov's principle of self-consistency" is much older than science, while Visser's "radical rewrite conjecture" does not, to my knowledge, predate Hugo Gernsback.

At most, we might say that we've heeded his warning. More often, we'd just say his prediction turned out to be wrong.

That's what we moderns would say: some ancients, at least, would say it was a false prophecy.

To put it another way: Rich noted, "As is sometimes said, you can pick at most two of {special relativity, FTL, causality}."

...where causality has the special technical meaning it has in current physics, as opposed to what it means in the dictionary.

But that's a much weaker statement. To say, "new discoveries in physics could cause us to change the highly specialized definitions physicists have developed in recent years!" just doesn't get me quite as worked up as "new discoveries in physics could cause us to throw out our bedrock notions of how the world works in an everyday sense."

If causality is a purely local phenomenon, that would be a striking and unprecedented change in our worldview.

If, on the other hand, we live in a predestined universe, that's interesting, but it's a return to perhaps the most popular historical understanding of causality.

Interesting conversation (I was pointed here by Ben's blog...). I'd like to weigh in from the surrealist dream logic camp. Here's a paraphrase of a post to my own blog on causality.

I've been toying recently with solipsism, the notion that the only reality is the reality that one perceives, and that the Other is simply a trick of consciousness. That my consciousness is real, but (for instance) my son Lukas is a figment of my imagination.

I have experiences where my mind imagines that a state is such-and-so (like my toothbrush is on the counter), but when I check up on the state, I find that the universe has rearranged things (my toothbrush is actually in the toothbrush holder). My position is not that I was wrong in the first place, but that I was perceiving a different quantum reality, and that the quantum reality has changed in the second place (or that my consciousness has entered a second quantum reality), thus updating my perceptions. The second quantum reality tends to be the one that "sticks," so that if I go do something else, then come back and check up on it, my toothbrush is in fact in the holder.

Julian Barbour has a theory that time is not a continuum, but is in fact a series of Nows, and that the continuity of time is an illusion generated by consciousness. (He discusses this theory in depth here: In this theory, my perception described above is consistent, since the Now in which my toothbrush was on the counter is unrelated to the Now in which my toothbrush is in the holder, except by the context my consciousness supplies for the Nows.

Which brings us back to solipsism. The principal objection to solipsism is one of volition. For instance, if my consciousness is the only thing in the universe, and I experience pain, why would I cause myself pain? Or more specifically, if I am the only thing in the universe, and I get hit by a car, why would I imagine such a thing as a car in the first place? Well, the problem with this is that it assumes that I have volition over my consciousness. If the universe exists only as a Now, then I have no volition, and I am simply perceiving the Now, and my consciousness is making up context as it goes along. This makes it hard to justify action (I just now got up and got myself a cup of coffee, as I can see by the steam rising from my cup - and I remember walking into the kitchen to do so - but does that mean it really happened? Just because I perceive coffee doesn't mean it actually exists...).

What this says of causality is that moments A and B are related only by the context provided by your consciousness, and that to say that A caused B is an act, not of logic, but of faith.

Actually, I think the principal objection to solipsism is that it doesn't go anywhere. It's certainly a nondisprovable, watertight system. You sort of have to respect it philosophically. But there's not much of interest to do with it. It's sort of like: "Solipsism. Cool. Wow. OK, moving on now..."

Barring any other reasons to adopt solipsism -- like a total, catastrophic breakdown in our ability to understand the world on the premise that there is a world, or aesthetic reasons -- Occam's razor suggests to *me* that the toothbrush thing is an event in the brain, not the world. Given how the eye and the brain works, and the fact that "vision" is cobbled together in the brain out of a blurry, grainy, jerky, mostly black-and-white input stream which is compressed down to edges and vectors, it's not surprising that the brain occasionally mistakes bits of counter for toothbrushes. The other day I saw, for a moment, a mailbox as an aardvark; I don't think that was another Now, at least not in the sense I think you mean.

Also, per "quantum", I find myself in Ted's position, wanting to quote Princess Bride: "I don't think that word means what you think it means..."

However: to say that A caused B, presuming A and B to be things in the world, is definitely and always an act of faith, paraphrasing (or, well, butchering) Hume.

Does anyone know whether Barbour’s idea has any testable consequences? I haven’t read his book, but what I have read makes it sound to me as though if you took out the consciousness bits, it would reduce down to not much more than an alternative mathematical model.

It’s probably only fair for me to admit that I tend to approach things like consciousness and qualia and free will from a rather skeptical Popperian perspective, so I'm not naturally inclined to take them as evidence for anything in cosmology or ontology. (I’m open to the idea that some of my experiences of deja or presque vu may not be neurological artifacts, but without any other evidence — yeah, like Ben says, Occam’s razor.)

As far as Novikov, I've often wondered if any spacetime that created paradoxes wouldn't converge to a Novikovian type of spacetime (A causes B, B causes A+C, C alters A's ability to create B, and continuing till the processes eventually cause one another).

Edit: I'd also like to add, that there's a common belief that "the next revolution is just over the horizon", so why trust any of this?

I would point out that we haven't had many real revolutions in cosmology, Relativity (Special and General) certainly wasn't one. It was an evolution.

So to echo Rich's earlier statement, anything that invalidates these ideas would need to encompass the other ones as well.

deja vu = the feeling that something like this has happened before

vu ja de = the feeling that nothing like this has happened before

vu ja deja vu = the feeling that nothing like this has happened before, again.

Actually, there is a way to have everything (Relativity, Causality and FTL) together. Suppose that we have one inertial frame, withing which instantaneous propagation is possible. And in no other. This does though make frame more important than others and thus contradicting the relativity principle itself, but all the relativity formulas would still work.

please let me know that m0 = m(1-v2/c2)1/2 follows the principle of causality.

Relativity kicks ass, and FTL is totally sweet, therefore causility has got to go. It's a drag anyway. BTW, does so-called "quantum teleportation" (the "let's share a spin by entanglement" thing) qualify as FTL?

Looks like a bunch of lines to me. but if you can make it work on on for that trip.

My only contention with this is the postulate "The speed of light is the same in all directions in all inertial frames". If e=mC^2, then C^2=e/m which means that the speed of light is directly affected by 'local' energy/matter, which would seem to indicate that the speed of light isn't (or at least may not be)the same in all inertial frames.

Could time travel allow me to go back in time just so I can achieve first post?

so, how did a straightfoward, textbook explanation spark all of this philosophy, meta-physics bs? go to school, do the math, then you are allowed to talk about relativity like you have any idea what's going on. Also why does the author keep referring to "classical mechanics" the idea of no speed limit permeated all of physics before E&M was really fleshed out. In MY classical mechanics book there is most definitely a section on special relativity.

This appears VERY closely "borrowed" from the book, "RELATIVITY IN ILLUSTRATIONS" by Jacob T. Schwartz, Dover Publications, Inc., New York 1962.

While this provides a rudimentary explanation of the EMR cone, the Schwartz paper goes into much more detail and is -clears throat- a bit more original. . .

All scientific breakthroughs have come from curiosity "What if?" and sometimes even from simple laymen's naive observations.

This quote caught my eye and I couldn't resist a comment . . "Einstein says you gain mass, and thus requiring even more energy to get you there."

A layman's naive observation : What if the mass IS the fuel?

i think this report is bs

This drives me crazy. I have a HS diploma and SOME college and I never took courses in this stuff but it makes perfect sense to me and it drives me nuts when people claim superluminal travel cause causality issues (IT DOES NOT) and that it causes time travel (IT DOES NOT) and that spinning a wormhole at C and going through can let you go back in time (IT CANT)

Speed does not in any way whatsoever effect time. Let me say that again SPEED in NO WAY effect times. Before you contest that let me correct it. speed effect RELATIVE TIME and ONLY RELATIVE TIME not time itself (overall time)

what you decribe above is NOT a causality violation its an incongruity of PERCEPTION of casuality.

Imagine this HIGHLY over simplified scenario. I walk out of my house and I video tape this and then mail it to you. I walk over to your house and into your door and then you get my video tape and watch it (the video tape is light) you just saw me enter my house before you saw me leave my hosue is casuality broken off course not your perceotion is just out of sync because my walk to your house took less time than the light image (video tape) nothing more its a PERCEPTION issue now a casuality issue.

I dont know what will happen if you manage to go faster than C but I can tell you this any TEMPORAL effects will only occur to YOU and not to those around you. RELATIVE time.

Just because he heard alice before bob does not mean that is how it happened its only how it was PERCIEVED. You have to look at things from relative time.

Lets say alice transmits at 0.00 (her time) at 2 c to earth from alpha centauri with 2 transmitters one C and one twice C

Transmission one will get there in 4.0 years (roughly) while transmission 2 will get there in 2.0 years. what is casually at issue with that. nothing. even if the communications were so fast as to be nearly infinite it does not matter it would be just like us talking next to each other.

the temporal effect of speed only effects THAT which is moving at said speed.

when you spin one end of a wormhole at 12 noon at near c so time stops and wait one hour the other end it as 1300 while this end is still near noon.

ehh thats where it falls in your ship are still moving forward in time normally and the time in the wormhole is still moving normally the only thing that slows down is the actual material that is moving near C not the surround space or material and not the space inside JUST the material moving near C has a relative temporal slow down. so IF you can make a ship go past c and IF doing so causes time to say go backwards it only does so FOR THE SHIP and anything inside it that is moving at this speed.

nothing else. and I dont even think time will REVERSE the way we think of time. I think it will "flip" like the difference between a positive and negative charge. (I have not a clue what that would mean for the matter or people inside such a ship but I dont think getting younger will be the result)

Chris Taylor

I think that it is quite odd to believe that "FTL travel"="time travel". My example is this: I'm somewhere in space and an FTL starship arrives. I didn't see that starship come toward me because it was traveling faster than the light reflecting off it. In fact, if I continue looking at the path the starship took when going FTL, I would expect to see what looks like the starship going backwards towards it's departure point, as the light reflected off the starship arrives at me. It only looks like causality is violated, because the medium (light) by which I can see the starship moves slower than the ship itself, but the arrival of the ship still happens after it left (just ask the crew). My reasoning that the effect would be like the "motion moire" seen in movies (motion pictures/cinema) where an object that is rotating faster than the camera can resolve it (like a turning wagon wheel) and it looks like it is rotating in the oposite direction to what it realy is.

Is my reasoning incorrect and why is that so?

Quantum teleportation can't be used to transmit information faster than light. Nor can quantum entanglement in general. See, for example, Deutsch and Hayden's "Information Flow in Entangled Quantum Systems" (PDF).

If e=mC^2, then C^2=e/m which means that the speed of light is directly affected by 'local' energy/matter, which would seem to indicate that the speed of light isn't (or at least may not be)the same in all inertial frames.

E = mc^2 (or, more generally, E = gamma mc^2 for particles not at rest) is a consequence of the constancy of the speed of light in special relativity.

so, how did a straightfoward, textbook explanation spark all of this philosophy, meta-physics bs? go to school, do the math, then you are allowed to talk about relativity like you have any idea what's going on.

That's very strongly my preference too. Indeed, part of the reason I've been writing these articles is the hope that perhaps people will understand something of the nature of relativity and quantum mechanics and it will help restrain the more vague of their speculations.

Also why does the author keep referring to "classical mechanics" the idea of no speed limit permeated all of physics before E&M was really fleshed out. In MY classical mechanics book there is most definitely a section on special relativity.

Physicists use "classical" in two senses. Some people consider Newtonian and relativistic mechanics to make up classical physics, thus distinguishing those two fields from quantum mechanics. Others, myself included, think that the conceptual innovations introduced by special and general relativity are so great that "classical" should cover only Newtonian mechanics.

This appears VERY closely "borrowed" from the book, "RELATIVITY IN ILLUSTRATIONS" by Jacob T. Schwartz, Dover Publications, Inc., New York 1962.

I haven't borrowed from that book as I've never read or even seen it. But I suppose when one attempts to describe special relativity graphically one inevitably tends to draw diagrams similar to these. I've certainly never seen the relationship between FTL and time travel laid out with - IMHO - anything like my clarity, but that doesn't mean that my presentation is necessarily the first of its kind, only the first that I have seen.

what you decribe above is NOT a causality violation its an incongruity of PERCEPTION of casuality.

No, this isn't the case. The effects I describe are those that remain when all incongruities of perception have been taken into account. Relativity is not - no matter what badly garbled accounts might suggest - about sophisticated optical illusions. And the experimental evidence strongly supports special relativity over Newtonian mechanics.

SVG usage is simply brilliant :)

Chris Taylor: Here's the problem -- although your theory no doubt sounds quite wonderful to you in words when you spark up a doob and run it through your mind, if you actually had bothered to get enough of an education to translate it into actual math that could be used to make predictions about the physical world which could be experimentally verified you would quickly find that it doesn't. Translate.

That's the thing about Einstein that people conveniently forget. Yes, he spent a lot of time daydreaming lovely thought experiments and yes you can do that to. But he also spent a lot of time translating those thought experiments into math where they could be examined & tested. If you are unable to do part two, PLEASE stop trying to convince anyone your daydreams have any merit or value!

If you adjust these models to demonstrate a 4 dimensional (or 5 dimensional) space you will find that it is possible. Just because we can't see it or understand it does not mean it is not possible.

Two leaves are floating downstream on two diffrent identical rivers one leaf arrives at the lake in one 10th of the time faster then the other yet they dropped from the same tree at the same time.

Conclusion? The rivers themselves move at different speeds...

If you adjust these models to demonstrate a 4 dimensional (or 5 dimensional) space you will find that it is possible.

Actually, you can formulate special relativity in as many dimensions as you like and it still won't be possible. The action of a Lorentz boost on the spatial dimensions orthogonal to the direction of the boost is trivial, which is why it's safe to suppress two of the four dimensions of our spacetime - or all but two of the dimensions of a higher-dimensional Minkowskian spacetime - in the discussion.

Two leaves are floating downstream on two diffrent identical rivers one leaf arrives at the lake in one 10th of the time faster then the other yet they dropped from the same tree at the same time.

Conclusion? The rivers themselves move at different speeds...

In which case the rivers are not identical. But I think you're alluding to the possible existence of wormholes in generally relativistic spacetimes. If these exist, they could be used to travel over large distances in conveniently short times, but they can also possibly be used to produce closed timelike curves, which are another way to violate causality. General relativity is full of such fascinating possibilities: it's a much richer and more elegant theory than special relativity, but also somewhat become the scope of this particular post.

Interesting that you shoot down my posting without actually disputing anything.

Reality stands. When they put the atomic clock on the space shuttle IT slowed down. nothing outside. nothing on earth nothing in my house slowed down IT slowed down (or equally you could argue we sped up) but you get the idea. speed effects relative time NOT overall time. You cant time travel just by changing speed and different speed WILL not cause any issues with casuality.

if any of your math says otherwise then you math is simply flawed thats all because it contradicts reality.

Chris Taylor

Interesting that you shoot down my posting without actually disputing anything.

This should be seen as evidence that I have very little free time to write articles and comments on my weblog, not that special relativity is flawed :)

When I do have some time, I will try to address your comments more fully.

Chris, what makes you so sure that Einstein and all the physicists that came after him are wrong and you're right? All we have to do to shoot down your posting is to say it contradicts Einstein. His theory was radical and given what a crazy headache it gives most people who think about it, it would have been eagerly rejected if anybody could figure out a simpler explanation for observed phenomena.

Hello :) I have read explanations of Einstein's theory of relativity and each of them involved the use of a few imaginary objects such as spaceships or other objects that are 'large' and have mass. I can safely say that none of these explanations has helped me understand the theory (or theories) any better :( Instead of spaceships, why are photons and neutrinos not discussed? According to observation, there are large numbers of these particles travelling across the universe, and at many angles to each other and to other slow moving matter, like stars and planets. Does relativity apply to these relative velocities as well? Or does it only have a measurable effect on objects that have more significant mass? If photons travel AT the speed of light, does this mean relativity doesn't apply to photons? Or is it because photons have zero mass? What if a particle had a negative mass? Could it travel faster than light? In a recent television documentary about neutrinos, it was discovered that only 1/3 of neutrinos were being detected. Further experiments revealed that neutrinos (which come in 3 flavours) were able to change flavours in mid flight, meaning they were not quite travelling at the speed of light. This in turn suggested that neutrinos do have mass. So, does this mean neutrinos are subject to relativity? If any pair of neutrinos are travelling towards each other, both near the speed of light, will space/time between them be dilated? If space/time is being affected, what would be the result of neutrinos slowing down or stopping their velocities? Would the universe shrink? In Tom's letter, he asked whether the atomic clock experiment affected only the clock travelling in the satellite, or everything else, or both. Is the answer both? I believe the answers to these questions would help me be slightly less confused about relativity!

Hi Allison :)

That's rather a lot of questions but I'll do my best to answer them...

Relativity does indeed apply to photons and neutrinos just as it does to planets and spaceships. I suppose the latter are usually used in discussions as they're easier for most people to visualise, but most of the actual experimental data supporting special relativity is in the form of observations of particle interactions in accelerators. Furthermore, relativity has a measurable effect on all objects moving at high relative speed.

As you've brought up particles, I really must mention some observations regarding muons. Muons are unstable heavier relatives of electrons. It's possible to produce slowly moving electrons in experiments on Earth and from those we can measure the statistical properties of their lifetime before they decay. Muons are also produced by collisions between cosmic rays and the Earth's upper atmosphere. However, even travelling at something close to the speed of light they should all have decayed before they reach the ground. So why do we see them? From our point of view, the answer is this: time dilation means that the muons "clocks" tick more slowly than ours and so their lifetimes are stetched out. You might like to consider how things look from the point of view of a muon: the explanation for rearching the surface is rather different.

As for particles with and without masses, special relativity is really used in two ways. Firstly, it's used to translate events in one inertial frame into events in another. This is what people do when they talk about observers in spaceships moving at different speeds. Secondly, it's used to discuss the mechanics of particle interactions from the point of view of a fixed inertial frame. The mechanics of particles moving at high speed is rather different to what we might expect from Newtonian physics.

These two approaches are of course intimately related to each other, and physicists investigating mechanics make quite a use of invariant quantities, which are things that look the same in any inertial frame. It's often possible to break down a complex problem into lots of little bits, each of which is invariant and so can be calculated in whichever inertial frame is most convenient. It's sometimes said, in fact, that Einstein wanted to call it the "theory of invariants" or "theory of invariance" rather than the "theory of relativity" because these quantities are so important.

The difficulty with the first sort of approach arises when one considers the frame of objects moving at the speed of light, but one can happily consider both inertial frames whose relativity velocity approaches that of the speed of light, and also problems in mechanics in which some of the particles concerned have no rest mass and so travel at the speed of light in any inertial frame. The standard undergraduate problems along these lines involve things like electrons and positrons annihilating into pairs of gamma rays.

If a particle could be accelerated beyond the speed of light, its mass would become imaginary (that is proportional to sqrt(-1) ) and not negative.

As for Tom's question, the answer is both. However, in most cases in which the two clocks are returned to the same location to be compared with each other, one clock will have accelerated more than the other. Thus, the situation is not symmetric and the time elapsed on the two clocks will not be the same. The simplest such case involves one clock remaining in a fixed inertial frame and the other moving off in one frame and then switching to another frame for its return journey.

(The situation is a little more complicated than this because it's not just special relativistic time dilation that must be considered but gravitational time dilation too. In fact, this gravitational effect is important in real atomic clock experiments.)

Does that help at all?


Thank-you for your kindly, timely reply :) I hope it will help...

Muons: If I understood correctly, for the muon time slows down, the muon is flattened in the direction of motion and space directly ahead of it is stretched out. These things occur so that the speed of light will not be exceeded (velocity=distance/time). It's not clear to me what the muon would percieve. If the muon's time slows down (according to our perspective), then maybe the muon percieves the universe speeding up. It's able to travel through the atmosphere in its short life and reach a point that it wouldn't normally expect to reach. I imagine the muon would not percieve its life as being any longer, unless it was aware of relativity and recognized its reaching the Earth's surface before decaying, as proof. In the spacecraft examples that confuse me, one involved a single spacecraft moving through space and the effect on it as it neared lightspeed. That seemed simple enough. But in another example, there were two spacecraft heading directly for each other. The speed at which the distance was diminishing between them could also not exceed the speed of light. It's unclear if this meant the relativistic effect is doubled simply by two half-lightspeed objects happening to move away or towards each other. Objects at right angles or alongside would not suffer this effect. I probably misconstrued these examples as saying that relativity acts in two ways: on all objects as they near the speed of light (in the direction of motion), and on the relative velocities of pairs of objects. But why would a time/space dilation occur if the relative velocity of two inertial frames does not exceed the speed of light?

FTL: So accelerating a particle towards light reduces its mass? Is this why light speed cannot be exceeded - because mass reaches zero? The square root of -1..... could not be negative or positive (1x1=1, -1x-1=1) - that is just strange!!!

Atomic clock experiment: I guess the answer to this question means the entire universe is affected by each inertial frame. The high speed particles would have the largest effect and because there are so many of these particles travelling everywhere, the universe is being stretched and distorted. Atleast this is the thought that forms in my mind...

Gravity: I saw a gravitational grid once, with planets and suns causing "dimples". It was easy to see that slower moving objects could be caught by the gravitational field, or heavier objects could. In the case of a black hole, even light particles might not move fast enough or be massless enough to avoid capture. When not captured, objects can still be deflected. For lightspeed particles, an animation showed the space grid lines being stretched out in front of its line of motion, while being compressed behind it. Would that type of represention be accurate?

I hope you won't find there are too many questions. A lot of them are based an assumptions I'm not certain of, or are confused about, and can easily be skipped when they're wrong.


Hello again,

Having thought about those space grid lines i once saw, the motion of lighspeed particles now makes more sense. They're like a boat travelling across water. The water in front of the boat gets bunched up and then stretches out in its wake. But after the boat has gone through an area in the water, the water returns to 'normal'. So i'm imagining it is similar with photons, neutrinos and muons - just that the compression and stretching of space is opposite. After the lightspeed particle moves on, space returns to its original shape. The doppler effect might also be an example. With these latest thoughts, am I closer to understanding relativity?

p.s. I don't know why I wrote Tom, Chris Taylor is the author of the letter in question

"And that's why faster than light travel or communication, special relativity and causality cannot coexist."

You only provided proof of why you think FTL _should_ not exist-- basically because it offends your tender sensibilities to think of enterprising Alice transmitting information into her own past, through a variety of means even.

I think the key word here is "violation", this being an irrational psychological descriptor of a rational phenomenology. There are more and more logic-mice eating impossibly away at this straw man:

There was a young lady named Bright Whose speed was much faster than light She departed one day in a relative way and returned on the previous night.

I'm still not quite convinced in the impossibility of the FTL communication. Let's discuss the following example which quite often introduced as a "prove" of casuality violation etc. Imagine a spaceship leaving the earth at noon sharp and flying away with a constant relativistic speed ~ 0.8C, so that the clocks on the spaceship are moving twice as slow compared the one on earth due to the relativistic effects. At 2p.m.(earth time) sharp the FTL message in transmitted from the earth to the spaceship. To simplify the things let's suppose the message gets to the spaceship instantaneously. It means that the spaceship crew will receive the message at 1p.m. of the local spaceship time (the clock on the spaceship is twice as slow as the one on earth). The spaceship crew responds at 1.10 p.m., and the reply gets to earth at 1.10 p.m., 50 minutes before the original message was sent! Casuality violation! I think the mistake here is the fact that the reply was sent at 1.10 p.m. only according to the local, "spacheship" time. By the time the spaceship clock strike 1.10 p.m., the clock on the earth would indicate 2.20 p.m.!(remember, it's twice as fast!) And this is the time when the reply message gets from the spaceship to earth! So, there's no casuality violation. It's just a matter of different time that different clocks are indicating.

I'm a staunch supporter of the impossibility of FTL due to causality violations, but I just happened to read this and I got an idea...

What if the flaw behind FTL is in it's design? What if FTL communication devices (ansibles, etc.) can only work between two objects in the same inertial frame? Like how two radios can only transmit information through tuning into the same frequency

Wouldn't that allow FTL?

i am a supporter of FTL ^^ dunno if itll ever be possible ( dont think so ) but i think over like 10000 years, if we humans still exist we probably are colonising space... thats a little hard without FTL... ( ok this all had nothing of science in it >

What happens to this theory if the 'c' in e=mc2 instead of being the speed of light is actually in fact the terminal velocity of everything and anything? We've always assumed that light is the fastest thing in the universe, and to approach or exceed that speed would affect the time we are in. But maybe there are already many other things travelling faster than light (too fast for anything to reflect from and therefore invisible to our sight) are such things not already subject to the above theory and if so wouldn't our interference risk some sort of collision with the unseen?

like the theory of slipspace travel from halo, where objects in space reach a speed faster than light and enter a seperate dimension of existance that doesnt affect the physical plane yet can still be traveled. what this implies is that right now a chunk of rock the size of the moon could pass through the planet at beyond light speed and not effect it because it is moving to fast in a seperate plane of existance. But back to the time travel thing....Ansible technology isnt impossible we just havnt stumbled upon the right theory or technology to make it believable yet. My proof of this is right now radio signals from the 60s are returning to the planet right now. Even if these signals just bounced off the moon they would still have a very small chance of reaching the earth because the earth is moving too fast. So if these signals bounced around the solar system for 40 years what are the chances that the earth would be in the position it is to recieve them only 40 years later? i cant explain it can you? signals getting sent into the future, sounds to me like the theorys and possible ideas for space travel are right in front of us we just havnt noticed it yet or cant climb over the mountain of theorys we made that make it seem impossible. Just cause our theorys have worked so far doesnt make them correct, they have been changing for years for all we know everything we thought about physics could only apply for this solar system or even just this planet. its just foolish to say anything is impossible in the universe when the only part of it we have actually seen is the very small rock we live on. if we just gave up on an idea and made it seem crazy and stupid to pursue then we would never advance as a race, how do you think technology got to where it is now? Flight was thought to be crazy and stupid and people that tried to build flying machines were considered insane yet there are people flying in giant boeings right now all over the world.

Who thought flight was crazy? Only crazy if you crashed. There's no accounting for doubting, and ignorance never accomplished anything. If you want to talk about possiblility, read some Douglas Adams first. :)

As for signals bouncing around for 40 years... so? What's that got to do with the any of this? Anyway, it's only 40 years based on (or should I say relative to) our clocks on earth.

Of course, I've always assumed that the idea of accelerating to the speed of light would mean converting all your mass to energy, at which point, you'd no longer be able to experience time. Thus if you rematerialized, after your energy bounced around space for X years, you'd have transported yourself X years into the future without aging.

Allow me to preface my post by stating that I am in fact from the future (So all you naysayers of time-travel... think again). Not only is time travel to the future possible (Which is well known and documented and can be learned in any high school physics classroom across America), but time travel to past events is possible as well. Many are unable to believe any of these theories and postulates because they are hard to prove on a massive scale, but I assure you that on December 2nd, 2106, you will soon be aware of the vast possibilities of time travel.

-William Stone Future World President (No pun intended)

Well everybody knows that nothing is impossible. I've also set my way towards proving that time travel for the future as well as past is possible. Sooner or later scientists will be able to prove that time travel is possible. Even i am deovoted and i know we will do it.


It would certainly be nice if this could be clarified a bit more for people like me and Chris. Because even after reading this description, I still don't understand how FTL travel constitutes *time* travel in any way other than a purely semantic sense.

Though I'm not about to say that Einstein was wrong, just that people's explanations of the repercussions of relativity always seem to skip over the parts that I'm confused about.

Wherever I've said things like "a faster-than-light message is transmitted" I could equally have well have said "the spaceship makes an FTL jump". It's then possible for Alice to travel around the path in figure 5 and meet her own past self. (This is true even if the FTL jumps are not instantaneous in the frame of the ship making the jump. It's just that it's a bit harder to draw the diagrams in that case and I found them hard enough to draw with my limited talents anyway.)

The only way to have both faster-than-light travel and causality is to discard relativistic spacetime and restore some nation of absolute time (which, I think, is what Chris is arguing for). Unfortunately, a number of famous experiments from the late 19th century on have disproven the Newtonian model of space and time and upheld the relativistic model. Indeed, as I mentioned in an earlier comment, special relativity in combination with quantum mechanics makes one of the most accurate quantitative predictions in all of science - the prediction of the gyromagnetic ratio for the electron, which matches experimental measurement to something like twelve decimal places - and relativistic dynamics has also been strongly and directly supported in experiments in particle physics.

Furthermore, the problems reconciling faster-than-light travel, relativity and causality are fairly "coarse-grained". The causality violations would happen in the sorts of domains in which relativity has already been tested rather than in some more exotic place like the interior of black holes. The problems are also entirely independent of the detailed nature of the faster-than-light communication or travel itself.

Which parts are you confused about?

Hi Rich

Thank you very much for the article. I am currently designing an science fiction setting and I was in need of a good "FTL implies time travel" explanation.

Another comment: You write "As is sometimes said, you can pick at most two of {special relativity, FTL, causality}.". Certainly. But which ones do you pick (to describe our current reality)? Scientists usually not even dare to consider wether to pick causality or not. The conditioning is just too much. But picking causality is more like axiomatic. I am not aware of any experimental setups proving that causality holds (please tell me about it if they do). Good proof exists for relativity. I firmly believe FTL communication exists (right now right here), but you won't see it as long as you hold on to causality.

At the moment I would choose {relativity, causality} but that's only working from a prejudice that causality is better than acausality. It certainly wouldn't throw me into any sort of metaphysical crisis if experimental evidence showing FTL communication emerged and I had to switch to {relativity, FTL} or even {FTL}. Actually, that would be very interesting and pretty exciting too!

On the other hand, it's certainly surprising that quantum mechanics has turned out to be non-local but in a way which doesn't allow FTL communication, and furthermore that it's the objective randomness of quantum processes that prevents causality violations from arising.

hi to everybody..... i'm here to put forward an idea.

when we speak of time travel,, what do we really ,mean? the first question should be whether time ,as an entity, exists. where can we see/hear/feel time. where can we prove that time exists?!

my point of view is the following: time is simply a word invented by us, human beings, in order to coordinate our lives and to be able to coordinate and even record events. according to me, time is just a notion which helps us to coordinate our living. time, contrarily to other phenomenas, does not actually exists in nature.

time is a word which automatically comes to our are examples:

1. "Sara it's TIME for you to go to bed" from the first example you can see that there could not have been any other word to formulate this sentence except the word "time".

2. "in a few MINUTES it is going to be NOON. i will go out to have lunch."

from the 2nd example: it is written nowhere that one is supposed to have lunch at noon. however just imagine, that if in a company anyone at any time goes out to would be catastrophic. so, here it is an example that time has been used to coordinate our living

"and now guys, its TIME for me to leave you..... :> the word time has been used for "la bienseance" [french word]

feel free to comment on my opinion guys and email me....hope you'll find TIME to email me.... :>

It seems like there are two ways to get FTL without violating causality.

Observe that causality can be violated only when two superluminal messages are sent, unless one can send a message directly into one's past. (What do we call that? Hyperluminal travel?)

One solution is to prohibit certain journeys. In this instance, Bob would not be able to use his ansible to send a message in Alice's direction until Alice would receive the reply after she sent the initial message. (Equivalently, if Bob was going to deliver the message in person with his hyperdrive, he wouldn't be able to turn it on until the journey would be properly causal.)

The other solution is to constrain all FTL journeys to a local special frame of reference. This might be the frame of reference of the dominant nearby celestial body; or it may be set at the time the ansible is built. With the former you'd need relay stations at borders between frames of reference, whilst with the latter, ansibles with different special frames of reference would have to interfere with each other to prevent them being used together to make a time machine.

If an infinite room of monkeys typing randomly for an infinite time would eventually produce the works of Shakespeare, it is equally likely that this would occur at any given time. So they might just as likely get it on exactly the first try as on exactly the 1 zillionth try. Since infinity is, well... infinite, it is just as likely they would produce the works BEFORE Shakespeare did as after.

So if an interaction from the future coached the monkeys to get it on the first try, this would not create any different effect than if they had typed it by accident.

Type Quantum Monkeys, Type!

You've got a serious problem in your "ausality violation" diagram.

Alice, Bob and Carol all carrying an instantaneous transmitter (not just FTL - that would have a transmission cone at an angle to the space line). If Alice sends a signal, that happens at a specific moment. That moment must be the same moment for Bob and Carol; there is no avoiding that they are all in the same universe. However, the signal does reach them - and can even get back to Alice - that moment. if there is a retransmission delay, Alice's reception of the transmission delay will be modified by the relative clocks in the sequence.

No causality is broken, except for the fact that the light speed "event cones" of the people involved have not intersected. A lack of knowledge about an event does not make that event not happen.

i do not know much, but just because an object(A) is moving FTL doesnt mean it is now moving backwards in time but time in, on, or with that object(A) is now moving slower than other variables(B) in timespace that are moving @ a slower speed because (B) time would be moving faster. but what i want to know is y is that y is (A)s time slower because it is FTL?

In your diagrams of light cones for Alice & Bob, you have indicated both positive and negative values for their space dimension. Their cones have both a left side and a right side. (In a conventional textbook diagram, 'right' would be x increasing positive, and 'left' would be x increasing negative).

But with Carol and Dave, you have only shown the right hand side (x increasing positive) of their light cone. The space' line points to about 2 o'clock, the time' line points to about 1 o'clock. That is, you have only put in half of their light cones.

You have then shown the superluminal communication (event Q -> event R) by showing it as an extension of the space' line to the left. That is, drawing it down towards 8 o'clock, which is what puts event R before event P in Alice's timeline.

I'm not convinced by this. My intuition tells me that, at event Q, Carol should have a space' line pointing towards about 10 o'clock. That would put event R after event P, not before it.

I fully confess that it's been a long time since I was able to do all this in my head, but what the heck?! What happens if you show Dave & carol's light cones in full?

Patrick, I think you've misunderstood the diagrams. The light cones at a given event are the same regardless of which inertial observer we're talking about. For example, in the "second superluminal signal" picture, the yellow light cone passing through Q is the light cone as seen by Carol, but also as seen by Bob.

In each case in which I've drawn a grid, I've extended it to show both positive and negative space and time. I've done this for the Alice/Bob frame in white the Carol/Dave frame in blue. You can see this most clearly in the "Lorentz transformation" picture. (The red line joining Q and R hides part of this grid for Carol/Dave just as the line joining P and Q hides part of the Alice/Bob grid.)

I think the best place to start is to realise that the thicker blue line labelled "Carol" is Carol's path through spacetime and so must also by definition be her time axis. It's then quite easy to see that all the other lines of constant position but increasing or decreasing time in Carol's frame must be parallel to her path - if they weren't parallel then they'd be at varying distances from her and so not be at constant position coordinates. By the symmetry of spacetime the positive spatial axis from every event in Carol's frame must be parallel to her positive spatial axis. This, and the uniqueness of the idea of "at the same time" in Carol's frame is then enough to generate the whole coordinate grid as seen by her.

You can also see from the blue grid how this fits with Carol measuring the speed of light to be the same in the positive and negative spatial directions: in both cases the rays of light travel one increment of distance in one increment of time.

Great article Rich, I love how people have proved you, Einstein and the scientific community wrong by just daydreaming up shit.

Rich, after (painfully) reading almost every single post and seeing so many people be completely wrong about relativity and FTL I'd have to recommend one change.

At the top of the page you need a link to an article describing inertial frames of reference. It seems in my opinion to be the concept that is most lacking in understand for many of these posts. They fail to fully grasp the concept and as such can't begin to visualize the effects of relativity on each observer.

Of course it really isn't Rich's job to fully educate the masses on physics so I'd suggest that anyone who has the desire to understand these things to have the dedication to develop your understanding until you can understand and apply the concepts of frames of reference, time dilation, length contractin, and gamma. Once you've done that you should be able to apply it to situations such as Allison's muons and explain the outcome from each frame of reference.

Thanks Rich,

You're right about me not understanding your diagrams. I only understand them when there's no FTL communication. With FTL communication, they don't make much sense! (I think you've acknowledged that somewhere, you can't have all three of S.Relativity, FTL and Causality).

I also get the idea that FTL communication in one reference frame looks like the signal is travelling backwards in time in another reference frame.

The thing I'm really struggling with is constructing a thought experiment that's equivalent to your scenario. The way you've constructed your diagrams so that Carol and Bob are co-located at event Q.

If you imagine Carol and Dave at the front and back (respectively) of a train going past Bob and Alice. In your scenario, Dave has to pass Alice (at event R) before Carol passes Bob (at event Q). By the time Carol passes Bob, Dave has already gone past Alice. So how can Carol send any kind of signal to Dave at a position he's already passed?

To Alice and Bob, it will look as though Carol's signal is going backwards in time (Alice and Bob's time, right?). I just don't see how the signal can get to Dave at event R, when he isn't there anymore!

Maybe my question is, I can see how Carol and Bob have the same light cone at event Q, but how can Dave have the same light cone as Alice?

By the way, my colleagues are practising scientists using a synchrotron, so they use this relativistic stuff all the time. They can't make sense of this example either! Except to say it's a reductio-ad-absurdem to show FTL isn't possible.

"By the time Carol passes Bob, Dave has already gone past Alice. So how can Carol send any kind of signal to Dave at a position he's already passed?"

Another way of saying that: in the scenario you describe, how can Dave still be on Alice's timeline when Carol is on Bob's? It seems like for your example to hold water, Dave has to be in two places at once, or two times at once, to begin with.

By the way, just going over everything for the umpteenth time looking for bits where I'm talking shite, and noticed where you say Special Relativity is founded on 2 postulates.

Your number 2, that the speed of light is constant in all inertial reference frames - this is not a postulate, it is a consequence of Maxwell's equation, and confirmed by the Michelson-Morley experiment.

In Special Relativity, the postulate is that nothing can exceed the speed of light.

It may seem like nit-picking, but I think you have to get that stated precisely, especially when you embark on a line of thought that includes special relativity and faster-than-light travel.

re. comment 79. I'll take that back.

My original source (from when I was an undergrad) says the constancy of the speed of light is often stated as an assumption in Special Relativity, but actually it's a given, and the really significant postulate is that nothing can travel faster than light. But lots of other sources give the postulate as the measured speed of light is the same in all inertial reference frames.

If we start arguing over which is a postulate and which is a consequence, we'll waste our time for nothing. So I take back what I said in 79.

On the other hand, I am going to insist that this

"The speed of light is the same in all directions in all inertial frames. It is this postulate that gives rise to all the strange consequences of special relativity, including those discussed here."

is definitely wrong. It's the idea of FTL signals that gives rise to the strange consequences of special relativity discussed here!

It's like saying, "If 2+2=4, then 4-2=2. But what if 4-2=1?"

Patrick said:

If you imagine Carol and Dave at the front and back (respectively) of a train going past Bob and Alice. In your scenario, Dave has to pass Alice (at event R) before Carol passes Bob (at event Q). By the time Carol passes Bob, Dave has already gone past Alice. So how can Carol send any kind of signal to Dave at a position he's already passed?

Well, that's the whole point of the relativity of simultaneity. Your use of "before" and "by the time" are talking about the Alice/Bob frame. In the Carol/Dave, Dave passes Alice at the same time that Carol passes Bob. "Before" and "after" only have frame-invariant meanings when talking about events within each other's light cones. For example, all four of our inertial observers agree that P occurs after R. In a world without FTL signals, the inability of people in differing inertial frames to agree on the time-ordering of pairs of events that are outside each other's light cones is interesting but doesn't have any practical consequences (that I can think of, anyway). In a world with FTL it has the consequence of being able to set up sets of transmissions that violate causality, as demonstrated in my article.

It's the idea of FTL signals that gives rise to the strange consequences of special relativity discussed here!

Yes proximately, but ultimately the strange effects of FTL signals are a consequence of all inertial observers measuring the speed of light to be the same. If it weren't for that, faster than light transmissions would have no stranger effects than faster than sound transmissions.

The constancy of the speed of light and the relativity principle together give the relativity of simultaneity, the Lorentz transformations, time dilation, length contraction, and other strange effects. (As well as such unusual things as the equivalence of mass and energy, antimatter, spin and so on when combined with dynamics.) The causality violations from FTL signals are a direct consequence of the relativity of simultaneity, and hence of the constancy of the speed of light.

Brandon said:

At the top of the page you need a link to an article describing inertial frames of reference. It seems in my opinion to be the concept that is most lacking in understand for many of these posts. They fail to fully grasp the concept and as such can't begin to visualize the effects of relativity on each observer.

I think that in the end I'll have to write such an article. These Light, the Universe and Everything posts are trial runs for a book that I hope to write one day, and it's interesting to see the things that people struggle with most. It seems that everything comes back to the most fundamental concepts, such as inertial frames, the principle of relativity, coordinate systems, proper time, intervals and so forth. I worry, though, that any attempt to explain these things will discourage readers who'll think that I'm being needlessly pedantic.

And I'm almost dreading the total misunderstandings that will be expounded in the comment thread to any future article on the "twins paradox" ;)

Update: I've just added a new article on Spacetime and Coordinates.

"For example, all four of our inertial observers agree that P occurs after R."

That's where you're wrong!

For Alice and Bob, event P and event R are one and the same event.

Tell me what I'm getting wrong here:-

(1) Alice and Bob see event P and event Q as simultaneous. (2) Carol and Dave see event R and event Q as simultaneous, with event P happening later (Carol and Dave's idea of 'later'). (3) To Carol, Alice's signal appears to travel backwards in time, coming from Carol & Dave's future to Carol & Dave's present. (4) To Alice, Carol's signal appears to travel backwards in time, but going from Alice & Bob's present to Alice & Bob's past.

In the scheme you describe above (Alice to Bob to Carol to Dave to Alice), the only way that communication circuit can be completed is if event R and event P are actually just one event.

I think you need to check out the "Length contraction paradox". The one where the ladder flies through the shed.

In that one, Carol and Dave are the front and back ends of the ladder respectively, Alice and Bob are the front and back ends of the shed respectively.

To Alice and Bob, length contraction of the ladder means it fits the shed perfectly: the front of the ladder reaches the back of the shed (event Q) at the same 'time' as the back of the ladder reaches the front of the shed (event P). That is, those events appear simultaneous to Alice and bob.

But to Carol and Dave, it's the shed that undergoes length contraction. To them, when the front of the ladder reaches the back of the shed (event Q), the back of the ladder still hasn't reached the front of the shed. This appears to create an 'event R' for Carol and Dave. To them, a bit more time has to elapse before the back of the ladder reaches the front of the shed. This is the time difference between event R and event P in your diagrams.

But this time difference isn't apparent to Alice. When Dave tries to tell Alice that the back of the ladder will soon reach the front of the shed (because he thinks event P is in Alice's future), Alice's response would be, "What are you talking about? It's already there!"

And that's the REAL relativity of sumultaneity. Physically, there is never any chance of violatiing causality by communicating with the past. All that's happening is that Carol & Dave and Alice & Bob don't agree on what happened when.

I think you've got to be careful when you think about FTL communications 'going backwards in time'. There's a physical difference between (1) 'going backwards in time' from the present to the past - which is physically travelling to an earlier time. (2) 'going backwards in time' from the future to the present - which is just an illusion that would be created by FTL travel.

In your diagrams, you've joined 'coming from the future to the present' with 'going from the present to the past'. That is a mistake.

Patrick said:

(1) Alice and Bob see event P and event Q as simultaneous. (2) Carol and Dave see event R and event Q as simultaneous, with event P happening later (Carol and Dave's idea of 'later'). (3) To Carol, Alice's signal appears to travel backwards in time, coming from Carol & Dave's future to Carol & Dave's present. (4) To Alice, Carol's signal appears to travel backwards in time, but going from Alice & Bob's present to Alice & Bob's past.

Yes, that's correct. But in (2), as I've already said, all four observers see event P happening later than event R. The net result is that a signal is transmitted by Alice at event P to Alice at event R. The loop is then closed by the simple passage of time from event R to event P, forming the causal loop. Although the loop is described differently by Alice/Bob and Carol/Dave, all four agree that there is such a loop.

In the scheme you describe above (Alice to Bob to Carol to Dave to Alice), the only way that communication circuit can be completed is if event R and event P are actually just one event.

They aren't the same event as all four observers agree that they occur at different time coordinates. (Alice/Bob consider P and R to happen at the same place at different times, whereas Carol/Bob consider the two events to take place at different places at different times.)

I think you need to check out the "Length contraction paradox". The one where the ladder flies through the shed.

You may be interested in the article in my series on Length Contraction, which in my opinion discusses the phenomenon rather carefully :)

And that's the REAL relativity of sumultaneity. Physically, there is never any chance of violating causality by communicating with the past. All that's happening is that Carol & Dave and Alice & Bob don't agree on what happened when.

Yes, that's true. However, no material vibrations in the ladder travel faster than light. As should be very clear, in the absence of faster-than-light transmissions it's entirely possible to create a consistent, causal, relativistic model of the universe. Different observers will have different descriptions of the same situation but there will be no paradoxes. This is not true of relativistic physics with spacelike signals. (One can still potentially achieve a consistent picture but it won't be a causal one.)

I think you've got to be careful when you think about FTL communications 'going backwards in time'. There's a physical difference between (1) 'going backwards in time' from the present to the past - which is physically travelling to an earlier time. (2) 'going backwards in time' from the future to the present - which is just an illusion that would be created by FTL travel.

I think there's no such difference. The key difference is between differences in ordering of events in coordinate time by different observers (which can be entirely harmless) and going backwards in proper time (which allows events to affect things in their own absolute past and so potentially leads to causal paradoxes).

In your diagrams, you've joined 'coming from the future to the present' with 'going from the present to the past'. That is a mistake.

No, I've joined two spacelike lines which different observers will variously see as joining simultaneous events or going backwards in coordinate time to achieve the net effect of going backwards in proper time. (And then closed the loop with a timelike forward-in-time segment.)

Well, if you can come up with a 'real' thought experiment (I love these sentences!) that matches your diagrams, I'll stand corrected.

In the meantime, the FTL signals you use are actually signals that travel with infinite speed, i.e. instantaneous communications links. That's just equivalent to putting our perspective into the problem, making Alice, Bob, Clare and Dave aware of some of the things that we're aware of.

>>>"The loop is then closed by the simple passage of time from >>>event R to event P, forming the causal loop."

This isn't possible. To close the loop, Dave and Alice have to be at event R for Dave to pass Carol's signal to Alice. If Alice waits until event P to send her signal to Bob, that passage of time means Dave is no longer in the same place as Alice, and cannot pass on the signal from Carol. (Except by subluminal means).

That circuit can only be completed if event P is the same as event R, which means there's no time travel.

Like I said, come up with a physical scenario, a train passing a railway platform, or something similar. You'll find that your superluminal signals all happen in a single blink, and there's no info going back in time.

I'll check out your length contraction article.

"They aren't the same event as all four observers agree that they occur at different time coordinates. (Alice/Bob consider P and R to happen at the same place at different times, whereas Carol/Bob consider the two events to take place at different places at different times.)" That should have been Carol/Dave? Er... right? :)

Sorry, but I don't get that. Alice and Dave are in the same place for event R. You're saying this is before Alice has sent her initial signal to Bob.

But if Dave is in a different Inertial Reference Frame to Alice, he's necessarily moving with respect to her. That means 'after a passage of time' when Alice sends her signal (event P, sometime after event R), Dave is somewhere else.

That means, whatever else is going on, when Dave receives Carol's signal ("event R"), he has to be somewhere distant from Alice (quite a large distance, if the relative velocity is 0.4c!). Then he still has to send the info to Alice somehow. That's a link that you haven't included in your scenario.

You can add in another superluminal transmission from Dave to Alice, but that would reduce the whole thing to the trivial case where everything is instantaneous and Relativity Of Simultaneity is just a dream. Or event R and event P are the same. And it certainly won't allow Alice to send a signal to her own past.

I checked your length-contraction article. It's fine in itself, you'll be glad to know! :) But it isn't relevant to the situation you're considering here.

Do your length-contraction article again. But this time, imagine Carol is sitting on the right hand side (RHS) of the rod (in your scenario), with Dave sitting on the LHS. So Carol and Dave are at rest with respect to each other, in the same Inertial Reference Frame.

Let's say Carol and Dave measure their rod to have length L (it's 'proper' length, in your usage). That means Alice would measure it's length as L0, length contracted by some amount so that L0

When Carol and Bob are in the same place, you have a situation that matches the one in your FTL scenario.

Alice and Bob will see themselves in the same places as Dave and Carol (respectively) at the same time, because they are a distance L0 apart - i.e. seperated by the distance of 1 length-contracted rod. However, Dave and Carol will see Carol in the same place as Bob, but Dave somewhere to the left of Alice, yet to pass her. This is because the distance between Dave and Carol, L, is greater than the distance between Alice and Bob, L0. (Note - the inverse length-contraction, where Dave & Carol think the distance between Alice and Bob is length-contracted, only exaggerates this effect).

That means Dave and Carol will think that, "After a passage of time", Dave will be in the same place as Alice. So Dave thinks he can instantly tell Alice (somehow), "I'll be with you in a minute". But if he did, Alice would instantly reply, "You're already here".

Carol/Dave only THINK they're telling Alice about something in her future because (from their point of view) they think it happened later than *they think* Alice thinks it happened. THAT's relativity of simultaneity!

Length-contraction and time-dilation effects are, as you know, complementary, and somewhat interchangeable. The FTL scenario you've been describing, and claiming a causality violation, is pretty similar to saying that a rod can be X metres long at the same time as being X+1 metres long.

It's like you're saying Dave & Carol can identify the instant that the rod's length = X-1 from Alice's point of view, and tell her about it. They can't.

Likewise, for any two events A and B, you can have Inertial Reference Frames where A precedes B, A & B are simultaneous, or A follows B. But there's no way an FTL link can really violate causality. That would be like giving someone a written message to take to your Dad and putting them on a train, at the same time as putting another note on a carrier pigeon, and phoning him. A while later, your Dad phones back to say your message hasn't arrived yet, and you say, "What message?". then you believe your Dad's phone call has violated causality.

By the way, I made an earlier remark, about FTL signals putting our perspective into the scenario, or something like that. What I meant was, when you and I discuss these scenarios, we know what Alice and Bob think, and what Carol and Dave think.

That is like all the original thought-experiments. E.G. as a train passes a platform, lightning strikes hit the front and back of the train; an observer at the middle of the platform sees the lightning strikes as simultaneous, whereas an observer at the middle of the train sees the lightning strike that hits the front of the train before the one that hits the back of the train.

This is the same but, rather than you and me seeing the situation from both points of view, FTL communication just changes "lightning strikes the back of the train" to "Alice transmits a superluminal signal", and "lightning strikes the front of the train" changes to "Bob receives Alice's superluminal signal". Again, there's never any suggestion that any information can be transmitted into anyone's REAL past.

Unless you know different, of course.

Come on, you've had a fortnight. You been on holiday or something?


I've been busy, but I have written two new articles in the series in that time ("The relativity of simultaneity" and "Absolute future and absolute past").

Would you like me to email you when I reply to your comments?

I'm just finishing up an introductory course in General Relativity at this very moment. I wrote the exam yesterday and now I have to submit a final paper. My topic is about the paradoxes in FTL travel, and extra-dimensional brane solutions to the horizon problem.

I have to say I found your article and diagrams very helpful for picturing causality violations. By this point, I should expect to know special relativity inside and out, but there are lots of subtleties and details that are real tricky to resolve.

Looking at some... well basically all of the arguments above against your claims, I can totally understand where they're going wrong. I used to have some of the same misconceptions, before I started actually learning physics and became quickly convinced. If I had more time on my hands, I'd love to just jump in and help sort out one misconception after another.

I'll vouch for you, Rich. The demonstration above is a 100% correct interpretation of special relativity. Pick 2 from this basket: {special relativity, FTL, causality}.

Folks, to truly understand what's going on here, you really do need to learn some of the math and science behind the theory. Otherwise, statements like "time dilation", or "relativity of simultaneity" lose their full meaning. It seems the 2 biggest misunderstandings here involve the concept of relativistic simultaneity, and the effects of switching from one reference frame to another with the need to keep cause and effect in the right order for everyone.

Science is hard work, no matter what. There's no "easy button" on this one, much as good Samaritans like Richard try to simplify things. At least the good news is, this stuff is accessible to anyone willing to put in the effort, and you don't have to be inducted into some secret order before you can learn it.

Hello. Sorry for my English, I am not English speaker, but the language of mathematics is one :)

Your article opened my eyes for yet another application of relativity - the FTL travel paradox, as it turned out.

The diagrams are fully convicting. Instantaneous travel is impossible if both casuality and relativity hold - and I believe they do.

Key word is 'instantaneous'. What if.

I redrawn the diagrams assuming ansible signal velocity lower than infinite, to make communications not to violate casuality. Using certain velocities, this is possible on this diagram.

Am I making mistake somewhere, or there is possibility, that FTL is still possible, only with maximum speed varied with relative velocity of sending and receiving spacetime frames?

It's certainly true that not all pairs of FTL transmissions, whether instantaneous or at some finite superluminal speed in a given frame, cause causality violations. For example, consider the instantaneous case with Carol moving towards Alice and not away from her. The situation is similar with FTL transmissions that aren't instantaneous in the frame of the transmitter or receiver - it will still be possible to construct a causality violation by using transmissions in two frames, so long as you choose the relative velocity appropriately.

(The most elegant way to see this is to realise that for any superluminal transmission there will be some inertial frame in which the transmission is instantaneous and to use that frame rather than the frame of the transmitter or receiver. The construction of the causality paradox then pretty much follows the case in the article, but using the first and second transmission frames rather than the Alice/Bob and Carol/Dave frames.)

It seems to me, however, that even the inability to send a signal can be used to transmit information into the past. For example, suppose that Carol at event Q tries to transmit an FTL signal to Dave at event R. If at the same time Bob at Q is receiving a signal from Alice at P then the Carol->Bob transmission must fail to preserve causality. But then wouldn't Dave at R know that in the future Alice at P will make a transmission? So not even the presence of some putative causality protection mechanism would prevent sufficiently clever conspirators from sending data from the future to the past.

Fascinating thread, but it turns out that the comment by arsaii on August 1, 2004 is the correct one. Light cones, and the tilting of the space/time axes, are built on the presumption that nothing can travel faster than light. They cannot be used in the FTL case.

If we use the equivalent scenario but avoid reference to light cones, the argument falls apart:

Let us replace the "ansible" with an FTL teleporter. Everything is the same except rather than sending a signal we are sending a person, Ed. Also, for simplicity let us assume that the relativistic speed of Carol and Dave are such that time dilation is exactly half.

Ed steps into Alice's teleporter and disappears, simultaneously appearing at Bob's teleporter and then instantly retransmitted to Carol's teleporter. Since the instrument is instantaneous and the transmission is FTL, no time has elapsed between Ed's disappearance at Alice's house and his appearance at Carol's spaceship.

Ed then spends one hour visiting with Carol and leaves after precisely one hour. He teleports to Dave's spaceship. Then he instantly teleports back to Alice's house, again no time has elapsed in the transition.

Due to relativistic effects, both Alice and Bob will have experienced the passage of two hours from the time of Ed's departure and his return. Carol, Dave and Ed will have experienced one hour.

To be precise, I have introduced an hour's delay at Carol's ship that was not in the initial example. If we remove that delay then all that happens is Ed arrives at Alice's house at the precise instant that he left.

Clearly, in neither instance does Ed arrive before he departed Alice's location, as your proof claims.

In certain frames of reference, for example if the observer of an FTL message between A and B was behind B, B's reply would appear to occur before A sent the original message. It also means that an FTL traveler, with a sufficiently powerful telescope, could arrive at his destination and look back and see himself before he left. That is all that this article actually shows.

Causality is intact, ladies and gentlemen.

I think a lot of the people who are disagreeing about the diagrams are missing an important point--the diagrams are just intended to show that FTL necessarily violates causality if the basic postulates of the theory of relativity are correct. If you are willing to violate these postulates then of course you can have FTL without causality violation. For example, in the comment above wTarasoff says:

Light cones, and the tilting of the space/time axes, are built on the presumption that nothing can travel faster than light. They cannot be used in the FTL case.

The tilting of the spacetime axes is simply a consequence of graphing the different coordinate systems related by the Lorentz transformation, and it is possible to derive the coordinate systems given by the Lorentz transformation from the two fundamental postulates of special relativity, which say that 1) the laws of physics should be the same in every inertial coordinate system, and 2) the speed of light should be c in every inertial coordinate system. If you accept these postulates, you must use the Lorentz tranformation to relate different inertial coordinate systems (any SR textbook should have a proof of this), and the Lorentz transformation implies that the different coordinate systems define simultaneity differently (two events that happen at the same time-coordinate in one system happen at different time-coordinates in other systems), hence the characteristic "tilting of the space/time axes".

Furthermore, if you use the coordinate systems given by the Lorentz transformation, it must also be true that for any two events with a spacelike separation, there must be some inertial coordinate system where these two events happened at the same time. And since the events of sending and receiving an FTL signal always have a spacelike separation, there is some frame where this signal travelled instantaneously from sender to receiver.

So, if you accept the first postulate of relativity, which says that the laws of physics must work exactly the same in every inertial frame, then if it is possible to send signals instantaneously in one frame, it must be possible to do so in every frame. But as the diagrams show, if you have different observers moving apart at relativistic velocities, and the observers each have "ansibles" which allow them to communicate instantaneously in their own rest frames, then it is possible to create a causality violation. The diagrams include 4 observers, with Alice and Bob sharing the same rest frame and Dave and Carol sharing a different rest frame, but it is really only necessary to have two observers moving apart at relativistic velocities--you could eliminate Bob and Dave and just have Alice send an FTL signal instantaneously in her frame to Carol, and then Carol immediately send an FTL reply instantaneously in her frame back to Alice, and you can see that Carol's reply will intersect Alice's worldline at an earlier point than when Alice sent the original signal.

Relativity is an illusion.

The space of Lorentz-transformation come from a moving camera.

The time is what the clock show.

Nothing more.

The time is what the clock show.

I entirely agree with this part: the only physically meaningful time is that measured by clocks. However, the behaviour of time as measured by clocks does not agree with most people's naive intuition about time, and to a very high degree of accuracy agrees with special and general relativity. See, for example, the list of tests of time dilation at Wikipedia for some pointers.

Relativity is not an illusion (although relativity does itself contain some interesting optical illusions and other effects from moving cameras, none of which I discuss in this series). Once again, there is a mass of experimental evidence supporting relativity over the classical theory of absolute space and time, especially when relativity is combined with quantum mechanics in the form of quantum field theory.

"that nothing can travel faster"

lies, touch this

Ed steps into Alice's teleporter and disappears, simultaneously appearing at Bob's teleporter and then instantly retransmitted to Carol's teleporter. Since the instrument is instantaneous and the transmission is FTL, no time has elapsed between Ed's disappearance at Alice's house and his appearance at Carol's spaceship.

How do you physically determine that the transmission and reception are simultaneous?

What you're describing is quite like the situation with wormholes in general relativity. However, with a pair of wormholes it's also quite easy to violate causality (unless some kind of causality protection mechanism destroys sets of wormholes just as they become time machines). I'll describe this in detail at some future time when I get to the sections on general relativity in this series. (Note, however, that after a couple more sections on special relativity I'm going to discuss quantum mechanics before moving onto general relativity.)

Apparently superluminal transverse motion in jets moving at speeds close to the speed of light almost along the line of sight is one of those relativistic optical illusions that I said I wasn't going to go into :)

Incidentally, the effect was predicted by Martin Rees on the basis of relativity before it was observed by astronomers. Martin Rees was one of the people who taught me relativity in Cambridge. (He was co-lecturer of the fourth year undergraduate "Relativistic astrophysics and cosmology" course, which was generally excellent.)

Everything is smaller, what to see the moving camera. This is the Lorentz transformation.

Every electron as like a camera. Live in a illusion.

Reality is real, but build on a illusion. The Newton physics is right.

Spacetime is not real.

Everything is smaller in the direction of the moving. Everything is bigger, if the camera look in the backward.

Check it, its simple.

However, the length contraction effect in relativity is along the axis of motion not transverse to it.

There are relativistic aberration effects too. One is that if two observers travelling along the same axis at different speeds look at a distant object along that axis at the point they pass each other then they will measure different angular sizes for that distant object.

This is seen the "other way around" in the "headlight effect" in which an object radiating isotropically in its rest frame will appear to be transmitting anisotropically when viewed from a frame in which it's moving (with a distribution biased towards the object's direction of motion).

I know this things.

You try to understand, what i write. Some help:

Lorentz transformation come from a moving camera. It is the final reality.

i dont agree with the ftl theory of gettin someware befor an event seeing as an event has no acual speed also since time is not an actual object of nature then how can an event take time and then how can you get somewhere befor an event pls comment my theory

sincerealy nik the great


You continue to astonish me by your endless patience. There are SO MANY people who assume "I don't understand it, so it can't be true."

Much the same sort of failure to learn or think happens also with Darwinian Evolution.

Many thanks for the interesting and informative articles. Best regards!!

I havn't the faintest idea what's going on. That is to say, im ignorant to concepts of quantam field theory, relitivism etc. and with my miniscule scientific brain i must say im one confused traveller:)

Wow... this has been going on for over two years... I didn't even read all of it.

Anyways, in a black hole, space and time switch their roles. e.g. Time goes in all directions, while space travels in a straight line. So, for the person in the black hole (let's call him fred) (if he/she manages to survive the Spaghettification, if time goes back (it can go in all directions in a black hole), then, to fred, he would be in the past, but, to the observer (michael), he would still be going forward in time (that is, if he could see through that spectrum of light, and, since there is no light, have some kinda super-glasses or something...)If fred manages to get out of the black hole with time set as backwards, his time would be reset to forward as soon as he exits, but to michael, he is either continuing into the center, or has reached singularity, either way, fred is in the "past". Even though he is in the past, michael can see that he is still in the present. If, fred managed to get to earth, and get a newsbroadcast (or whatever kind of publicity) of what happened to him, then that would notify michael, who is still in present time, which would mean that it already happened. Which also says that, before takeoff of fred, they knew that fred had already taken off, and, fred may have already died (lol, imagine fred visiting fred in the cementary). But, the fred that died, is the absolute future of the present, before take-off, fred. Of course, if before take-off fred has any common sense at all, he would probably not take his spaceship for a ride that day, which would mean that, the fred that was in the past never existed, which means that he would have never notified anyone, which means that before take-off fred would have went on with the trip without hesitation, which, would make a never ending cycle. So, fred has an absolute future to take the trip on his spaceship.

This is why time-travel to the past is impossible. Because, time is set, or fixed already. Nothing can change it. In other words, if someone from the future would have come to the current present now, we would have known it, already.

This doesn't mean that travel to the future is impossible, though. As I said, time is set. So this means that time can be set for something to happen, that, makes one go to the future. Of course, the person who went to the future wouldn't be able to come back. And, if when the person went to the future, the sun had engulfed earth, which means he'd have an absolute future of death due to futuristic time travel.

If he only traveled a day ahead, he would be fine.

Let's say someone traveled to the future with a live video camera... what would happen then? Well, it would probably not be live anymore because it has no access point any more. Unless they made a device that could split its signal into a parallel dimension and then back to our dimension.

Now we come to another question.. paralleled dimensions.

Responding to: 50. Comment by David Piepgrass on February 5, 2006>

There is indeed a much simpler way of dealing with special and general relativity. Mass-metric accepts that mass increases with speed, and this makes real meter sticks shrink. Same results, but using scalars instead of tensors. See full paper at arxiv/physics/0012059. in theory of relativity...E=MC2 ever herd of that?

Dear Dr. Baker, I am completing a book for MIT Press on the History of the grid (Life of the Grid: From the brick to the World Wide Web). It will appear next Spring in a number of 2,000, with black and white images and international distribution. I would like very much to use the 1st diagram in this article, it is clear, understandable to a general audience, and would reproduce well. I am an art historian by trade, so these qualities of very much to your credit. I have very little to offer in the way of funds, but would consider it if necessary. Thank you, Hannah Higgins

I've been to the past. I've been to the future. Forget the theories. Timetravel does, indeed, exist. It only takes a couple bong hits and a blot of LSD.

Hello there to whom it may concern:

My name is Jason R. Thrift I have just recently had a science fiction novel published called The Civilization Loop. The main premise of the book is that time travel is possible and that people from our future founded the first civilizations on Earth due to an unexpected paradox in the future that wipes out the Earth.

The time device in my story is called the Time Displacement Assimilator (T.D.A.). This device essentially pulls two time frames together in space. You have to travel through the portal, connected to a wormhole between the two points in any type of space craft you desire, in this case a space shuttle.

I've been working on the next story line to follow up this novel and I'm trying to explain further how the TDA functions, but in a way that makes sense and could sound believeable. I was going to suggest it here and see what you think of the idea.

There are three particles in existence that travel at, near or beyond the speed of light. Tachyons, travel faster than light (in theory, if they exist), luxons travel at the speed of light, neutrinos travel just below the speed of light.

The TDA is designed as a cone shaped, metallic device that sections the energy output for the three particles. A nuclear reaction is necessary to help generate these particles, thus the device has its own reactor core. The device effectively will pin point neutrinos in space (which are everywhere), and accelerate them to the point of light speed, in a circular motion. The Tachyon emissions will been what accelerates the neutrinos into this circular, spiral of sorts, forming a small black hole to a certain degree. Then the luxon will start at the edge of the neutrino spiral, moving on a linear plane. Once in the spiral, the luxon will move around the spiral accelerating beyond the speed of light, moving into the center of the vortex and resulting in a time portal. The luxon acts in this way because it has no mass and effectively is not interacting with time itself, allowing for it to pass through the fabric of time and open the time portal to allow an object of mass, space shuttle, to pass through the orifice into the past. Then the portal closes back up shortly after.

Interesting theory, curious what you think and if you think it is interesting. Remember, this is for the purposes of entertainment, not science fact.

Thanks for reading

Jason R. Thrift,

Your TDA sounds good, assuming a massless luxon has the capability to accelerate faster than the speed of light in your mechanism. You're gonna need to specify for your readers because it will be your most critized point.

A Simple Resolution to the FTL Causality Violation Within Special Relativity

As shown by your diagram there is indeed a transmision of information into the past from Alice and Bob's relative viewpoint, as well as from Dave and Carol's relative viewpoint. However, there exists no causality violation simply because of the necessity of conservation of energy, in this case temporal energy (if one can entertain such a notion for the duration of this comment) Let me extrapolate on how the conservation of temporal energy needs to be satisfied in this specific case.

When Dave receives the information, his position in space equals Alice's, although he is in a moving reference frame. This is irrelevant. The requirement for further remediation in time to preserve conservation of temporal energy and prevent causality violation is due to the fact Alice and Dave are not in the same time, when Dave receives the information. Although it appears by the mathematical geometry of your diagram Dave is in Alice's direct past this has no bearing on Alice's own personnal recollection or observation of her past, which has already occured and is unchangeable. Dave has no influence on Alice's present observation of anything when he doesn't exist in her present temporal reference frame. It would be like someone editting a scene out of a movie you've already watched. What you've already seen cannot be in any way changed. If you look closer at the mathematics you will discover this is a direct consequence of the relativistic nature of this problem.

In order to again communicate with Alice he needs to shift temporally into her present. At which point temporal energy is conserved and causality is no longer violated. In order to communicate with Alice and effect her present reference frame any information he sends to her would, by neccessity, need to travel forward in time by the exact amount the original signal travelled back in time.

This solution satisfies the problem for all observers because both Alice, Bob, Carol and Dave would observe this signal travelling forward in time by the required amount.

There is an error in your diagram because you assumed the final path of the signal could travel through normal time to reach Alice which it could never do. It would forever race to catch up with her and never could because Alice, Bob, Carol and Dave all continue to move forward through time at the same rate as the final leg of your causal loop.

My own website details some interesting science regarding the possibility of interstellar propulsion systems. I am quite amused with the continued interest in your blog here and am encouraged to continue my work in this field. I have yet to publish my ideas of time travel and the resolution of paradoxs for new propulsion systems but hope to do so in the near future.

"if any of your math says otherwise then you math is simply flawed thats all because it contradicts reality." - Chris Taylor

"If science contradicts the divine scriptures, then the SCIENCE is wrong!" - Russel Carlisle, "Time Changer"

Sorry, If Dave and Carol are unbiased to each other, the distance (of the transmission) is a perpindicular line between the two within THEIR time. Instantaneous or not, 6th grade geometry will tell you that the resultant is directly proportional to the distance (or time) traveled (delta).

All the arguments that have been presented so far are failing to convince my intuit, although they might be formally correct.

Let's say that there is a relativistic moving tachyon mirror, and I send my tachyon to the mirror as the mirror is moving through my location (point A). I receive the tachyon back as soon as I transmit it and everybody is happy.

Let's say now the relativistic moving tachyon mirror is moving through point B, far from A. Since it's relativistically moving, I don't know it's there... I will know it's there just later, due to the speed of light. Nevertheless I fire my tachyon toward point B, and instantaneously I receive it back.

Where is the causality violation here?

And is it after all so important the speed at which the tachyon mirror is moving?

You might be interested in some of the new history of set theory, which sheds a great deal of light on Poincare's understanding and his influence on Einstein. For some reason, we seem to be enjoying a renaissance in this field. It has importance for relativity, because Poincare's responses to the set theory discussions found their way into Science and Hypothesis, which so influenced Einstein. I think it is becoming more clear that Einstein's adoption of natural mathematics (what he called "practical geometry") through Poincare and others, was really the important step in his thinking, with consequences which were not so good. Above all, you should read Garciadiego's book on Russell, in spite of its many typos. If you haven't read that yet, you should do so first thing. I discuss some of the new work in the essay below. Cordially yours, John Ryskamp Ryskamp, John Henry, "Paradox, Natural Mathematics, Relativity and Twentieth-Century Ideas" (May 19, 2007). Available at SSRN:

I know when you or anyone reads this, you won't believe it. But that's ok with me, I know the truth, and quite frankly...enjoy it! Time travel is possible and exists. I don't know if anyone, object or event has experienced it...but I, on November 27th, in the year of our Lord, 2007, have just successfully completed, in what seemed to be 5 years, 3 months, 6 days, 4 hours, 17 minutes and 44 seconds, my the years 1632-1637. At this time, I can't reveal how I've achieved this, but once the proper channels of governing bodies are pleased, a media report will be released. Gentlemen...and women, this is a new coming of age for man and mankind. I am very pleased to be a part of this history changing event and I assure you our world will change for the better, because of this. Our world will become what it was meant to be!!! I apologize for not being able to reveal more to you and to the scientific community. I ask you to be patient and everyone will discover my truth in the very, very near future...past and present!!!

I have seen this explained many times and this is the first time that I really understood it (instead of just accepting something that didn't make sense)

Hmm i Sat here for 5 hr (almost non stop) and Read this mind boggling science/Phisics lecture. Now i Have a few questions to ask anyone who cares.

first..... As everyone knows you cant hear sound in a vaccum and sound is caused by resonance of a medium. so if sound has to be moving at a varying rate to be heard.

a)"doesn't light have to be moving at a varing rate to be seen?(is this why space looks dark?) i must claify that if i were at a 90 degree angle to the sun and earth would i be able to see the light particles from the sun to the earth? NO Why? because light is NOT a constant it shows us an illusion of a constant. Yes? Or is it travelling to fast to be seen? if it is it must change velosity to be seen.

b)"If traveling at the speed of light ment you would be travelling at a varing speed (as do Tachyon's, neutrino's, luxon's relative to each other) who says you will be traveling within time at all? Who says anything will exist at all? If light IS a constant you wouldn't be able to travel (or send a message) BACK in time only back to the same point in time as the message came from.HELP?

c)"If you were to travel the adverage speed of sound (assuming you knew what this was) wouldn't time stop? everything we use to calculate time is set to the sun even if we had clocks motion would be paused wouldn't it?.

d)assuming you could send a message at the speed of light it would only work between two point travelling in the same direction or towards each other other wise the signal would be travelling the speed of light+signal actual this correct?

Having said all this im off to bed can someone please shed some light on my assumtions? mabey point out some web links/books to read?

Another wild idea what if the universe itself were a sphere? (the inside of one)

Relativity defines the limits of accessibility within the electromagnetic universe. It cannot rationally describe the quantum mechanics that underlies the nature of matter. This is where physicists -- namely those dealing with relativity, are weak in conceptual logic.

If one assumes relativistic behavior, then as a mass approaches the speed of light, it increases in mass -- approaching infinite mass as it nears light velocity. Thus the mass would require an infinite energy to propel it to light speed -- an impossible outcome. However, lets assume that we have a very efficient fusion space engine that fuses helium to oxygen. As the mass of this engine begins to increase, as it approaches relativistic velocity, so does the mass of the fuel, and the fusion process increases energy output in concert with this mass increase. (we view entire galaxies traveling at a pretty good relativistic velocity, and there is no evidence that some imbalance of energy/mass is taking place, so mass/energy still operates in the same quantum mode as our local galaxy -- as far as we can determine).

So, as mass increases, energy output increases in proportion. The effects cancels out and the advanced fusion engine goes faster than light. But, since we are limited by electromagnetic observation, we cannot observe that the engine has gone faster than light.

Relativity and the inability to accelerate an object faster than light speed is sensible -- that is, to externally accelerate an object (mass) to the speed of light is impossible.

Causality is very intuitive and simple: If I switch a laser on and the light that leaves the laser moved at superluminal speed, it would only ever reach any destination however fast or however close that destination was, IF I switch that Laser on. So it is a quation of intuition and common sense vs a mathematical complex. mathematics will never find new truths. It is a toll to verify, validate or question our intuition and questioning, nothing more. So the speed limit and causality have no relation. Mathematics cannot counterproof this. It is funny that many people look at the tool (mathematics) like at a hammer and believe everything must be a nail. Einstein reached his limit where he himself started to believe that his tool would point to all other solutions. It did not help him find ralativity, it was his intuition that did and then he used the tools to describe it in a more formal way. But causality was not what he thought about. he should have thought about causality freely without the burden of relativity and the tool-construct he created to describe it. this is why he couldn't move towards understanding/feeling quantum mechanics nature. He himself let his intuition free one last time with the EPR Gedankenexperiement- but let himself drag down by his own legacy to deny the very quintessence his unrestricted mind had found. There are two morales which have been valid for a long time in human science history. The revolutinary, inventor, creator becomes the protector and dogmatist. There is a point where revolution ends and becomes a new dogma that is defended against new revolutions. Now we all wait for that new intuition to sink in. where we will accept B-Theory and understand that particle strings are the solution to non-locality and that being faster than light does not affect causality. Causality far more leads to a interesting connection with will. We will only see and understand new things when we never get too attached to existing wisdom. That is not disrespect for the works of the ancient and old, but it is true, that probably for a very long time we will not have found the final godlike wisdom and that means every century is just another step and discovers new truths and corrects old beliefs. Once we are free and open minded we will see new things and find new questions and new answers more easily. Nowadays not only engineering and space projects have become so complex that it takes the minds of many to achieve results but also science. It will i all likelihood not be one new Einstein that will open up space-time to us but probably networked groups of minds that will achieve this in a series of cascading works and papers building on each other. So the internet, as basis for a connected/collective intelligence was necessary for the next stage of insight and discovery. So how long will it take? I though it would be fun to happen around 2005 but may be we are looking at another 5 to 10 yaers beyond that date. I don't think the old theories will be able to protect new insight very much longer from the massive intelligence that a collective mind of thousands is capable to think and create. This is the domain of the young and being middle age myself I try not believe and not to attach too much to existing wisdom. this allows me to be more creative and inventive than many of my contemporaries- follow your natural intuition!


That name makes me think of the Never Ending Story! Love that movie.

You bring up a good point and if you have ever seen anything about Dr. Ronald Mallett, he says the same thing as well. That it is impossible to go back in time before the point at which the time machine has been turned on. For that reason, to actually travel back in time would require that a time machine had been invented thousands, maybe even millions or billions of years ago by a super advanced ancient civilization we know nothing about and somehow sync with our time machine. How does this syncing occur? Could be as simple as switching an actual time device on or it could be never. Regardless, until Dr. Mallett or some other scientist creates a real time machine, we'll never know.

So experiencing time at all? You know a guy I've worked with made that statement, time is a human thing. As you said, we measure it based on our relative position with the sun. So the truth is, when you travel back in time, you really wouldn't be traveling in time. In space, time has no meaning, especially in the presence of a black hole that completely violates the laws of physics. So, if time doesn't exist beyond the scope of human reasoning, then would it not be possible that by interacting the right particles at the right frequency, at the same point in space, would not generate this small potential portal-like black hole that allows you to go anywhere, anytime, based on our concept of time?

You have a point about light not being a constant for the very fact that images we receive from distant stars and galaxies maybe millions of years old. Those images are based off the light we see, a reflection like a mirror. So what an astronomer sees is a delayed image, by a million years, if it were a million light years away. That very nature of light suggest a plausible ability to travel faster than it. There has always been a delay in sound, such as when a nuclear bomb detonates in the distance (the light reaches you first before the sound does) and we broke that barrier which has spawned the ability for trans-continental flight, space exploration and so forth. I believe it is only a matter of time before someone develops a way to harness the necessary energy needed to crack the light barrier. People always hold to Einstein's theory of relativity as a preventative measure of faster than light speed. However, if what you're saying turns out to be true and suddenly Einstein's constant of light is no longer constant, then the theory or relativity could be proven false, one day. Probably not in our lifetime though.

I thought that was very interesting you picked out the particles I suggested for my story to comment on. I love a debate about this stuff, especially about time. I think that is why I wrote a book about it, because it is so hard to understand time. Its an easy concept to learn, but so hard to figure out why it is even necessary, other than defining our own existence here on Earth. Another thing, why I believe we have not achieved time travel or faster than light speed (aside from the obvious fact we just don't know how yet), I feel those two things would put us on the same playing field as God. To be able to go anywhere, do anything, see anything, be in any time, is that not God-like? It would probably be a glimpse, but I still think it would not be possible for us to be God-like no matter how advance we become or think we are. But, that's just my own opinion, I could wrong.

Needless to say, stuff like this just keeps me inspire to be creative and write my stories I love. So, please do keep the debate going and try to figure this stuff out. You never know, we might find a solution right here one day.

As for pinner44, what the heck? Why the elusiveness and why come in here broadcasting something? Just say it if you want us to listen. I'm afraid the time of John Titor is over! So spill it! That is unless the government has already gotten to him.;)

hello, this is suraj from India. very interesting fact yet. i've been very keen in the matter of time travel right 4m my childhood & many times i used to think about 1) "wat wud happen if i go to 18th century (to england) and kill james watt, george stephenson and all the scientists (issac newton, heisenberg etc) who contributed to industrial revolution ? d world v c today wudn't b so if i come back to 2008 A.D." 2) wat wud happen to me if i go to year 1912 (my grand father was born dat year) & kill him ? will i dissappear instantaneously ?"

then i began to think abt this time travel. wen v speak about travelling to past, the world won't b as v c it today ? E.g: there was no london bridge in d year 1000 BC. no taj mahal in 1000 BC. hoe cud london bridge & taj mahal dissappear from this existing world ? not feasable !!! hence, i came to a conclusion dat travelling to past means dat v go to a paralle world (apart from the present world v live) wer the history v read is the PRESENT there. if v set the time machine to 1000 BC, it'll not take us 2 the same world wer v stand. it'll take us 2 a new earth somewhere very far away in universe, in which the year 1000 BC is happening. similarly, for the future (e.g 6000 AD). it'll will take us 2 a new world wer year 6000 AD is happening. kindly add ideas to my comment & reply. my id: thank you.

Hi, If you were able to go "back" in time say, in theory, why not also have a theory that says you are not able to chance what has already happened? You were part of the history, but were not able to change it.

with ref to comment by pk on april 5 2008 at 3:55 pm, i would strongly agree to his/her point coz of the fact that many paradoxes which will arise if v try to change the past, like that of the grandfather paradox (killing one's own grandfather by travelling to past). autoinfantism is also such kind of paradox i.e killing one's own self when he/she was a baby by travelling to past. hence, there might be a supernatural power (Indians say PARAMA AATMA) which prevents us travel to past or future. in many ancient indian scriptures and epics, certain yogis and rishis travelled to VAIKUNTAM (where the protector of all beings exists, vishnu) and come back. these rishis have also made god to come to earth and grant wishes. again, there are quotes in ramayan and mahabharat that one who does penance for more than 100 yrs, we wud b able to walk on water, fire etc. plz believe it. these miracles have happened in India. when these can happen, y not time travel can happen ? certainly it can. but only with the help of self realisation, meditation, penance and sacrifice of all worldly possessions. v may not b able to make any changes in the past nor talk to any famous personality in the history, but can only c the history happening right b4 our eyes. lets cum to future travel. there r many theories which state that if v travel exactly at the speed of light to a distant star or planet (certain light yers away 4m earth) in a spaceship & cum back to earth, the earth would have aged a lot than us. let me show u all.

consider some crew members travel in a spaceship to a distant star/planet which is 5 light yers away 4m earth. they leave the earth on jan 1 2007 which contains 365 days. the ship travels at exactly d speed of light, by some special propulsion mechanism. therefore, time reqd to travel to planet and cum back, t=(2d/v), where d is the distance of planet from earth, v is the speed of spaceship. we knw dat, d=5 L.Y = 5X9.46X10^12 km (convert L.Y to km) = 4.73X10^13 km. v = speed of spaceship = speed of light = 3X10^5 km/sec. hence, t = (2X4.73X10^13)/(3X10^13) = 315333333.3 sec = 9.999 yrs = 10 yrs. when travelling at speed of light, any object ages less than any other stationery object by a factor of zeta (E, greek alphabet) which is given by E = sqrt(1-(v^2/c^2)). therefore, in this case, E = sqrt (1-(3X10^5/3X10^5)^2) = sqrt(1-1) = sqrt(0) = 0. that means, the age flow and time flow of crew members would affect by factor E. i.e. age of crew members = E*10 yrs = 0*10 yrs = 0 yrs. crew members would not have aged at all ! but people on earth would have aged 10 yrs when spaceship comes back. this proves that the crew members have travelled to future. add 10 yrs to 2007 = 2007+10 = 2017 AD. wen they return, it wud be 2017 year running on earth. but practically, no machine can be designed to travel at such speeds. hence time travel to future or past would remain a dream for scientists and researchers. kindly add more mathetical proofs. thank you

As far as FTL being equivalent to time travel, the above explanation is correct. As far as FTL being impossible at present, it is not quite. Richard's explanation lacks a mention of black holes. An object (with non-zero mass), falling into a black hole from rest, will cross the event horizon AT THE SPEED OF LIGHT. Unfortunately we (the distant observers) would not be able to witness this event, since the falling observer would take forever (from our viewpoint) to reach the event horizon. In the falling observer's reference frame, however, he'd be flying at the speed of light all right! Moreover, he'd probably be able to time travel as well, as his speed continues to increase (to >c) inside the event horizon. Whether this would lead to any causality violations is unknown, since we can't see past the event horizon, and the unfortunate falling observer has a short time to live before he hits singularity, causality violations or not. However, from a purely theoretical point of view, we know that FTL travel is possible with black holes.

I started to write a comment replying to StarGate but it's turned into a whole post on "The causal structure of black holes".

You people are very versed in the theories of FTL travel but the problem with all these theories is that they can neither be validated or invalidated by current science. Besides all this, E=mc2 is very restrictive in allowing us to travel anywhere near the speed of light. Rest mass and transient mass would rip your vehicle apart and there would never be enough thrust to accelerate to that point. We are on the wrong road to FTL travel and need to throw the many quantum theories in the can.

Hi. Thanks Rich for the great diagrams and explanations.

I know you didn't particularly want speculation and so on, but the interesting conversation is the main reason I've read numerous posts here. So I hope you won't mind my stating some thoughts to see what the reaction is.

Any signal is in the form of a wave, and any signal returning to itself has a well-defined phase relationship with itself becuase it has a common source; i.e. the phase relation it is not random or stochastic. This allows interference phenomenon of any wave with itself, which we usually think of as occurring when "part of" a wave meets itself, such as in a hologram using a beam-splitter.

Is it possible that the Novikov principle can be satisfied if (i) instantaneous (or near) interactions of waves occur and (ii) therefore instantaneous (or near) self-interaction occurs, and is part of the state of a signal as it exists?

For example, in Rich's diagram Alice sends a signal, in the form of ftl e-m waves, to her younger self through Bob. Now, the argument here seems to rest on a problem with Bob signalling *younger* Alice *based on* a signal already received from Alice. For Novikov self-consistency to hold this can't occur. The possibility I've mooted is Alice's any self-interactions necessarily exist in Alice's signal. This kind of thing is said to be tautological, which may be true, but I am not sure that it precludes non-local interactions.

The seemingly "obvious" problem is that Bob could decide to send that signal, and there seems no reason to suppose he can't do so. On the other hand, I could simply assert that Bob cannot send it, just as I can't simple decide to override the gravity when I've just fallen.

Is it possible we simply haven't yet conducted experiments that show conditions under which signals that would result in self-interference violating self-consistency are impossible?

In other words, paradoxical effects only seems to preclude superluminal signalling when it self-interferes (which it would do instantanously). Precluding this does not seem to preclude other superluminal signalling.

Excuse me if there are already arguments dealing with this.

Hi Snap. I think I should clarify my position. I don't mind speculation or comment, but I don't want anyone to think that if I don't attempt to refute something said in a comment then I must therefore endorse that commenter's theories. I simply want to avoid this scenario from xkcd:

Rich I googled into this looking for a quick review of how ftl travel violates causality in special relativity and thank you very much for a lovely job. And thanks Benjamin Rosenbaum for discussing the expanded causalities. Very cool. And thanks google.

Most of the rest of you folks are kind of like ants at a picnic. It repeatedly amazes me how kind and patient so many science guys are with the unwashed masses.

Thank you for your kind words.

I'd imagine that we're kind and patient because we can all remember very clearly what a struggle it was to understand this stuff in the first place, and how kind and patient those who taught us were.

For that matter, it's still a struggle. When I started my undergraduate degree I thought I was on the verge of understanding everything about physics; nine years of thinking for many hours per day about the subject has left me with a deep appreciation for the the depth of my (former and current) ignorance. But even though understanding new physics is a struggle it's a fun struggle.

while i dont pretend to have the slightest grasp of higher physics theroy (eg anything beyond Nm, watts, Henerys etc) i enjoy attempting to learn and understand. i would like to express my appreciation for your free sharing of knowlege.

thank you

Fascinating. I'm almost beginning to understand this stuff. However, I'm still confused about time dilation.

When it was first explained to me, I was told that if I were to leave earth on a spaceship going at almost the speed of light and then turn around and come back after what seemed like a few minutes later for me, the amount of time that would have passed on earth since I left would be days/years/centuries, depending on how fast I was going. However, now that I consider one of the most important points of the idea (that there is no such thing as an absolute reference frame) it doesn't seem to make sense. To the Earth, it would seem like time is passing more slowly in my spaceship. However, it would also seem to me like time on Earth is passing more slowly. If time treats us both in the same way, what causes the discrepancy between our clocks when we eventually get back together and compare how much time has passed for each of us? Yet, hasn't such a phenomenon been verified by experiment?

You're 90% of the way towards understanding time dilation, Rory.

If a spacecraft flies past the Earth at constant velocity then you're right that people on the Earth see time passing more slowly on the spaceship and people on the spaceship see time passing more slowly on the Earth. This symmetry is a consequence of the postulate of special relativity that says that the laws of physics are the same in every inertial frame, as the rest frame of the Earth and the rest frame of the spaceship are both (to a good approximation) inertial frames. (Remember that any pair of inertial frames move at constant relative velocity with respect to each other.)

However, if we consider a spaceship travelling at constant speed to a distant star and then instantly turning around and travelling back at constant speed then there are not two but three intertial frames frames involved: the frame of the Earth, the frame of the spaceship as it travels away from the Earth, and the frame of the spaceship as it travels back. It's the acceleration of the spacecraft as it turns around and travels back that breaks the symmetry between the Earth and the spaceship and leads to less elapsed proper time for the spaceship than for the Earth between the spaceship's departure and its return.

To see this more clearly, consider this diagram from my article on time dilation:

Imagine that event Q is the arrival of the ship at a distant star, the white frame is Earth's inertial frame and the blue frame is the ship's outward inertial frame. Let's suppose each unit of proper time is a year. For the return journey, the spaceships's simultaneity surfaces tilt the other way. When the ship arrives back on Earth, forty years of proper time will have elapsed for the ship. However, take a look at the other diagram from that article:

From this, it's clear that by the time the ship returns more than forty years of proper time will have elapsed for the Earth. In fact, in this particular case 43.6 years will have passed on Earth. If the ship travels closer to the speed of light the difference in elapsed proper time will be even bigger.

This has indeed been verified by experiment, in experiments involving pairs of atomic clocks, one of which is carried on a aeroplane. However, the case in the experiment is a bit more complicated as there's not just special-relativistic time dilation but also gravitational time dilation to take into account.

Sorry but I do not believe the validity of this example.

You are simply mixing up reference frames arbitrarily. If Alice and Bob are at the same "now" when they communicate, and Bob and Carol are at the same "now" when they communicate, and Carol and Dave are at the same "now" when they communicate, then Dave and Alice are also at the same "now" when they communicate. Never mind how they got to "now", or what their clocks display; at the moment they communicate, their time flows overlap.

Why should the communication between Bob and Carol be any different than any of the other communications? Just because they happen to be in the same place at the same "time"? I'd buy it if Carol stopped and shook hands with Bob, but she doesn't. And she can't stop because that would break your example.

Just because time flows at different rates for them doesn't mean they get stuck in the past in an absolute sense, communications or not. The atomic clock you city didn't suddenly pop out of our time and into the future.

Also, you're not understanding the relativity of simultaneity as Einstein formulated it.

In fact, you're very behind the times in understanding Einstein's "practical geometry." He had to formulate his mathematical approach before there could be the relativity of simultaneity, special relativity or general relativity.

You don't take "practical geometry" because you don't see where Einstein uses it in the formulation of the relativity of simultaneity. This is where:

Paradox, Natural Mathematics, Relativity and Twentieth-Century Ideas

John Ryskamp

And to show you just how far you have to go in understanding the relativity of simultaneity, you have not read, and should read, A. Garciadiego, BERTRAND RUSSELL AND THE ORIGINS OF THE SET-THEORETIC 'PARADOXES.'

Once you've read everything, then you still have a BIG mountain to climb:

do you have the brains to understand what you are reading, or are you so screwed up that you're a hopeless case?

Here's a way to find out:

Where is "natural" coincidence in the Pythagorean theorem?

yaa i m a time traveler here. anything else to say in this manner u dumbs......

Rich, I've been trying to square this away for two days, and I think you have a logical error here.

You're confusing frames of reference. In proper time a space ship traveling at .4 c traverses 120 million meters in a second. Within the frame inside the ship the time is (1 second * .917 [Lorentz factor for .4c]) .917 seconds. However, this means the ship reads that it's going .43 c internally.

Thus, at 100 seconds into the mission, you have 100 seconds in proper time and 91.7 seconds in the special frame. Now, if you performed your superluminal transmission with just this information you may, indeed, conclude that the transmission could violate causality and hop backwards over eight seconds. However, when the mission ended at 200 seconds, (183.4 seconds internal) you would see that both events occurred simultaneously at 50% mission time.

What I believe was the problem is the graph. Apparently that system is flawed, if extremely quick to pull answers from. Visual representations, as we both know, are very powerful, but an incorrect model, be it an equation or a graph, will output incorrect answers.

Now, this is science, so I must admit I could be wrong, but this simple example provides a counterpoint for the violation of causality.

I've seen some argue that you cannot "experience" time dilation and the like. This is incorrect. Clocks, even atomic clocks, run slower at higher speeds. Being beings based on electromagnetic physics, when the system slows down, we slow down.

As an aside, this means at high fractions of C, you'd need a computer correction on pitch for transmissions.

Perhaps the system breaks down at many iterations, but seeing as how the frames of reference all are internally consistent, I see no real reason why a zero-error system could encounter compounding errors.

So either I misunderstood what you were trying to get across completely, or your explanation is flawed.

Mike F said:

You're confusing frames of reference. In proper time a space ship traveling at .4 c traverses 120 million meters in a second. Within the frame inside the ship the time is (1 second * .917 [Lorentz factor for .4c]) .917 seconds. However, this means the ship reads that it's going .43 c internally.

This is incorrect. Firstly, you're using "proper time" in a confusing way. Proper time is just the time as measured by a clock, and so each inertial observer will have his or her own proper time. What you really mean is the ship's proper time and the proper time of the other inertial observer, whom I'll call the "planet". As I have a little time this evening I'll analyse your example in more detail...

First, let's consider things from the point of view of the planet. For definiteness, we'll say that the journey begins when the ship passes the planet and ends when it passes a distant space station, which is 24 million km of the planet's proper distance away. As measured by a clock on the planet (or the station, or more realistically, both), the ship takes 200s to travel from planet to station. The ship's speed as measured in the planet's inertial frame is thus 0.4c. That's not very surprising.

Now, consider things in the inertial frame of the ship. The crew of the ship can consider themselves stationary and see the planet and station race past them during their voyage. In the ship's inertial frame 183 seconds elapse during the journey. But, and here's the part you've missed, there's length contraction as well as time dilation at work. For the ship, the planet, station and, crucially, the intervening span are all shrunk along their direction of relative motion by a factor of 1/gamma. The ship thus travels only 22 million km of its proper distance. The crew of the ship therefore measure their speed as 0.4c too. Really, that's not very surprising either as the situation is entirely symmetric between planet and ship. The gamma factors just cancel in the division.

But in any case I've very carefully constructed my violation of causality without any explicit mention of time dilation or length contraction at all. The relativity of simultaneity is in a sense a more primitive or fundamental phenomenon than either. If the planet makes an instantaneous transmission - in its frame! - to the station then the transission will be backward-in-time in the frame of the ship. If the station makes an instantaneous transmission to the planet in their frame then the transmission will be forward-in-time in the frame of the ship. This comes directly from the Lorentz transformations as t' = gamma * ( t - v*x/c^2). In this case, the undashed frame is the planet's frame and the dashed frame is the spaceship's. If the planet makes a transmission at t=0, x=0 which is received by the station at t=0, x=d then the coordinate time of the reception in the ship's frame is -gamma * v * d / c^2, which is clearly negative for v and d both positive.

You can see this at work in my Figure 5. The superluminal transmission from event P to event Q is instantaneous in the frame of Alice and Bob but backward in time in the frame of Carol and Dave. The superluminal transmission from event Q to event R is instantaneous in the Carol/Dave frame but backward in time in the Alice/Bob frame. Observers in both frames agree that a causality violation occurs but they differ on why.

I think I understand how the paradox emerges using the Lorentz transformation and even the math (as I've seen posted elsewhere), so I can't easily dismiss the predicted behaviour. Still, I have this sneaking suspicion that the complexity is hiding something.

For instance, the only way anyone could ascertain simultaneity of P and Q in Alice and Bob's context would be to observe it in the future once the light reaches each other, and make deductions back in time. Likewise, simultaneity for Q and R in Dave and Carol's context could only be deduced from a future observation. We know that the views of simultaneity will differ, and we've seen this empirically confirmed.

This would suggest that simultaneity of anything outside of the cones of light for all 4 individuals is like Schroedinger's cat (if that is a good comparison to use); unknown until you end up observing it in the future.

However, wouldn't instantaneous communication be a judge of simultaneity and thus implicitly the inertial frame of reference?

Suppose Alice and Dave send an instantaneous signal to Bob and Carol respectively the moment they pass each other. Now suppose Bob happens to receive Alice's message at the exact moment that Carol passes by. In Alice and Bob's context, Carol ought to receive Dave's signal at the exact same time that Bob received Alice's signal.

However, I presume that this is not what Carol nor Dave would suspect. Correct me if I'm wrong, but according to Carol's view of simultaneity, she would have already passed by Bob a while ago at the moment that Dave passed Alice. They would deduce that they passed by their neighbours at different times.

The result is that each context has its own expectation for simultaneity. However, given we are dealing with a hypothetical method of instantaneous communication, both expectations cannot prove to both be vindicated. Bob and Carol cannot both receive the message in a manner that conforms to their own view of simultaneity. It is more likely that one is correct, or neither.

For instance, if Carol does receive the message from Dave the moment she passes by Bob, then knowing why Dave sent the message, she might conclude that the message came from Dave's future based upon her frame of reference. However, since the receipt confirms Bob's view of simultaneity, then isn't it more reasonable that Carol's view of simultaneity is invalidated by the message? Likewise wouldn't Bob's view be invalidated if Carol's view of simultaneity is confirmed? Or isn't it also likely that both views are invalidated in favour of a third unknown frame of reference? It ends up being a way to validate an inertial frame of reference.

Perhaps why I am having difficulty with this example is that the proposed mechanism for instantaneous communication behaves differently depending on the context. If it is instantaneous relative to all contexts, then it is not consistently instantaneous. In fact, I think that the concept of instantaneous communication presupposes a favoured frame of reference. If that is the case, then we'd be presupposing what we are trying to prove (or disprove) which might be why this example is so confusing; it is actually nonsensical to relate true instantaneity to more than one context.

Therefore, instantaneous communication is either impossible because it requires a special frame of reference when none can exist, or it is possible because a special frame of reference somehow exists. I understand that special relativity has much empirical support, but I don't know if that means a favoured frame of reference has been ruled out, or it has merely been rendered irrelevant.

I've been awake since 3:30am this morning so I'm not going to be able to write a long reply, or at least not a long and coherent one. However, I think that what you're saying is essentially correct. In relativistic physics as it's currently understood the notion of simultaneity plays no role as physics has to be formulated in a frame-invariant way and there's no way to impose an idea of simultaneity that isn't relative to a particular inertial frame.

As my intention was to show an explicit construction of a causality violation using an FTL communication system I had to decide on some specific properties of the system. As I didn't want to throw out any of special relativity I couldn't specify that the FTL system only worked in a single preferred inertial frame so I did the next best thing: the communicator only works if the transmitter and receiver are at rest relative to each other and in their common frame the transmission is instantaneous. It seemed to me that this gave the very simplest possible diagrams. This is also the reason that I have four rather than just two observers.

However, it's possible to construct causality violations even in general cases such as transmissions which move at some superluminal but non-infinite speed in the frame of the transmitter. I just didn't think that my skill at rendering graphics was up to drawing that case. However, I've now had an idea for a way to show the generic case so perhaps I'll find time to draw an additional diagram soon.

Perhaps the system breaks down at many iterations, but seeing as how the frames of reference all are internally consistent, I see no real reason why a zero-error system could encounter compounding errors.

So either I misunderstood what you were trying to get across completely, or your explanation is flawed.

Causality: Being the curious type, and believing myself interested in things like relativity, I frivolously typed into google the keywords "time travel", which led me to wikepedia, which then led me to this link.

You see the oddity is, if Alice and Dave, simultaneously consume sour pastries and tea, and thusly as a direct result, pass odious methane expulsions into the frames of Bob and Carol, who traveling at relative FTL speeds, still manage to gag, do they do so before Alice and Dave have even flatulated.

Oh, I know what you're thinking - this guy is spoiling the almost 4 year party of this running thread! But I actually think this thread is awesome. In another world, or maybe in a parallel universe, or at least in one of my previous closed time loops(and I do guard those jealously - which is why they're closed), I might have been a physicist that understood perfectly all these intricacies. But in this one, I'm a writer and musician. So what do you expect?

All truth is relative to the sphere in which it resides.

In the mean time, isn't it nice to smell the rich and heady fumes of a field of wildflowers, set in the panoramic vista of a mountain meadow, surrounded by the vast trajectories of a lupine forest? Or silently meditate on the rocky outcrop of an ocean overlook, listening macroscopically to the pounding sea as it undulates like the beat of an earthly heart, the wafting pungency of salt and seaweed tweaking ever so delicately upon the twittering nostril. Or the delicate taste of a simple ice cream sundae?

I applaud all these fantastical posts. Those who really know their stuff, and those who love to blab and postulate, but haven't really got a clue. But hey, this is 2008 - the new millennium of discovery! The age when such queries should be entertained, like, "I blog, therefore all should hear my opinions!"

Carry on ladies and gents, 2020 is just around the space-time fold corner!

If you lower something's temperature to zero degrees Kelvin then it has no energy.

Does that mean it no longer has mass?

I thought the two were related.

Does this mean that all you need for FLT is to lower your ship's temperature to absolute zero?

In relativistic theories, an object's rest energy and rest mass are related by the equation E = gamma mc^2, where gamma is a factor that is 1 for an object at rest and increases without limit as the object's speed approaches that of light, m is the object's rest mass (or more accurately its invariant mass), and c is the speed of light. At rest, this reduces to the more famous equation E = mc^2. (The difference between the energy of the object in motion and at rest is the object's kinetic energy.)

The energy content of an object is the sum of the energies of the particles that make it up (and, strictly speaking, a contribution from the interactions between those particles). Thus, an object at rest and at absolute zero has the relationship between mass and energy given by the equation above with m being the sum of its constituent particles' rest masses. (If we don't ignore quantum effects then it has a "zero point energy" at absolute zero too.)

In any case, objects with no rest mass travel at the speed of light not at superluminal speeds.

I am currently working on a device that has thousands of turns of coils in a (TENSOR coil formation). At present (actually in the past) there is 12 Volts DC applied. In the Future,I plan on applying thiusands of more volts towards the copper insulated wire. This should produce many more SCALER waves. I am also interested in inventing a device that records movement of waves into the past. I am also interested in forming a team whom are interested in time travel (OF INFORMATION).

(The conventional spelling is "scalar" - Rich)

There is a simple example to show that FTL travel (if it was possible) it not time travel. Say we are playing catch. We're about 30 meters apart (100 nano light seconds (nls)) If I throw the clock to you at 2c, then it takes 50 ns for the ball to get to you, but the information about the throw doesn't get to you till 100 ns after the fact. the sequence from the catcher's point of view is catching the ball, seeing it streak back towards the thrower and then the throw will appear to occur. But in the intervening 50 ns of the catcher's observation, he will see the ball in 3 places, in his hand, in the throwers hand, and traveling backwards to the thrower. When the information of its journey appears to reach the thrower, the two images will merge and vanish. The sequence from the thrower's point of view is that the throw travels 2/3c to the catcher.

Now, if you used a clock, and you take Lorenz's translation to its logical conclusion, as the clock reaches c, it becomes 2 dimensional and its time stops. Once it's velocity exceeds c, its physical structure reverses front to back and the clock would begin to run backwards. But the clock is still moving forward in time. It it just experiencing that time in reverse.

(The causality violations caused by FTL communication in special relativity do not arise because light arrives after the signal, nor have I ever argued that this is the case. Instead they're a consequence of every inertial observer's measurements giving the same speed for light. This gives rise directly to the relativity of simultaneity, and it's this that allows the construction of causality violations described in my article - Rich)

I reread through your article and believe I have the solution. The first postulate of relativity is inviolate. Any theory that contradicts the principle of relativity must therefore be flawed. It is only through the second postulate that causality vioations occur. The second postulate should be modified to say that light APPEARS to travel at c within all inertial frameworks. I agree, the first postulate has been supported to the nth degree by a lot of evidence, but you CANNOT prove the second postulate! The velocity of light cannot be determined by any measurement between two points. It must always be measured as a function of a round trip. Through the Lorenz transformations, the round trip transmission of light is always c. Any deviation of relative velocity in one direction is always undone on the return trip. FTL communication or a stabalized wormhole would prove this by being able to measure the velocity of a single leg of the trip. With such a device, we could calculate how fast and in what direction our galaxy was moving and determine about how far we were from the center.

Hello, it's me again. Still writing away Rich. But I came back because I've been thinking about some of the things on your site here and some things I've seen in recent months on Discovery Science Channel and online. I've been thinking about membranes.

I'm fascinated by M-theory and the idea that each parallel universe can exist on a membrane that flunctuates and occasionally bumps into other membranes. I loved the loaf of bread anagoly to the interaction of these membranes. A very disconcerting aspect to membrane interaction to the creation of our universe is the fact that membranes can collide. That begs the question, if our universe was created from a collision with another membrane, what happened to the membrane that collided with ours? Accordingly, what happens to our membrane if we collide with another later on? Insane in the membrane!

Anyway, I completely understand that there is no way to propel an object past the speed of light with current thinking. Even if you harnessed enough energy to do so and got to a speed twice the speed of light it would still take you 14,000 years to reach the galatic center (28,000 light years away; 28,000 years at the speed of light to reach). So obviously, no one will ever be able to propel anything faster than the speed of light, because it would still be a pointless effort. It would still take years to reach the next closest star.

But the membrane stuff got me thinking. What if membranes, in regards to time travel (or interdimensional travel) act more like a rolodex? With a loaf of bread you sit in one plane and as you're sliced, you break away. The split is permanent which does not allow for further interaction between relative branes. But on a rolodex, that separation is still present but you're linked by a central hub that can bring branes back around and cause continued interaction (meaning collisions). Perhaps these collisions aren't as violent as we think also.

For instance, maybe the membranes fold over on one another from time to time, giving the multiverse a hurricane looking feel (or even a galaxy for that matter). Just like with a hurricane or a galaxy, these membranes constantly interact and can even allow something within one membrane to propel (pull) to another membrane (with the right interactions). Could these connections be black holes, WMAP cold spots, or something we haven't seen yet? This pulling effect, would that accelerate you to a speed that is well beyond the speed of light, such as c to the infinite power?

In a sense, it would also allow for the creation of a paradox because if membranes do cross between one another, inadvertently, that reality of one membrane could intermix with another and cancel out substantial events that have occurred within one membrane, thus leading to an alternate outcome that should have never been (much like the paradox from my book; moving back and forth through time was allowing too much interaction between membranes that caused a shift in time that lead to events that should have happened to never happen, thus a paradox occurs for one or both membranes). This paradox could simply destroy said universe and in the process of interaction cause a new universe to be created.

This is the hypothesis for my book The Civilization Loop suggesting that traveling through time is inherently dangerous and should not be done. This interaction would also explain why our knowledge of reality never seems to go further back than about ten to twenty thousand years because when a new universe is created, it picks up the same information that the now ceased universe once had. It doesn't create a wholly new universe that starts from scratch, but an identical universe with all the same laws and parameters as we have now. So this interaction would explain the paradox of the Chicken and the egg for instance. Which came first, neither, they duplicated!

But that still leaves two questions. Where did the first membrane come from? Where did the first universe start? There had to be a beginning unless we begin to equate the universe to a supreme consciousness that there is no explanation for. Also, what keeps holding the rolodex/hurricane/galaxy universe in place and keeps it spiraling and interacting? That might be more a question for philosophy than science, but how cool would it be if science proved philosophy?

Sorry, my "brain" was leaking out today and I have to add something because it's been a while. I hope you find this interesting and let me know what you think.

It is impossible to travel faster than the speed of light, and certainly not desirable, as one's hat keeps blowing off

--- Woody Allen

Very interesting and accurate article. Nevertheless, my eyeballs almost left their orbits when reading some of the replies in here. Please, for the sake of all, if you are interested in physics, get a degree in a scientific field. You will develop a scientific mind that will greatly help you understand current physical research and why it is pointless to argue against some contemporary physical notions. You will also see where humanity lacks understanding and where research is to be done. Reading scientific american and watching discovery channel will get you nowhere.

Very good graphical explanation of how FTL is incompatible with relativity. The fact of the matter is that much of this is rooted in some deep mathematics, the likes of which even Einstein needed help with (we thank great people like Lorentz, Hilbert, Friedmann and Minkowski for that).

To those naysayers, I say go learn the math and prove it to yourself. What? You don't understand covariant derivatives, gauge invariance or Ricci curvature tensors? I guess you don't really know what you're talking about then.

It's this prerequisite of years of formal mathematics that's a barrier to accepting the beautiful logic, whereas the Joe Schmoes who are so desperate for Star Trek to be real can't handle taking the scientists' word for it.

I'm a young college student, studying art education at school; my art professor challenges us to explore new ideas, and investigate and research information towards conceiving a project. I was curious about time travel, and found this site searching through the web. I have been reading alot, and I certainly have no prior knowledge of any of these theories, and therefore cannot contest whether they are wrong or right. What I do know and believe, without any doubt, is that God controls everything; yes, this statement is by faith, and not scientific fact. But, I feel if God wanted time travel to exist, he would will it to be so; I started researching time travel because I thought I wanted to know the future, or even the distant past; but after pondering the idea of seeing those things, i realized this; why speed the duration of time as to not experience it? life would be skipped; every little detail that makes life interesting i would miss out; the information of the future is'nt important enough for me to sacrifice time spent living for God to search for a way to discover my destiney. We should live life day by day, and each one for His glory. God is love, and love is what I seek. Jesus Freak

'Evolution.' lol

use your brain, not only say what you learn as robot

spacetime is light in newtonian space. Lorentz transformation for space is an optical effect.

i more understand relativity i win.

#include #include #include

int main() { long double v,b,x1,h,t1,c,y2,Lx,tang,tang2,t2x,t2,s,x3,y1;

c=1.0; v=0.7435; b=1.0/sqrtl(1.0-v*v/(c*c)); x1=100000.0; y1=1099.0; h=sqrtl(x1*x1+y1*y1); t1=x1/(c*x1/h); printf("%Le %Le %Le\n",x1,t1,h);

y2=2.0;//nem a tavcso hosszat adom meg tang=y1/x1; t2x=y2/tang; t2=sqrtl(t2x*t2x + y2*y2); s=v*t2/c;//s=v*dt t2=c*dt => s=v*t2/c

Lx=t2x-s; tang2=Lx/y2; x3=y1*tang2; x3*=b;


x3=(x1-v*t1)*b; printf("%Le\n",x3); return 0; }

Been banging my head against a wall to understand Figure 2. I just cannot understand why event Q occurs after event P in the blue frame - it still seems to be before to me. Perplexed.

The blue line labelled Space' passes through all the events that occur at the same time as P in the blue frame. Event Q is above that blue line in the diagram and so happens after event P in the blue frame.

There are not 'after' and 'before' on the blue area. You believe it only.You cannot send a light signal from Q to P, neither back. The moving clocks are working more slowly, which is not an illusion,. But the reason of the changing of the distances an optical illusion. This makes the special relativity one which can be understood difficultly together. The reason of the deceleration of the clocks though it, than the reason of the deceleration of the light clock. The mirror ahead the light runs away ahead, the back being runs. A light clock, in which bosons move, is atom, quark on all of them. The relativity is the world of the light. The special relativity the dimension of time the path of the light in Newtonian space. Is added to all this yet, that the moving clocks are slow in course. His moving co-ordinate system is so lopsided because of this. This light is because of synchronization happening to a sign.

The gravitation really the curvature of the space-time, but the space-time himself the light. The light bend in a medium with a changing refractive index though. The gravitation so not something else, than the refraction of the light in vacuum with a changing refractive index.

Hi Rich, and thank you for the best article about this subjects that I have yet seen.

But I still have to say that if you look your article and this specific example with logic, it says: false implies false, and we all know that this is true always. So to elaborate my thinking (and this is really not against the concept of FTL not being possible, only against of this example):

You say: "For any event P (where P is a label for something happening at a given place at a given time), the events within P's future light cone make up its absolute future and those within its past light cone make up its absolute past: the former are the events that P can influence and the latter are the events that can influence P."

So as I understood this, it means every two events that are causally connected, must lie in each others light cones (if event A causes event B, then B is in A's future cone and A int B's past cone).

Then you bring up this figure 3, where are two events, P and Q, that are causally connected (Q can't occur without P, and P must occur first). But as the picture already says, they don't lie in each others light cones, so the causality is already broken. I think its evident that if you create scenario, where causality does not apply in the beginning, then the result can be either it applies or it does not, either way, you should not make any conclusions out of it...

This is the thing that has always confused me and still keeps on doing so. What I would like to see, is the second half of this example: This first half makes assumption that light speed cannot be exceeded (light cones themselves make that assumption), so if this assumption is false, outcome is not reliable. So if someone could prove that FTL implies time travel with assumption that FTL is possible, then we could safely assume that FTL implies time travel.

And now little OT. When you (or anyone else) says that "in special relativity faster-than-light travel is not possible.", do people mean that any kind of movement that appears to exceed speed of light is impossible, or just the kind of movement where you follow certain path, with length s, and it takes time t so that s/t > c? Because I do not understand how causality is broken in case of wormholes. If I had an instant means to get to Alpha Centauri from earth, so that my spaceships "real" speed (traveled distance per time) is slow, even tough it seemed to travel much longer distance, how could I cause problems with causality? I do not think it can be explained with accelerating inertial frames, because I don't need to accelerate at all, I just pass through a hole with constant speed.

You say: "For any event P (where P is a label for something happening at a given place at a given time), the events within P's future light cone make up its absolute future and those within its past light cone make up its absolute past: the former are the events that P can influence and the latter are the events that can influence P." So as I understood this, it means every two events that are causally connected, must lie in each others light cones (if event A causes event B, then B is in A's future cone and A int B's past cone).

Yes, I may have been a little sloppy there. The idea that light cones are about the causal structure of spacetime is deeply engrained in physicists. Let me have another try being more careful. We're really interested in five sets of events related to a given event P:

  1. Events which occur before P according to all observers.
  2. Events which occur at the same time as P according to all observers.
  3. Events which occur after P according to all observers.
  4. Events which can influence P.
  5. Events which P can influence.

In classical, Newtonian physics the situation is easy and intuitive. Sets 1 and 4 are the same, and are the past of P. Sets 3 and 5 are the same, and are the future of P. There's a non-empty set 2, which is the "present" of P. All events other than P fall into one of these three classes. Signals that are as fast as you like don't change this.

In special relativity without faster-than-light signals things are a little more complicated. Sets 1 and 4 are the same, and are the absolute past of P. Sets 3 and 5 are the same, and are the absolute future of P. (People sometimes talk about the "chronological" and "causal" pasts and futures of an event but the use of the word "causal" used in that way would make things even more confusing!) Set 2, though, is empty: there are no other events that all observers agree happen at the same time as P. There is, instead, a large region of spacetime which is not in any of the five sets: events that can't influence or be influenced by P, and don't take place absolutely before, at the same time as or later than P.

In special relativity with faster-than-light signals, sets 1 and 4 are no longer the same, and nor are 3 and 5. Sets 1, 2 and 3 are still the same as in the case without faster-than-light signals. The Lorentz transformations only rely on the principle of relativity and the invariance of the speed of light and so faster-than-light signaling doesn't change the temporal ordering of pairs of events within each others' light cones. However, it's fairly easy to see that with FTL signals the sets 4 and 5 become the whole of spacetime! Events in P's absolute past can influence P anyway. Events outside P's absolute past or future can influence P via superluminal signals in appropriately chosen frames. Events in P's absolute future can influence P through the construction shown in figure 5 (although there it's an event in R's absolute future affecting R.) Causality is quite hard to define at the best of times but if any other event can influence an event P then clearly we're very far away from being able to give a conventional description of causal relationships between events.

This is the thing that has always confused me and still keeps on doing so. What I would like to see, is the second half of this example: This first half makes assumption that light speed cannot be exceeded (light cones themselves make that assumption), so if this assumption is false, outcome is not reliable. So if someone could prove that FTL implies time travel with assumption that FTL is possible, then we could safely assume that FTL implies time travel.

I don't think it's strictly true that special relativity assumes that light speed cannot be exceeded. Instead it postulates that the speed of light is invariant. Relativistic dynamics then prevent any object that is moving more slowly than light being accelerated to the speed of light or faster but we can still use special relativity in a consistent way to analyse what would happen if we had faster-than-light signals. (I've been deliberately avoiding the phrase "faster-than-light travel" as special relativity doesn't make sense, so far as I can see, for observers in superluminal frames.) As I've shown, if we allow FTL signals in special relativity then we can generate causal loops without a great deal of difficulty. I've said before that you can pick at most two of {special relativity, FTL, causality}. That doesn't stop you picking, in principle at least, {special relativity, FTL}, but that doesn't appear to have been the choice of the real universe. (The real universe appears to have picked neither special relativity nor FTL!)

And now little OT. When you (or anyone else) says that "in special relativity faster-than-light travel is not possible.", do people mean that any kind of movement that appears to exceed speed of light is impossible, or just the kind of movement where you follow certain path, with length s, and it takes time t so that s/t > c? Because I do not understand how causality is broken in case of wormholes. If I had an instant means to get to Alpha Centauri from earth, so that my spaceships "real" speed (traveled distance per time) is slow, even tough it seemed to travel much longer distance, how could I cause problems with causality? I do not think it can be explained with accelerating inertial frames, because I don't need to accelerate at all, I just pass through a hole with constant speed.

Well, in special relativity wormholes don't exist. To discuss wormholes we really need to get into general relativity, which is a much deeper and more sophisticated theory and one which I don't currently have time to try to explain. However, in general relativity the universe looks more and more special-relativistic as you look at ever smaller regions, and this means that material objects like spaceships can't travel faster than light in a general-relativistic universe any more than they can in a special-relativistic universe. There are, though, even more strange aspects of time and causality in general relativity. For example, it's possible for the sets 1 and 3 in my list above to overlap. This happens for spacetimes that contain closed timelike curves, which is a fancy name for paths along which objects can travel slower-than-light and find themselves in their own pasts.

It's quite easy to see how this works with a pair of wormholes in the approximation in which the wormholes are small so most of spacetime looks special-relativisitic. The key idea is that it's possible to use time dilation to "age" one mouth of a wormhole relative to the other. Suppose we have two wormholes, each with a mouth at Earth and a mouth at Alpha Centauri. We can then create a situation just like my figure 5. Suppose one wormhole is such that if you enter the Earth mouth at event P you emerge at Alpha Centauri at event Q. We can use time dilation to arrange for the second wormhole to be such that if you enter the Earth mouth at event R you emerge at Alpha Centauri at event Q. So then if you travel through the first wormhole from P to Q you can then travel through the second wormhole from Q to R (i.e. into the past). The system consisting of the pair of wormholes thus contains curves that are both timelike and closed and so collectively make up a time machine.

In fact it's possible to do pretty much the same thing with a single wormhole. Keep one mouth at Earth and send the other out on a long journey at close to the speed of light to some place far away. If you have a clock attached to the mouth that stays at home and another clock attached to the mouth that goes away then the two clocks will remain synchronised if you look through the wormhole. Suppose the journey starts in 2010AD, takes one year of proper time for the travelling mouth and finishes at an event with coordinates 2020AD and somewhere-far-away in Earth's inertial frame. In 2011 you could then step from the Earth mouth through the wormhole into 2020 in some faraway place. This is quite strange but not much of a danger to causality. However, suppose the travelling mouth makes a similar journey back to Earth. Another year of proper time elapses for the travelling mouth and it gets back to Earth in 2030. However, you could now step from Earth in 2012 to Earth in 2030, or if you're already in 2030 you could step through the wormhole in the opposite direction to get to 2012. Once again there are closed timelike curves and traditional ideas of causality must be thrown away.

[I've converted this comment into its own article]

isn't light just another wavelength, like sound. so really if somebody is moving faster than the speed of light, they are just...moving really fast. has nothing to with time. and time travel. Light is just that. light. now, moving faster than the speed of time? much better. :)

Thanks Rich. I love the discussion, truly inspirational. Keep it up!

Hi Rich, Love the article although like a few people that have commented my knowledge is very limited and I really praise you for putting up with and answering back to everyone... that's dedication. I apologise in advance for the simplicity and lack of total understanding of this concept in my queries.

Is it fair to say that even if FTL travel was possible that it would really have no bearing on time travel on Earth?

It would ony be possible in space, for example the long range space telescopes that look at other solar systems far off into space recieve images that may be 10's of thousand of years old and vice versa if there was a similar device looking at Earth and our solar system it could show images that are of a similar age.

If you travel FTL towards or away from that image you would effectivley move back or forward in time, but there would be a point where you reach the origin of the light and its present state if you continued you may not necessarily go forward into the future? So time is only relitive to an objects current everchanging state?

I suppose the real question is in the relationship between speed and time and where does speed cross over to relate to time?... if that makes sense.

E8 x E8?

Let me simplify this (perhaps to an extreme) and you can tell me where I'm going wrong.

Me and my flatmates blaze up a storm and decide to give this whole time travel/FTL travel thing a crack. I decide I'm gonna shoot down to the dairy for some munchies, so I jump in my modified Honda Integra and get ready to go. FYI I'm in the car, one flatmate is at home, one flatmate is at the post box down the road. Me and my flatmates all have a stopwatch and at the EXACT same moment press start and I hit the gas. I accellerate to 3c and boost it down the road - to be realistic we will take into account the time it takes to accelerate (5sec). In what takes an imperceptible length of time, I'm nearly at the dairy and somehow, while in transit, manage to hand my mate at the post box a note asking if he wants burger rings. Surely the note will reach him 5secs into the journey, by his stopwatch and mine; not in the future, not in the past. Anyway, I decelerate (another 5sec). I get out of my now super-heated Integra and swagger into the dairy, get my redbull and burger rings, then hop back in the car (all of which takes 30sec) and I then make the return journey. Beside the fact that a stoner just drove a highly modified Honda to the dairy at three times the speed of light, what is wrong with the conclusion the all stopwatches would show 50seconds to have elapsed by the time I return? Forget 'perception of motion relative to the first observer', time has not been altered for any of us.

"Time" is a human-invented constant by which we measure our lives. It cannot be bent, stopped, or altered in any way by anything. Matter (and therefore light and our perception of what happens around us) can be, and travelling at such a high velocity would do that, but time-travel cannot possible through FTL alone. So I ask, how can the initial statement in this discussion "...faster than light travel is equivalent to time travel..." be accurate?

Does it mean: A - it is actually impossible to travel through time? or B - we're so limited in our understanding of the universe and how it operates that we actually just make sh*t up to explain it to ourselves.

I vote option B and look farward to what we "know" next.

While the way this is presented certainly leads to the conclusion that FTL communication leads to paradoxes, the approach makes the erroneous assumption that Alice can be in two places at the same time, i.e. when P happens, Alice is both at P and at R. If such was the case, then of course Alice could send signals to her past, leading to causality violations. But does this happen in reality?

This does not happen in reality. For example, a superluminal signal sent from Alice in 40 Eridani to Bob on Earth does not allow Bob to affect Alice in any way, even if Bob sees an image of Alice that is 16 light years in the past!!!

So, in the presented example, when Dave receives the superluminal message from Carol, Dave can not affect Alice in any way: Alice is already in the future, even if Dave sees a past version of Alice!!!

If Dave tries to sent a normal message (i.e. a message with speed less than C), then that will never reach Alice, because Alice is in the future.

For example, if I had a beam weapon that could shoot stars out of the sky, I could not shoot down Sirius, because when the beam will reach Sirius, Sirius will not be there.

If Dave tries to sent a superluminal message to Alice, then Alice will receive it in a state that is Dave's future.

I just don't see where the problem is, actually...

I'd like to add that the diagram shows Alice to be in the future light cone of Dave. This never happens in reality. Two observers are in always in the past light cone of each other, because the light of one has not reached the other.

To put it with an example: We see a previous state of Sirius, and Sirius sees a previous state of us. We are both at each other's past light cone.

And therefore a superluminal message does not cause causality violation.

when P happens, Alice is both at P and at R

Everyone agrees that P happens later than R. In Alice's coordinate system these two events happen at the same place at different times. In other people's coordinate systems the two events may happen at different places as well as at different times. In no frame are they simultaneous so Alice is never at both P and R at the same time. I don't think it's in any way controversial that people can have a history that puts them at the same place at different times. For example, I was at my house both this morning and this evening.

For example, a superluminal signal sent from Alice in 40 Eridani to Bob on Earth does not allow Bob to affect Alice in any way, even if Bob sees an image of Alice that is 16 light years in the past!!!

Again, none of this depends in any way on one observer seeing another in the past because of the finite speed of light. The Lorentz transformations, the relativity of simultaneity and so on are what's left when such trivial things are taken into account. Of course, in the absence of superluminal effects the relativity of simultaneity doesn't have any particularly significant effects because the laws of physics are such that they don't depend on notions of simultaneity.

Two observers are in always in the past light cone of each other, because the light of one has not reached the other.

This is not just wrong but such a totally bizarre assertion that I'm having trouble understanding what it could mean. Observers don't have light cones: it's only events that do. Any pair of events, say A and B (each of which could be one event on the world-line of an observer) could be in any of three causal configurations:

  • A is in B's future light cone and B is in A's past light cone, in which case A is in B's absolute future
  • B is in A's future light cone and A is in B's past light cone, in which case A is in B's absolute past
  • A and B are outside each other's past and future light cones, in which case the two events have no absolute temporal ordering and are causally disconnected in the absence of superluminal influences.


Great article. Now i finally understand why FTL implies time travel.

Science: crushing the dreams of SF fans since 1905

This debate is fantastic. Why go to university when there is all this for free?

Great stuff Rich.


This is the clearest visualization of how space-time is subject to relativity that I have ever seen. Thank you for the enlightening walkthrough! And thank you for all of the time you have spent on thoughtful rep[lies to various questions and ... erm, disagreements.

In trying to arrive at an analogy for why faster than light travel won't work if special relativity is true, I hit on this:

Saying that it must be possible to go faster than the speed of light is a little like saying that it must be possible to stand in New York, pick a compass direction, and fire a laser in that direction that will hit a target in China.

It's only possible if the world is flat. And we're really pretty sure that's not the case. :)

Hi Rich,

Thanks for a great article, and nice diagrams too.

I have a question about how this extends to general relativity. How does the chronology protection conjecture work?

It would seem from your comment about wormholes above that you automatically create the possibility for FTL if you accelerate one end of a wormhole. Okay, so the CPC would imply that it's not possible to accelerate a wormhole without immediately destroying it.

Now a wormhole can function basically an ansible. So if you have two in the same reference frame, you can communicate FTL without causality violations. Great. But unless these are the only two wormholes in the universe, or all the universe's wormholes are in the same reference frame, we've got problems; someone could just use a different set of wormholes in a different reference frame for time travel. So then wormholes can't exist.

So if we assume the CPC is true, wormholes can't exist, and FTL is impossible. So what's the point of the CPC again? How is it more than just a restatement that FTL violates causality?

I know I'm missing a rather fundamental step in GR here. The CPC deals with wormholes; obviously my conclusion about them not being able to exist is incorrect. Is the CPC just a larger generalization of the impossibility of FTL, i.e. it fully implies it but implies other things as well (e.g. the impossibility of closed timelike curves, which don't involve FTL)?

(I'm here because someone on Slashdot has a bunch of posts modded +4 that say FTL is possible without enabling causality violations because of the CPC. Basically I'm wondering whether that's true, and why.)


So if Dave had 3 apples and Alice took two of them, Bob takes the rap?

Still fiddling around with your nonsense? Look again at the train experiment and try to understand that when Einstein says that point M' "fallt zwar...zusammen" with point M, the "zwar" is his constructivist intervention. That's why there is no logical content to the relativity of simultaneity.

You would sense the problem better if you looked at the Italian and French translations of RELATIVITY. The English version is quite correct. But the Italian and French translators actually change what Einstein wrote. If you look at HOW they changed it, you will see WHY they changed it. Because they had seen this logical flaw and were trying, unconsciously, to correct it.

In short, you are a very poor scholar and thinker. You refuse to look at the history, refuse to take Einstein's "practical geometry" seriously, and so you continue...fiddle around.


Search Results

1. SSRN-Paradox, Natural Mathematics, Relativity and Twentieth ... Ryskamp, John Henry,Paradox, Natural Mathematics, Relativity and Twentieth-Century Ideas(June 17, 2008). Available at SSRN: ... - Similar by J Ryskamp

Was it the juggling or the green hair that gave it away?

In any case, the causal structure of special-relativistic spacetime, relativity of simultaneity and all, is a key ingredient of modern quantum field theories of particle interactions (in QFT operators corresponding to measurements at spacelike separation must commute), and quantum electrodynamics agrees with experiment to one part in a trillion. So I guess that nature is on the side of the clowns.

I'l get to Nick's question about the Chronology Protection Conjecture when I have a little more time.

Well all seems clear,all is what you think in your head.Scary so we will never be transfer the real equation we be died at this stage.Its clear that others had already did it .We can even imply this as a religious belief.Good sake of the world.One should know how to cross the border line.Securely.I just believe in god .My safe man

There is a way you can preserve both causality and special relativity and still accept the possibility of superluminal effects.

You usually do not allow for messages back in time because they pose a paradox. One could send a message back in time with the instruction not to send a message.

The way this message takes in your example is simplified Alice -> Bob -> Carol -> Dave -> Alice.

One solution to the paradox is to propose that when Dave gets the message from Carol, the universe branches off into two time lines. Alice1 gets no message and therefore proceeds to send a message back in time to the past, it will be received by Dave2 who carries it to the other branch that has Alice2 getting the message and therefore sending none, which is what Dave1 experiences who will arrive at Alice1.

Causality is preserved for each branch. However, you will receive messages from parallel universes.

Firstly Rich: you're really doing yeoman's work here, especially continuing to respond to comments (and such comments!) 6 years on. Pearls before swine and all that.

I do have a question for you, though: if sending a superluminal signal how do you avoid colliding with the past until the correct moment?

That is to say: for the response to actually reach Alice *before* she sends her initial message then her past states must "continue to exist" (in some sense); if they no longer existed there'd be nothing for the response message to interact with when it showed up in her past, b/c her past wouldn't exist anymore, right?

But if Alice's past continues existing (in whatever sense is appropriate) shouldn't that hold for the rest of the matter in the universe?

Wouldn't that make the path the superluminal object would want to take heavily obstructed?

The intuition here is that if you draw a lightcone projecting out of the front of the superluminal message in the direction of travel then each of Alice, Bob, Carol, and Dave's paths-through-time look like "walls" blocking the trajectory of your superluminal object; I understand you've thrown away 2 spatial dimensions but I think the imagery is suggestive.

So regardless of the causality issue it seems like there is a navigational conundrum: a backwards-in-time has to be able to interact with the past in order to do anything, but if it can interact with the past the route from present-to-past is full of obstructions (the past), making transit difficult.

What am I missing?

Its not, but if causality is "A before B", backwards-causality would just be "B before A". You still couldnt have "A before B before A".

It would be more dramatic if you put the Alice to Bob communication before the Carol to Dave communication in Alice and Bob's reference frame. Bob would carry the information to Carol in his timeline, creating a figure-eight.

where does a ghost classify himself.Does a ghost becomes old. Peaple who always tink about the past are crazy,,goes crazy.So what if 89 turns to 68 instead of 98 .

Rich u been on for 6 years. lets say u know the past 6 yrs now u r now and lets say future 6 make the future..futur depends what you do now.but i somehow believe in destiny the thing big question is what control us through our descision.dnt know may be soul .so do you know ur soul as u know urself just thinking may be we should meditate.if u had meditate for 6 yrs waw u should be top of the top.just as u know material world u shyud be able to walk evrytime u want in paralell world.there might be council etc there.may be lets all go for it and we all meet on one spot at a certain address.lets work through sure its risky with regulations .so who are with me

I. 1st of all, with regards to original assumptions here...physical theories can of course be proven. This is just a play on words on how one might define 'proven'. They all have had and will in the future be found to have varying degrees of accuracy ranging from 0 to 100 in percentage terms. Proof enough for me.

II. With regards to the diagrams and predictions made via special relativity, causality is indeed violated among the 4 observers when using 'ansible'

III. As in special relativity, in the 'real world' the proposed FTL transmitter would obviously also violate causality relative to the 4 observers involved.

IV. A Previous poster was correct, use of the FTL by observers within the graph mean that relative to the observers, their own timelines, velocities, and directions represented within the graph become irrelevant.

V. Logic does not forbid the reality of a causality violation. Rather, a causality violation's reality is never expressed in nature relative to any observer because its expression negates its propose. It would be this 'overlapping' that acts as a sort of self-defeating mechanism. Perhaps one could think of it as a possibility never (or perhaps hardly ever) observed because there isnt anything 'to' observe from most or all perspectives. Simpler perhaps is, if one can leave point A and arrive at B so fast that one finds themselves already at point B before leaving point A, then there was never a reason to leave A, because they were already at B previously.

anonymous you were so right.taking speed into in paragraph (v).lets think ,,how to spend more time to different time ,I mean what sort of energy should we use ,,i think some peaple are considered mad because their body is fix like an engine thst goes older and older but their soul is crazy lost in another world or chamber/years.on the contrary a body travalling faster than light turns probably to ashes,ah got another idea,some peaple are possessed means a conflict of time.its like going to differnet country drive another cars,money can b part of energy.

example I have aneighbour, mental dnt talk to anyone and also scary, who speaks a different language unconsciouslly.he is very very personal.used to b my dads best frend. he had been to madagascar /africa something,a very difficult language when he was back he speaks the language without consciuos.means he got connected with a different soul may be past or future.

I think i or we should work out things.imagine we are travelling in time.things will change started from good to probably catastroph.may be if we are good enough ,time travel peaple can like we say give us a ticket.for example what if i go to past like a movie,,i tell my grandfather play this u will win millions dollars. I think deeply thers a lot of tests of honesty to be at this stage. Thers probably a council for time travell. It is probably top secret. So again can they make us make descision without our consent like a computer program.

May b if I was good enough ,i would be travelling now..lets say like a licence.

I think we are close t the equation.

Another Idea is what if theres no life in moon but thers soul.what if its like that in lots of planets.As in religion we say souls never dies.if moon used to be living ,,where are the soul.

Tests ..on full moon sleep at night by looking at the moon .You will make worth nightmares,so can be negative vibe fron the moon.or negative energy from the moon.

If you pay me millions to go on moon.I wont probably.

I did not have time to read all 193 comments, but what if you could somehow stretch those little blue lines? Causality could be suspended for however long you keep the device doing that going. Perhaps this great achievment could be done with the right frequency of energy to effect the time flow, or artificial gravity could be used.

As in the case of men from the future, no ordinary man could get that liscense. If for 30 years, 2,000 people got liscenses and traveled 10 times a year, that's 600,000 people where they don't belong. I think 5 people, switching off, 10 times a year, (some super squad or something) that could be around for 200 years, looking at 10,000 people spread throughout 5,000 years? That MIGHT work.

My time machine will be done any day now...

as ur talking about gravity ,all materials ,atomic structure even human comes to positive and negative.evry thing is like a magnet.gravity is like a magnet .we can say we live in a culture of positive and negative electro or magnet whatever.evry planet got a vibe thats why im nt sure but lets say it thats why wev got horoscope planet which match.anyway blA BLA BLA.

U VE MENTION RIGHT FREQUENCY OF ENERGY .thats my idea too.can artificial gravity be proportional to proper energy.if u ca find an equation ..

ur time machine will be done any day,but what about licence ,,can i be a passenger.

without a licence its a fraud ,ull nt have direction,u can end up in or doing unproper stuff ,start reading books .

im just getting a few ideas about what ive heard before.fairy tales etc talk about full moon,ghost vampire etc.lets now talk as if we had no age ,,we dnt die. O>K th eidea of peaple doing voodoo stuff preliminary prevent something for smeone,which mainly .for example an apple goin to fall on Mr X hand on 30/09/ mr y knows in advance that Mr x will have smething by doing his dnt know smkind of voodoo he can go and get the apple without Mr X knowing.This create a diversion in Mr x sm cases considered crazy,,because hes nt suposed to do what hes doing.

It is known/proven that gravity affects time. Perhaps FTL is not possible, but light does vary according to the field of gravity it is traveling through. Time on Mercury moves slower than Mars because of the proximity to our Sun's gravity. Time moves slower for your feet than your head because they are closer to the earths gravitation center.

Hi, and thanks for posting this page. After reading all the comments from crackpots, just thought you might like to know that some people read this page who (1) are not here to argue that special relativity is wrong (2) just wanted to understand the "FTL Transmission = time travel" thing and (3) have not built time machines in their garages.


math.... ugh...

what is it about math that makes people think math is an incontrovertible proof/disproof for the possibility of a set of circumstances you can/can't define mathematically?

I used the word "math" a whole bunch of times just now, because I'd hoped it would illustrate my point; the reasoning behind our deference to math as the ultimate authority is circular. Our acceptance of mathematical axioms is just as bad as a theists acceptance of the tautological "proof" for the non-causal existence of god.

Math is a descriptive tool, it's purpose is not to define the behavior of the universe, but to DESCRIBE the behavior of the universe. We assume that because math describes objective phenomenon we've observed, math will always describe objective phenomenon, and anything that equates to a non-object mathematically, is also a physical non-object... as I'm sure you can see, this is a fallacious assumption (negative proof fallacy).

Why is it such a ridiculous idea that FTL travel is possible, or even that it is possible and doesn't invalidate relativity? Couldn't there simply be a mathematical object that makes this possible, one that we won't quantify until (when/if) we observe the physicality of faster than light, AND SO HAVE NEED of this mathematical object?

Furthermore, math isn't even an ACCURATE lexicon for the artifacts of our physical universe. there is an infinite amount of "numbers" (

I have an IQ of 198... I'm pretty sure that's more than einstein could say, so we'll defer to the "intelligence quotient postulate" (which I just invented; such is my genius :P) and listen to the biggest dick in this proverbial (and hypocritically austere) circle jerk called the pursuit of knowledge:

1. Math is not an incontrovertible proof of anything other the fact that a mathematically impossible conjecture is mathematically impossible (which contrary to the popular consensus of birdwatchers, does not equate to the physical non-possibility of the aforementioned conjecture).

2. At some point in the future it is entirely possible that we will have to invent new theories (even mathematical ones) to explain the confluence of the fictional and the actual (that's correct; we do this all the time), and people shouldn't be so apt to denounce the possibility of anything, especially considering the absolutely insane things we know today to be ordinary occurrences, just ask the cat in the box (I know what your going to say after reading this part and yes, earlier I did called you a lair for maybe saying that infinite quantities are possible. Well as it turns out, every statement ever made is self contradictory [if again you point out the obvious here... well you simply aren't operating on a level of mutual respect and I'll brain you {you know what I'm going to say here as well I hope... }]).

3. You are not that clever. Neither am I "that clever", simply because there will always be something more clever than you and I, and at some point we lose sight of exactly what our definition of "clever" is, and give up trying to actually make my point.

To sum up... shut up, and continue posting masturbatory aides for the brain. As useless as I think all this stuff we suppose we figure out on our journey to the grave is, the work you physicist types are doing IS important to a lot of people, and you really should continue figuring exactly what it is you figure you should be figuring out.

P.S. I'm a little fuzzy (even after all the posts here) on why FTL travel equates to time travel, and why time travel (backwards) invalidates causality. If I were to say, go back in time and sire my own father.... how exactly would this be impossible?

As far as I understand it, you dummies (I have fun. Of course I don't mean to actually call any of you dumb, and it's probably a little disrespectful, but know I'm just having that fun at your expense) just can't wrap your inexplicably small heads (probably why you can't wrap them around it) around the idea that causality works like this: A portal (is it a portal? I have no idea. In any case, the mechanism by which I arrive in the past after traveling there from the future [don't cum in your shorts, you know very well I had to say it like that because of the language we're speaking, I'm going to explain why it's possible in just a sec]) opens up in my grandmothers bedroom, (cause) I step out of it and impregnate my grandmother (we're calling this the effect), then I open another portal and return to the future (from my relativistic position in time of course). You'll notice that all these things happened SEQUENTIALLY, and so did not violate causality. The fact that I could not have been born unless my father had already been born, and my father could not have been born unless I had already been born doesn't violate causality either, because my impregnation of my own grandmother is an object in the past (before my fathers birth) and my fathers impregnation of my mother is an object in the future (before my birth); so both of those events happened sequentially, exactly as causality says they should.

Just because I can see you not being able to get your head around this one either (I'm talking to no one in particular, and again I'm just playing around), I'll explain why me having to activate my time machine after all of this had already occurred (and so you would think, before I could have gone back in time and done any of that in the first place, which you would think would make this scenario impossible) doesn't violate causality either. In the past, (respective to his relativistic perception of it) a man stepped into his grandmothers bedroom out of a portal, knocked her up, and she later gave birth to that mans father. It was possible for him to do this because his activation of the portal was not the cause of the portals opening in the past, it was only the cause of the opening of the portal he stepped into from the future (of the past). The cause of the portal opening in the past, was whatever natural process by which the portal could be opened in the first place, in other words; it was a natural phenomenon the time machine took advantage of (which is the only way it could work, but if there was such a thing, yes, you could actually be your own grandfather).

You can apply this same principle to the people on the telephone, it doesn't matter if Laura or whoever receives an answer to a question she hasn't asked yet, because the events leading up to whomever answered the question answering it happened sequentially. The phenomenon Laura experienced was simply a man shouting words at her through a telephone (don't ask me why's he's shouting them), and eventually she will ask the question that he gave her the answer to (notice that it makes absolutely no difference that Laura got an answer before she asked the question, because in Laura's relativistic experience of time, nothing like that actually happened, all that did happen was her receiving an answer, and asking a question [again, SEQUENTIALLY]).

In other words, yes. No really, that's it. I'm kidding haha, but that illustrated my point rather well; any insane situation you can come up with while pondering time travel can happen, and does not violate causality exactly, and only because what happened in the past happened in the the past.

Agh, I still can't grasp it, I get lost somewhere around event R... which is maddening because I remember a time when I totally understood it.

Thank you for your explanation of FTL communication Rich, it's exactly what I've been looking for, and it all seems very clear and concise, even if I don't quite get it!

While I understand that FTL communication violates causality, I can't quite wrap my head around your example. I hope I'm not being too much of a pain by asking, but would it be possible to "re-label" your example so that it is described with a little more detail, and with actual places and events (planets/ships instead of locations etc)? I've tried myself, but since I don't understand exactly what's going on I find it very hard to do so. I know that it would help me understand it more, and maybe other people as well :)

My main interest in studying this is that I'm trying to write some fiction, but want it to be as scientifically accurate as possible. That means no FTL travel, but FTL communication would be nice, so there can still be interstellar fights. So I need to break a few laws (physical, not legal), but I'd like to limit the damage. Would it be possible to have a 'special' frame of reference, to and from which information can be received and sent, but there is no FTL outside of this frame? So although causality is broken outside of this special frame, if you're inside of it, everything seems in order.

Thanks for any help :)

Seems to me the causality violation described by special relativity is only an illusion. We see differences in the ordering of events only because light takes its "time" getting to us. The event didn't happen when we see it.

The causality paradox assumes we don't have a clue that the event happened before the light from the event arrived at our retinas. But we do know that. Knowing that, we are capable of calculating the time when the event actually occurred, not the time we saw it occurring. We do that all the time when we say the light from such-and-such an astrological body took such-and-such amount of time to get to us, that we are really seeing into the past when we look at starlight.

We can simulate the situation using a much slower frame of reference: the postal system. Someone sends us a letter telling us event X happened. After they mail it, they decide to call us and tell us. The call is the "instantaneous" event. We learn about the event, then days later we get the letter telling us about the event. The letter is the information arriving at "the speed of light."

If we were stupid, we might think the phone call came from the future, because it told us the exact information in the letter days before the letter arrived. But we are not that stupid. We don't get confused that the telephone call violated causality because it gave us the information sooner than the letter did. We know the letter took time to get to us and that the event didn't happen the moment we opened and read the letter.

People in space-time communicating by ansible will have the same experience, and they will understand the violation of causality is just an illusion too. Just because the light signal got there later than the ansible signal does not mean actual causality went backwards in time. It just means it LOOKED like it did.

At least that's how it seems to me.

The causality violations that would be caused by faster-than-light effects in special relativity are not some kind of optical illusion. They aren't analogous to seeing an event before you hear it, or to telephone calls being faster than letters. I know there are a myriad garbled attempts by people who don't have even the slightest grasp on relativity that make it seem so, but it's those explanations that are wrong. It's for that reason that I wrote this article in the first place, because I do have some grasp of special (and general) relativity and I thought I could explain the problem concisely and clearly. (It seems, given the many, many comments here over the years that I've largely failed.)

If you want an analogy in everyday terms, it's as if there's a special postbox with the property that the postal service will deliver any letter placed into the box yesterday rather than tomorrow. One day you receive a letter written in your handwriting that you don't remember writing. The next day you write the exact same letter and post it. That letter is the same one that arrived the previous day. In the case of the phone call being faster than the letter, it's clear that in both cases the effect - receiving the letter or receiving the phone call - occurs after the cause (the letter being sent or the phone number being dialled). In the case of the magical postbox, there's no such clear separation into cause and effect (and substantial problems for things like free will besides).

Great article and discussion (some aside). A few questions:

1) Wouldn't FTL simply widen the "light cone"? For example, instead of a "light cone" we might call it a "tachyon cone," which we would then draw the same as the light cone, however it would have a wider dispersal rate. How would this change anything at all except to allow events to be detected (observed) at earlier points, and decrease the time-frame between a cause-effect relationship? The maximum width would then (in theory) be a simultaneous/instantaneous transmission, which would no longer be a cone on the diagram, but rather a quadrilateral (after the event)? Would this simply allow the event to be (potentially) observed instantaneously (within the range of the signal)? Would this also mean the cause-effect chain to be nearly instantaneous - the effect occurring as soon as possible after the instant transmission of the "cause" event?

2) Does the light cone at the focal point of the event reach a "zero" width, or only approach a zero width? The difference is of significant importance since if it reaches zero, then on a quantum level, all the "rules" stay the same. However, if the focal point only approaches zero, then there are interesting changes at a quantum level. Let's assume for a moment the focal point does not reach zero: How do we now describe an event between two quantum particles that are next to each other, interact with each other, and are closer to each other than the width of the light cone focal point? Are these quantum interactions happening, for all intents and purposes, instantaneously?

3) If we accept that the focal point of the light cone only approaches and does not reach zero, the next questions are how small, and what defines minimum width? I like the idea of the minimum width being a photon - it keeps things nice and neat to some degree. However, this is only convenient. Consider a planet exploding in space. On a quantum scale, the explosion itself is a series of causes-and-effects. However, the explosion is also an event that can cause other effects. Is the focal point of the light cone on the graph as wide as the planet, smaller, or larger? If you were an inhabitant of the planet, the destruction was probably just less than instantaneous. However, to an observer light years away, there is only a single event - the explosion. The light cone of the death of an inhabitant on the planet has dissipated to nothingness, leaving only the macro event capable of causing any effect. Does this macro light cone have a minimum focal point that is relative to the size of the planet? Or are we allowed to trace it back to the quantum effects that caused the explosion? I would guess that the macro light cone is an effect brought on by the cause of the quantum events, and therefore has its own unique light cone. If this is the case, the light cone focal point is limited in size to (roughly) the size of the planet. If this is the case, we now have the same problem as presented in question 2, but on a macro scale instead of only limited to a quantum scale. For example: two planets are next to each other. One plant explodes, causing the other to explode. From an observer light years away, the event is a single event, and which planet exploded first would probably be indeterminable.

Thinking on this topic a little more, I remember at some point earlier in my life having a problem with time itself. The problem is a circular logic that is self-defining.

1) Time is a measurement of movement (how long does it take for an object to travel from point A to point B?). How long does it take for the second hand to travel around the clock? We define this as one minute.

2) Movement is measured using time (velocity = distance/time). We can measure the speed at which the second hand travels around the clock at one cycle per minute.

Note: Have you even bothered to time how long it takes a second hand to travel around a clock? If you have, it was probably to check the accuracy of the clock and not to prove that the second hand actually takes a minute to complete a cycle.

To further illustrate, the inverse logic holds true as well.

1) If there was no movement, "time" would not exist. 2) If "time" did not exist, there could be no movement.

Basically, all we are saying is:

1) t = d/v 2) v = d/t

Which is, by substitution:

v = d/(d/v)

True, but not very useful.

Using this as a basis, I have a feeling that we will continue to have discrepancies with physics until we are able to define movement without the use of time.

Here is an illustration of the first question I asked: Wouldn't FTL simply widen the "light cone"?

I'm not sure, but if this is the case, then wouldn't this allow for the co-existence of faster than light travel or communication, special relativity and causality. However, I do accept that this only shifts FTL into the realm of happy co-existence with the other two theories, but instantaneous communication is still problematic within that trinity.


This brings up an interesting concept. What if light, being “absolute” is only absolute because it is the stick by which we measure everything else by? In other words; using Newtonian Physics, one might use a standardize ruler to measure distance, and a standardize clock to measure time, and within these two measurement standards, the measurements work. One could call these instruments “absolute.” We know now that Newtonian Physics were “highly inaccurate,” but we have also changed the measuring stick to a different standard – the speed of light. For example; we can use a ruler to measure liquid. In one dimension, the ruler doesn’t do much good, just as in two dimensions. However, if we measure liquid with a ruler in three dimensions, we can get some pretty qualified measurements (eg. cubic meters/feet of water). However, even this measurement system is highly inaccurate for measuring liquids. So, we developed a new measurement system to measure liquid volume; like liters or gallons. These are far more accurate when measuring liquids.

The issue with light is that we cannot easily dismiss it since it is difficult for us to observe our universe without it. Take a hypothetical intelligent life-form that only developed the ability to hear the universe. Let’s assume that these intelligent aliens were able to not only explore their world, but space as well – only using sound. This race might theorize about the existence of light, but they would have extreme difficulties in ever proving the existence of light. These aliens might also develop their own theory of relativity in which sound is the absolute by which everything is measured. This concept is difficult for us to grasp (it is alien to us) since we have gone well beyond the measurement stick of sound.

Think of how the universe might be defined by these aliens. Let’s assume these aliens develop the technology, eventually, to surpass the speed of sound. To the alien’s, the traveler in the supersonic craft is able to arrive at the same time they left. And what do these aliens think of a sonic boom?! I suspect the initial conclusion might be along the lines of ‘leaving the known universe.’ Again, thinking of this from the perspective of an alien race whose best sensory input is limited to the ability to detect sound: Their ability to “see” might be similar to the sonar of a bat. What happened to the craft that went faster than the speed of sound? For a moment it seemed to be elongated and in two places at the same time. Even the best scientific instruments of this alien race might not be able to discern the time between the craft’s starting point at the speed of sound, to the crafts exit-point. Not because the instruments cannot detect time on a granular enough level, but rather the sensory input of these devises might not be capable of receiving other information, such as light, which would allow the detection of the arrival of the craft at a point in time later than when it left.

Let’s also consider the occupant of the craft. Inside the craft, things might have been a little noisy for this alien traveler. However, the alien would likely be able to still “see” (remember – using sonar) all the craft’s instruments from within the inertial frame of the craft. This means when the alien returned and everyone relayed how the craft was extended and in two places at once, the pilot would reply that everything “looked” the same inside the craft and no elongation was detected. From this observation, the scientist would be able to conclude that when going faster than the speed of sound, time slows down for the occupant of the craft in comparison to external observers.

Nothing about this alien race’s developing the ability to detect speeds faster than sound would allow them to defy causality. Instead, the alien race would eventually simply adopt a better measuring stick. I suspect this is why relativity works so well and yet seems to have some gaps. Relativity defines the measuring stick by our best sensory input, which allows us to measure accurately our observations, which in turn is currently limited to (but beginning to exceed) our measuring stick – light. And by “beginning to exceed,” I mean that we are starting to understand that there is something more beyond light, and while we can theorize about this something because we are vaguely aware of it through causality, we are still very limited to our sensory input.


Now that we are 6 years in the future from which you wrote this article and diligently responded to the uppers and lowers of the worlds education system, what would your note say delivered right before you wrote out this article? I don't see how you could keep on the same path with the infomation knowing you would spend x amount of time wrestling comments that don't need to be wrestled. I agree in the last 6 years I have probably spent an equivelent amount of hours trying to get that last piece of walnut out of countless shells but I feel like if I got a note from me that said "buy a bag of shelled walnuts and go spend 60 hours with your Mom - Me" I probably would. Which would then changed/not change anything right. I just wondered what your note would say. I loved the site, loved the comments I cheated over about 100 of them but you had six years I had an hour free. Thanks for the hour, ~B

I think my note would say something like "Be much clearer in what you write. No matter what you say, most people will misunderstand you, or not even bother reading it, or they won't actually think about it. Spend some time pre-empting fallacies and misunderstandings." I'd certainly still write the article though!

If only I had time to write the rest of the series...

Rich, doesn't your diagram only show that if Alice were looking through a telescope at Dave when she sent her FTL signal, she would receive an FTL reply from Dave before she could observe him (or rather his reflected light) through the telescope operating the ansible?

Likewise, if Dave was looking through a telescope at Alice, he would receive an FTL signal without ever seeing the reflected light of Alice operating the ansible, and he could even send an FTL reply before seeing her operate it.

An event in Alice's "past" light cone just means that the LIGHT from that event was observable by Alice, NOT that the event actually took place in her past in an absolute universal sense.

Because we have not yet observed FTL travel or signaling, we can say, in a practical sense, that anything in an event's past light cone occurred prior to that event. But with FTL transmissions, even though event R is in Alice's past light cone, no such event actually took place before Alice sent her first signal. She would receive the reply back instantaneously, and then much later, she would "see" Dave sending the reply.

This is more easily understood with a different visual representation that you might be able to make for your site (if you haven't already). Instead of a diagram with one spacial dimension and one time dimension, use a diagram with two spatial dimensions and represent time through animation.

Events and observers could be represented by stationary and moving dots, and future light cones could be represented by expanding circles from the dots. Since light is constant, the circles would all expand at the same rate. FTL signals could be represented by lines advancing from one dot to another at a rate faster than it will take the expanding circles to reach other dots.

In this new animation, it will be easier to understand what is going on with Alice, Bob, Carol, and Dave. A line (the FTL signal) will reach Dave before the circle (light) from event P ever reaches him (before he can visually observe Anna sending a signal). Then, a line will reach Anna before the circle from event R reaches her (before she can visually observe Dave receiving her signal).

Although the expanding circles represent the future light cones of their respective events, they also represent the past light cones of dots they overtake. When the expanding circle from event R reaches Anna, it represents how event R was in Anna's past light cone in your old diagram, but now it should be apparent that causality was never violated in either diagram.

Patrick's diagram may be more cogent than his text but the essential point is valid and I will try to articulate in a more sophisticated way. The concepts of space and time are, I assert poorly understood by contemporary physics, at least below the Planck length and in comparison with the certainty that existed until about a hundred years ago therefore we cannot rule out the possibility that non-local effects such as those addressed by the Bell Inequality or other as yet unknown physics could result in apparently instantaneous communication between distant objects. It is clear from the asserted dimensionality of quarks and strings that at that scale our understanding of the notions of space and time are sketchy at best and so it is prudent to say that we cannot at this time rule out such interactions.

we measure speed in time right? how could it possibly be anything less than instant whether we see it or not? ftl isnt even instant, its somewhere between instant and light speed. to suggest with ftl we could recieve a reply before we send the signal, well, i think a few more "cones" are in order.

Hi dear all, Since young age i am very much interested in this topic of time travel. Today i have bought book of Stephen hawking & Leonard mlodinov about briefer History of time. The Model of train example for relativity is what i had thought many years back.But i could not pursue it as whole time assignment for my future career.I am glad to read that so much study has happened and many are equally interested. Definitely i will comment in coming days.

Due to human mind limitations, Science is a game of observation and Math. New observations introduce new parameters and/or quantities to fit into older equations somehow, extending them to a new level or dimension of understanding. What I believe, is that some more advanced math and some innovative observations (that may utilize newer technologies) will come some day to make Einstein the second Newton. his equations will become special cases of extended ones that, in my belief, will not only allow FTL, but also will tell us how to realize it. It's a matter of time since Relativity is a milestone in human intelligence evolution. Just like Newtons' were and took some centuries to be revised.

My question as a non physicist (An Electronic Engineer rather) about the diagram is: Aren't you already breaching casualty by the assumption of instant transmission?

I enjoy reading and thinking about this kind of material, and I agree that FTL movement does not necessarily mean time travel by the definition most people consider. There are many reasons for this, but possibly the briefest one hypothetically entails running in a vacuum, so that the only gravitational forces acting on you are those of yourself and what you are wearing. If you somehow run FTL, then there will be effects on you, similar to standing in a high-velocity wind tunnel, but none of them will be from a breech in constant “normal” time passage. One reason for this is that light speed is not a speed limit; similarly, neither is the speed of sound, the speed of a turtle, or the lack of speed.

Some thinkers decide to look at things in a virtual reverse perspective, in which events are deemed potentially possible if their virtual reverse is possible. For example, we ask, “Does FTL movement equate time travel?” The virtual reverse perspective is to imagine a different world where only one known “thing” does not move at all, and all other “things” move at any desired speed short of infinite velocity. People who live here never cease movement, because the do not know how, and for them, only one known “thing” does not move at all. In this case, the virtual reverse perspective question would be, “Does lack of movement equate time travel?” So one way to look at this is to, instead of asking, “Does FTL movement equate time travel?” ask, “Does lack of movement equate time travel?” It’s not an exact reverse perspective, but it’s as close as I can think of right now.

So by most people’s definition, FTL travel cannot induce time travel. I would like to mention, however, that moving FTL can mean time travel by a different perspective. To illustrate my point, imagine two parallel universes in which an event in Universe 1 occurs simultaneously to the same event in Universe 2. For example, if Jane 1 in Universe 1 kicks a soccer ball, the parallel Universe 2 version of Jane 1 (Jane 2), who is identical to Jane 1, will kick the ball at the same time in the same way with all possible forces and conditions occurring the same way at the same time as they do in Universe 1. This is difficult to explain in words, but I did my best. From now on in this comment, when an event, person, force, etc. in Universe 1 is labeled like Zippatydooda 1, then the Universe 2 equivalent will be titled Zippatydooda 2. Now imagine that you are able to see everything happen in Universe 1 and Universe 2 simultaneously. A good way to put it is that you are watching a video on your TV, and the screen is split in half; on the left side, you view a specific area of Universe 1, and on the right side, you view the Universe 2 equivalent of the specific area of Universe 1. On the left side, you see Jane 1 walk into her car, ready to drive to her local grocery store. You see the Universe 2 equivalent happen on the right side. However, there has been a breech in the consistency of the parallel universes, and someone has made Jane 1’s car so that it travels FTL, while FTL travel is unheard of in Universe 2. So Jane 1 goes to the grocery store FTL, while Jane 2 travels there at an average of 35 mph. Jane 1 will reach the grocery store right after Jane 2 starts driving. Thus, all events resulting from either Jane reaching either grocery store will happen earlier for Jane 1 than for Jane 2. If Jane 2 does not know that Jane 1 could travel FTL, then from Jane 2’s perspective, Jane 1 has gone forward in time.

But I suppose this is just an idea, so I would like to hear what you guys think of it.

In Eisenstein's theory, Light is the maximum speed of any known particle. Then that means that the electrons in the components of the clock facing the direction of travel can only travel at the speed of light, that means that the forward speed of the object has to be subtracted from the speed of light to make this possible and not added to the speed but only sustained in the parts facing the other direction, correct. As in a coil of wire rotating as electrons pass through it. No matter how fast you spin the coil the electrons will never reach a speed faster than light, even if the wire's moving in a forward direction. thus causing the clock itself to slow down not the time.

Woo , i just travelled through time .

The people posting comments refuting the author are silly tards and are only doing so because this is the internet and one can get away with looking like a complete fool in a consequence free environment (which is pretty much the same reason I am bold enough to point out said retardation). Why don't you all glom the nard?

To anon of comment 217 above: Just an FYI, but unobjective arroganance does little to advance knowledge.

There ARE other theories on this subject. You are free to choose which one you wish to put your faith into, but it won't change the fact that it is still just one of many largely unproven/unprovable at this time theories based on very limited understanding expressed in a subjective manor that is limited by that same limited scope of understanding.

Even Prof. Hawking has been wrong and while that may come as a surprize to many, it didn't to those who never subscribed to his theories to begin with, like Preskill (who I suspect would be classified by you as a silly tard in the Pre Hawking "I was wrong" admittance era.)

As of yet, there is still no TOE (theory of everything). One of the big stumbling blocks being that accepted theories such as quantum mechanics and general relativity don't work together. In and of it self proof that we don't know or understand very much. As far as we know, things like causality and paradoxes might not even actually exist. They only exist now as a cheap way to discredit something we don't honestly understand beyond the assorted conflicting theories, of which maybe none are even correct.

It wouldn't be a first time science has had to change it's theories based on new discoveries and new understanding.

As it stands now, for all we know, everything we think we understand about how the universe works could be wrong. The universe works the way the universe works and it doesn't care how we human THINK it does or should. Much the same how bees don't care that we humans say they can't fly, and do so anyways. We might observe 42 and decide the equation was 21x2, and that might work to explain said observation for the time being, but it means nothing when the actual equation was ((2+8)*4)+2). The theories and rules we created to describe our observations are just that, things we created to describe what we saw, and not inherently indicative of what the universe is actually doing.

The more we learn, the more we discover how little we know and how much more there is to learn.

Richard, this is a beautiful article. Your explanations are well-written and your diagrams are models of clarity.

However, the first sentence ("faster than light travel is equivalent to time travel") is misleading to the point of wrong, and your repeated assertion in the comments that "you can pick at most two of {special relativity, FTL, causality}" is incorrect.

You are absolutely correct that "ansible-style" communication would cause the causality-violation that you describe so well. However, FTL need not take that form. Another possibility is the one that Patrick is getting at in the comments above.

Suppose that physicists discover a phenomenon that they call "super-light". Super-light is much like light, except that it travels twice as fast as light. In particular, super-light, like light, *travels the same speed in every reference frame*. Super-light would then, as Patrick says, "widen the light cone".

Suppose that we figure out how to use super-light to send signals. Then we would have FTL communication. But, as you can check with Minkowski diagrams, super-light would *not* open the door to causality violations. We would have all three of {special relativity, FTL, causality}.

If we had the right relative motion with respect to each other, then super-light would allow me to send you a message that you receive before it was sent, according to your reference frame. And you could then use super-light to send me a return message that I would receive before it was sent, according to my reference frame. Nonetheless, this would *not* result in a causality violating loop. I would receive your return message *after* I sent my original message.

I can't make diagrams as beautiful as yours, so I'll just ask you to verify this yourself with Minkowski diagrams :).

Whoops. In the previous comment, I shouldn't have written that my hypothetical super-light "travels the same speed in every reference frame".

That would be impossible, and I apologize for making such a howler. I should have stuck with the objective Minkowski geometry, instead of trying to describe what I meant in terms of reference frames.

But my point remains that super-light would allow FTL communication without introducing causality violations. Let me try again to describe what I meant when I said that super-light is "much like light". Consider the following important properties of light:

(1) The events in the light cone C emanating from a particular event E depend only on the position of E in spacetime, and not on what is happening at E. For example, C does not depend on the worldline of whatever object passing through E emitted the light.

(2) The light cone C' emanating from another event E' is just a parallel translation of C by the vector pointing from E to E'.

Super-light is supposed to be like light in that properties (1) and (2) continue to hold if you replace "light cone" with "super-light cone".

The additional properties of super-light that I need to make my point are the following:

(3) Super-light travels faster than light for all observers. That is, the boundary of the light cone emanating from E is contained in the interior of the super-light cone emanating from E, except where their boundaries coincide at the event E itself.

(4) Though the super-light cone is "wider", it is still a *pointed* cone, meaning that it does not contain any complete line in Minkowski spacetime.

These properties mean that every observer would see super-light as traveling FTL, but you couldn't use super-light to create a causality violation. So I think that you can still say that you have all three of {special relativity, FTL, causality}, as I claimed.

I had made the thoughtless and false inference that all observers would see super-light as traveling at a constant speed, like light. But this would only be true if observers started to use super-light, instead of light, to calibrate all their clocks. And, if they did that, light would stop traveling at the same rate for all observers. Normal light would take the place of sound in Patrick's analogy above.

In fact, if both light and super-light existed, then all but one reference frame wouldn't have an isotropic spatial dimension. Super-light would, in effect, introduce a privileged reference frame — the unique reference frame where the speed of super-light is a constant multiple of the speed of light in all directions.

Perhaps this justifies saying that super-light would violate your first axiom of special relativity. I don't think so, but it would be a reasonable position. Nonetheless, you can certainly say that you have all three of {Minkowski geometry, FTL, causality}.

The more I think about it, the more it seems to me that super-light could be indisputably consistent with both axioms of SR.

I wrote in the previous comment that "In fact, if both light and super-light existed, then all but one reference frame wouldn't have an isotropic spatial dimension. Super-light would, in effect, introduce a privileged reference frame — the unique reference frame where the speed of super-light is a constant multiple of the speed of light in all directions."

But I now think that you wouldn't need to have a privileged reference frame or to give up isotropy. It's true that there would be only one inertial reference frame in which super-light has the same speed in all directions. However, I can think of a situation where it would *not* be reasonable to call this reference frame "privileged", or to say that the other frames lack isotropy. The laws of physics would work the same in all inertial reference frames. The two axioms of SR would be perfectly satisfied, and yet you could have both FTL communication and causality.

Here is how I think that this could work. Imagine that the universe is pervaded by an exotic substance called "super-aether". Super-aether has the following properties:

(1) All the super-aether occupies the same inertial reference frame. The speed at which the super-aether travels with respect to any other reference frame is less than the speed of light.

(2) Because of the exotic properties of super-aether, it is impossible to change the velocity of any portion of it. Every part of the super-aether remains at rest with respect to every other part of it.

(3) However, using some kind of exotic device, it is possible to propagate a signal through the super-aether. Such a signal always propagates at a certain constant superluminal speed k > c with respect to the super-aether.

It's not really fair to call the super-aether's reference frame "privileged". The super-aether constitutes a physical system like any other, and it's entitled to its reference frame. I'm not assuming that there's anything special about the super-aether's reference frame, other than that it's the one that the super-aether happens to occupy. If, hypothetically, a chunk of super-aether found itself in a different inertial reference frame, then signals propagated through that chunk would move at the superluminal speed k with respect to the new frame. So, we still have the same laws applying in all frames. But it's just a brute physical fact that nothing can move super-aether into a different frame.

Now, I haven't explained the mechanics of how signals could propagate through the super-aether. It's especially difficult to see how this could work since each portion of the super-aether must remain at rest with respect to the remainder. This means that we can't displace any of it, so the signals can't propagate as mechanical waves. Nonetheless, the possibility of super-aether is not ruled out by the two axioms of SR.

The upshot of all this is that the super-aetheric signals satisfy the conditions on "super-light" that I gave in the previous comment. I could use such signals to send you an FTL message, and you could send a return FTL message, but your reply would always arrive after I sent my original message. We could therefore have FTL effects without the possibility of causality violations. We would have all three of {special relativity, FTL, causality}.

I created a tachyon wave using a silver tube a halogen bulb a brass bowl and three magnets in a radon rich area in san diego california a few years ago the light from the bowl hit the wall three days before i first turned one of my experimental lasers on. FTL is quite possible

You idiots are still making these ridiculous comments, and yet you haven't read A. Garciadiego, BERTRAND RUSSELL AND THE ORIGINS OF THE SET-THEORETIC 'PARADOXES'? And you STILL haven't inquired into the way Einstein used his constructivist orientation (what he called "practical geometry") in formulating the relativity of simultaneity?

You are all REAL clowns.

John Ryskamp:

This is a voice from the future. Everyone reading these comments wishes a giant St. Bernard would find your unconscious body on some snowy mountainside... and piss on you.

You are an abrasive little toad with no respect or professional courtesy. If you are actually a degree holding physicist, shame on you. If you aren't, then all I can say is I hope someone somewhere slaps the stupid out of you.

yes. i hope we are able to travel faster than light sooner than later. definitely. :) FTL possible? And if so, how do we harness the power to make us travel time? LOL my science is not powerful and I am only sec-1. Jus passing!

Rich, after reading all this I am thoroughly convinced that any mention of FLT leads to ad nauseam.

Okay... so if our spirits are light spirits, then would it be possible to time travel based on mind. Considering our spirits would have no problem handling the transition of dimensions. ;) wink wink mother fuckers

how many of u nerds have felt a boob?

>I created a tachyon wave using a silver tube a halogen bulb a brass bowl and three magnets in a radon rich area in san diego california a few years ago the light from the bowl hit the wall three days before i first turned one of my experimental lasers on. FTL is quite possible

Im sorry Terry but i must call out a severe case of BS on your "breakthrough". Not only have top scientists failed to do what you claim to have done, if this were true wouldn't you have recreated this experiment publicly and claimed your title as the most famous scientist ever? I fully support the study and experimentation of QM but when i see someone make a claim as stupid as that, i laugh knowing that scientists being funded millions of dollars havent even been able complete any kind of FTL. Go back to watching star trek instead of trying to think of "sciency" stuff to say in hopes of receiving any kind of praise.

PS Tyrell, i find your take on this very interesting.

Traveling faster than light will be amazing, I hope it sooner than never, exist people putting big efforts to achieve this goal.

Fusion-powered Warpdrive

@Terry - I think what you said actually argues AGAINST the idea of FTL travel causing time travel.

Think about it. Even if you really did complete that experiment with those results, it would not make sense. If the light hit the wall three days before you turned the laser on, you would have no reason to turn the laser on, because your experiment was proven a success. If you never turned the laser on, than no light could have hit the wall, because it NEVER EXISTED.

I hope you understand that, because I wrote it in a convoluted manner.

Lucas brings up an interesting aspect of bi-directional causality. Take three events in a hypothetical universe in which time travel is possible (events A, B, and C). Let's assume at Event B, there are two possible outcomes resulting in Events C1 and C2. Let's also assume at Event C1, one could go back in time to Event B and change the dividing factor so Event C2 occurs. The question of Causality is, does Event A change, even though it precedes the dividing event, Event B. Consider the possibility that Event A has changed even though it precedes Event B.

Here's a little story to explain why.

A time traveler has a special device at Event A, which can record the future and discovers that at Event B, her husband will be (has been) killed. At Event B, her husband dies. At Event C1, the time traveler goes back to Event B and saves her husband. At Event C2, in which her husband is alive, she watches the recording made during Event A. What does the recording show?

Curious by the results of watching the recording, the time traveler returns to Event A and watches the recording over her past-self's shoulder. What does the recording show?

If we assume the recording shows a future in which her husband is alive (because she saved him), then how was the recording at Event A (preceding Event B) altered? And if so, why did she travel back in time (from Event C1) to save him?

One possibility is that causality goes in both directions - forward and backwards in time. I am here today because of my actions yesterday. I performed those actions yesterday because I am here today. If anything changes the causality of future events (for example - time travel) then both the past and the future events are altered.

In the story, if we can accept that the recording was altered to show the husband as being alive, we should also accept that the time traveler's memory (a recording as well) would also be changed. Once she traveled back to Event B and saved her husband's life, the time traveler from Event C1 would cease to exist and all memory of the event would be as if Event B ever only had one outcome - even memories prior to Event B.

Therefore, any perception of time travel would be eliminated the moment it occurred. We could not perceive time travel even if it were happening all the time (so to speak). It is extremely difficult to measure anything we cannot perceive (not saying "impossible").

Oddly enough, this is not an argument that proposes that Event C1 ceases to exist and prevents Event B from resulting in Event C2. Only that we can never prove Event C1 ever existed since we would have no way to perceive it.

Take this to the nth degree and it seems that even proving time travel exists (for example, Terry's tachion experiment) would create a bi-directional causality unraveling of events (both past and future) that would result in time travel being un-proven. That is, it was proven, just no one would ever know it was proven, which is no different than being unproven.


PS: By the way, I invented a Tachion gun that hits before it's fired. It saves a ton of $ on bullets.

@Lightspeed. Warpdrive's already available. No need to invent it. Perfecting it to a useful state will be the trick.

Think of an ant on the groud at the toe of your foot. You take a step and the other foot is on the ground some insane distance (relative to the ant) in front of you. To the ant, you are in two places at the same time! That's the essence of warp drive.

The trick is to get a ship to grow to a size large enough for deep space travel. I assume this will be handled by a warp bubble, which creates a pocket universe in which the three spacial dimensions inside the warp bubble are different than those outside the warp bubble.

Let's check back with the ant. Grow the ant to the size of a person, have the ant take a step, and then shrink back down to normal size. The ant just crossed a vast ant-distance in no time at all.

While effective for travelling massive distances, I don't think warp travel quite quallifies as FTL for some odd reason I don't understand.

Interesting site. I have heard it many times FTL implies time travel. I cannot really get my head around this "tilted frame of reference" business or more properly two separate frames being overlaid in one image. I guess where it falls over for me is the last diagram where actual time travel happens or message along blue X axis (instant) is translated to white Y axis as-is. Then again, relativity is not known as being easy to digest.

By the way, my favourite way to get around the superluminar dot on the surface of the moon -case is to turn the idea of the laser pointer away from a water hose and into a machine gun firing photons.

And in any case, I suppose original message really says "according to special relativity, FTL implies..", SR being true as far as we know at the moment.

Is this an accurate thought experiment?

A long train moving at a constant velocity fails to trigger the gates at a level crossing, and hits a car. At that instant, the engineer activates a fail-safe that sends an instantaneous (in the train's frame) message back to the caboose. The conductor, riding in the caboose, transfers the message to an instantaneous (in the track's frame) messaging system embedded in the track. The message is then sent to the crossing gate, which lowers. But due to the relativity of simultaneity, this happens before the train reaches the crossing, so no crash occurs.

Besides the problem of time being based on velocity (movement) and velocity is a function of time and distance, and the cyclic logic problem that implies, there is another issue I am struggling with and perhaps someone can explain:

We accept that the "distance" between two points in time can only be positive (forward in time) but question if backwards in time (a negative "distance") is possible. We don't think like this in terms of space. The issue is that distance is always positive and can never be negative. Basically distance in space is calculated: d = Sqrt(a^2+b^2+c^2), which is always positive. The coordinates system that we overlay in space has "negative" values, or can have "negative" distances, but this system is only a convenient way to divide up space. Travel through space really implies that one cannot travel a negative distance, even if one were returning to a point of origin or travelling "backwards" based on one's "forward" perception.

The graphs used (so far) to illustrate the problems of simultaneity and instantaneous messaging seem to have been on hybrid distance-coordinate graphs. I have a nagging sense that travelling from right to left on these graphs is every bit as wrong as travelling from top to bottom.


Considering many of the other comments, I thought you might appreciate hearing that for me, this article was nothing short of epiphany-inducing. I've never before had a true grasp on what relativity is or why it works the way it does. With this article, the "light bulb" came on. Thank you!

[You’re welcome — Rich]

I can't believe some of the comments. The article was right on and the comments were horrible. It's like the scene from Billy Madison when he gives the speech at the end. The guy says " everyone in this room is now dumber for listening". Rich did a good job of explaining it. For those of you who STILL dont understand after years of this post, I offer another movie quote from Caddyshack... " The world needs ditch diggers too!!!"

Oh my goodness...poor Richard has been dealing with these comments for over six years now.... Faster than light = time travel The concept is so simple! Unless someone has an actual time machine, ready to be tested, do the technicalities really matter at the moment?

Just curious: would it be at all possible to set up a real-world experiment to confirm these ideas using satellites traveling at high orbital speed opposite to one another, each equipped with atomic clocks?

I've heard that relativity has been confirmed by detecting differences between satellite and ground-based atomic clocks, so would it be possible to set up enough of a speed differential between two clocks that you could try to send a signal into one satellite's past, even by just a few picoseconds?

[It’s not possible to do this because a transmission by into the extremely recent past requires a faster-than-light signal and no method for transmitting information faster than light is known — Rich]

Thanks for a very lucid description. I worked through the math of this while an undergraduate but didn't really grasp it (nor do I yet, but your description is getting me there). Sorry so many people would rather criticize than try to understand.

travelling through ,,,faster than light ,,,got rules and regulations.,,,its like having a pass to go onboard.similar to develop ur what type of skill csan someone develop simillar to light or faster,,,what materialss can be used,,communication method,,,nt any part of our body,,,it will be like water and vapour,,nt the same..,,what if u are able to travel ,,,wont let you for sure,,,rather to be killed,,,why try to smoke weeds and see if it happens. sorry for the joke..but learn life to the fullest then mingle on the other side...

we had already travel through communication ,but not proper,,only t.v,dvd etc.visual.but communication should be on two sides,send and receive.why dnt you start sending program for let say 2020 and tryin to receive on 2013..plan exact date..time..means you get a time table of futur which keep on modifying so that you wil receive..though the receiver should not be same time and date or else ther be no progress..

we need an object or structure to represent suposed say machine through time ,,,do we have it yet.where is it ,,may b oldest energy ,,what energy,,a soul on a stone,,or a soul on a body..lets go to history to find out,,80 % of history have changed to lies,,i did psychology at school,,its all about arabic countries ,,americans,,.just close to non civilisation.find the truth and youl find everything clearly..

lets work out materials which can carry human nature we had already develop.even very long ago materials that can tavel ,,to past and future..but carries memories...example gold,diamond.i just got an idea diamond..very strong..if we travel very fast we melt up with heat or may be cold.i dnt knw much about fast should we travel faster than .....(?)to go to one day before in one second or less in 24 hours.will this material stays compare if its travelling 2 days,probably 2 times more strength and energy.every one says im a good mathematicians because i use my finger smtimes to get good because i do things in order and with maximum cool head.we should start with materials first ...that carries its own energy .suposed in 12 hour travel what energy is constant.even if we send a laser ot full speed its going to future already ,,and end in vision..

what is the structure of diamond ..elements etc.actually does not go through aging .but we do,what things in us that does not go old ,,or go younger..[albert einstein believe in spirituality ,paralell world]why dnt we .. we are working on something if we suceed means we are travelling through future.(thats a really good motivation)positive.most peaple who tend to live the past normally dnt suceed. example someone died in an accident at a junction ,23 yrs old beautiful woman..after 10 yrs peaple still see her at 23 yrs old beautifull,she stays and still got energy of past and repeat what she being doing means she got stuck same history for years until the real time comes where she suposed to be dead in next may be 40 yrs.some who got haunted are nt strong go sick or mental,means they are living the past..i think sometimes that a technick that voodoo peaple make peaple suffer...put an energy on ur body to control with no progress..

The key is the soul,,why materialistic or modern world ignore spirituality.because the oldest and stronger one are still a knowledge of every years.And if you search for it peaple had changed the history already long ago,,live in lies.oldest civilised cultured for example tamil lot were killed in sri lanka.nobody knows what were happening until end .Its always been a game ,,true resource is fading.what is the first script ,writting ,school.but i learn at school the first uni was in arabic countries .la mec where muslim go to pray long ago was a central market ,,every thing was one india,due to communication and transport peaple found a different muslim took pocession and lock all hindu godess matter what this have created a positive vibration,,with lots peaple focusing on it.history is precious ,,some are lucky to see the light ....albert einstein says "life is a waste of time if nobody does something for a better future of the world"keep ur money to help richess of the world and helping peaple.

The key is the soul,,why materialistic or modern world ignore spirituality.because the oldest and stronger one are still a knowledge of every years.And if you search for it peaple had changed the history already long ago,,live in lies.oldest civilised cultured for example tamil lot were killed in sri lanka.nobody knows what were happening until end .Its always been a game ,,true resource is fading.what is the first script ,writting ,school.but i learn at school the first uni was in arabic countries .la mec where muslim go to pray long ago was a central market ,,every thing was one india,due to communication and transport peaple found a different muslim took pocession and lock all hindu godess matter what this have created a positive vibration,,with lots peaple focusing on it.history is precious ,,some are lucky to see the light ....albert einstein says "life is a waste of time if nobody does something for a better future of the world"keep ur money to help richess of the world and helping peaple.

thursdays in hindu as well ,most peaple those who pray etc.. gain more cosmic ray ..

suposed someone been travelling through time ,,what would you do.steal lotterie,unless you are a real saint.if youv work out how to travel you would run and never hear from you..probably enjoying with 10 woman around.or maried once lot of time for the first time. time travel have already been discovered ,,in old bhagavat geeta already anounce round earth nine close planets etc.why dnt we follow sme little rules.CREATE A STRONG ENERGY SPEND MONEY ON IT TO MAKE THE PERSON WHO INITIALLY DISCOVER OR CREATE TIME TRAVEL .DO A DONATION TO POOR PEAPLE..THIS EQUATION WILL MULTIPLY IF UR ENERGY ,OUR ENERGY IS STRONG.CONTRIBUTE TO WAT ALREADY EXIST AND LISTEN TO ADVICE TO MAKE IT day we will all travel through space may b as a guardian to help our little kids.some of u already experience what you are advice to do.dnt be a kid that dnt listen to parents and old age'ah i regret nt listening to old man'spend ur energy on smthing beautiful ,adopt a kid in egypt cost u nt even 1 dolar per day..all we are discussing coming to a sense ,and this will help we are achieving what we want,at the same time those who want to continue the theory can still.DNT EVER THINK YOUL GET PERMISION AND WILL BE ABLE TO TRAVEL AND B A KING.USE PHYSICS ENERGY,,PRECIOUS ENERGY DEVELOP PRECIOUS ENERGY.SAVE THIS FUCKING WORLD OF EGO AND IDIOTS.KNOWLEDGE GRAB IT FROM THE START OF LIFE.LIKE LOTUS GROWS ON MUDDY WATER.SEARCH FOR GOOD THINGS.

The author never said FTL is impossible only that causality and FTL cannot co-exist. Take your pick.

It also needs to be said that science cannot say with absolute certainty that every trace of matter and energy in the entire universe is deterministic although it would seem to be.

The Modern Relativity website is back up at if you'd like it for an external resource reference link. Thanks, David Waite


Thanks for your time, effort, and patience. I had tried for years to understands some of these concepts. For me, the most important factors were the graphs and your thorough explanations.

I am still optimistic that FTL transmissions of signals (not objects) are possible, even if something else has to give a little.

Keep up the good work.

Yes SR says FTL signals will violate causality.

So now I want to calculate this using Lorentz transformation. Assume FTL signal not is infinite, as it is not easy to calculate with. Assume it is 5 times the speed of light.

Will the gamma not then blow up in my face?

Do the Lorentz transformation breaks down for FTL?

V>c and we get square root of a negative number.

To clearify, I was thinking if a signal can be sent FTL, then also a frame can travel FTL.

But frame transformation blows up when the frame is traveling FTL.

That is SR is inconsitent with FTL, as the author of this page already have pointed out.

If FTL is truly observed, that is true FTL signal (not illusions like laser pointer towards/accross moon from earth) then we have to reject SR.

but since no FTL signal is observed SR is still "fully" intact!

Get ready for a whole lot more comments now rich :P

Very clear, I just hope people take time to read your article carefully, maybe reflecting on the important role of the ansibles in your explanation. Could FTL communication work at speeds less than instantaneously?

There is a flaw in the reasoning saying that inversion of time would violate causality.

For example, an electromagnetic field would cause an electron to accelerate on some direction, but a positron would do it exactly on the opposite way.

So, if you invert time on a positron, it would behave like an electron.

In some sense, is possible to state that a positron is an electron moving backwards in time.

Yet, an egg made of antimatter will not naturally evolve from broken state to unbroken state. We would not see antimatter behaving like a picture running backward in time. Even if the egg is made of particles running �backward in time�.

We say �causality�, but it really is not a measurable property of the universe. What we can measure is entropy. We know that entropy increases on the future, so if the system can be on two states, we say that the one with larger entropy is on the future.

So, if a signal were moving faster than light, some observers would see it as if were moving the opposite way, but still both would agree on who haves the larger entropy.

I didn't have time to sift thru all of the comments, but it seems to me there's a critical error in this whole example.

For the first message, Alice sends the message to Bob through space in their own inertial reference frame, which is fine. But for the second message, Bob sends the message to Dave THROUGH Dave and Carol's inertial reference frame.

Bob is not traveling in Dave and Carol's inertial reference frame, and thus cannot send a message along the lines of their reference frame. Any message he sends must necessarily travel across the lines of his own reference frame, (i.e. back along the same line that the first message traveled across), thus, the message reaches Dave at exactly the same time as it was sent (assuming everything is instant), and there is no violation of causality.

What seemed to cause a violation in causality was actually the problem of Bob instantly receiving a message from Alice, then suddenly and violently shifting from his inertial reference frame to Dave and Carol's inertial reference frame (i.e. traveling at near the speed of light in one direction, then traveling the speed of light in a different direction at the same instant), and then instantly sending a message to Dave in that reference frame.

That's a lot to do all in one instant.

Ah, sorry for my earlier comment, I didn't see that Bob sent the message to Carol and then Carol sent it to Dave along the lines of their reference frame.

But! Even in that case, you're comparing times across reference frames. You can't compare time A in reference frame 1 to time B in reference frame 2 because each time is dependent on its own reference frame, that's kind of the whole concept of relative time. If you're going to compare the times you have to do the lorentz transformation to whichever reference frame you're comparing in.

Consider this as proof of the fact: The only time causality is violated in the diagrams is when Carol sends the message to Dave, this is the only instance where the message "goes back in time". If causality were truly violated when instant messages were passed between reference frames, then Bob's message to Carol should also go back in time. It doesn't, because (well, partially because in the diagram they happen to be occupying the same space, there's a WTF right there) we assume that the message is moving along the lines of Bob and Alice's reference frame.

Bottom line: All message lines must follow one reference frame, they can't jump between the two without the appropriate mathematical conversions.

Alright, I'm smart and I understand a lot of physics, but this just blew my mind.

I�d like to invite you to read my article, �Causes of Relativity� at

This article shows that the Lorentz transformations can be derived from the Doppler Effect in combination with the assumption that the stability of systems of particles is based on standing light waves in the ether.

Wow, my brain hurts from trying to wrap this into an easily to understand ball. But this one thing doesnt make sense to me. please respond if you can.

Wouldn't moving in a faster reference frame make your cone change shape, if you are now experiencing time differently to the rest of the universe then the possible things that can influence you in a given time (from your perspective) are different than if you were stationary. Also, why did the space axes change in comparison to the still object, isnt distance te same irrespective of the velocity you are going.

[There isn’t just time dilation in special relativity but length contraction too. It’s the combination of the two that causes the light cones to be invariant. Or, as physicists would say, the invariance of the light cones produces the other two effects. — Rich]

I just dont get it.

As far as I understand Fig. 5 shows the following situation:

Alice and Bob are located on Space Stations with a huge distance between them, lets say Alice is on Earth Starbase and Bob on Deep Space One, a whopping 3 lightyears away. They share the same inertial reference frame, because their stations do not move relative to each other. No relative movement = no time delation.

Dave and Carol however are space pilots. They fly in their fancy space fighters at a whopping speed of 0.4c and they fly in formation on a parallel course, side by side at a distance of 3 lightyears. This is important! They do not move relative to each other.

Now, Daves mission is to pass by Earth Starbase (with Alice in it) while Carol will pass by Deep Space One (with Bob in it). Their angle of approcah to their targets is the same, because both fly at a parallel course, remember.

A few days later, the logbooks of all of them are checked. And here is what I dont understand:

The logbook of Dave shows, that he passed his target (Earth Starbase with Alice) at 16:00 bordtime. Thats the time his clock showed him and thats the time the computer marked in the logbook.

The logbook of Carol shows that she passed by her target (Deep Space One with Bob) at 16:00 bordtime. No time delation, because Dave and Carol fly in formation, no relative movement between the two.

Bobs logbook shows that Carol passed him on Deep Space One at 20:00 bordtime. There is a time delation, of course. Carol moved at 0.4c relative to Bob. Relative Movement = Time Delation.

But here it is: Alice logbook at Earth Starbase marks the fly by of Dave at 17:00!! Thats way earlier then what the logbook of Bob marks for the flyby of Carol. Thats a time delation, isnt it?

How can that be? How can the logbooks of Alice and Bob disagree on the time of the flyby of Carol and Dave? What causes this time delation?

Thank you.

I don't get u guy, I mean u who are talking 'bout something like 'superlight' or speed just above the speed of light. I mean, it doesnt matter for SRT if the lorentzviolating factor is just small or infinite, does it? When u say, u have a problem with infinite speed but not with FLT, I think it's inconsistent, because u can find a reference frame, in wich FLT is instantaneous (keyword: relative future/past, look @richs article 'bout that). To avoid that, u have to say, that this super-speed is constant for every observer. But in doing this, u can't keep 'c' constant for every observer, an this may cause a lot of problems, since this is measured to high precision.

But I may be mistaken. Greetings & a Happy New Year!

Thanks for the explanation this was just what I was looking for. I especially like that you point out time and time again that you're not proving whether FTL travel or time travel are possible, but just how they cannot coexist with the theory of special relativity.

I have some physics background, but certainly not PhD level. However, one of the things I learned early on in physics was that physicists love to work with idealized systems that don't actually exist in the real world. So, with that in mind, I have one comment/question:

This whole argument rests on inertial frames. An inertial reference frame is one in which no acceleration occurs. However, no such frame of reference exists in the physical universe. All particles experience, at the very least, some amount of gravitational force and therefore undergo some amount of acceleration.

How does the fact that there is no such thing as an inertial reference frame affect your proof that FTL information must violate causality?

It would seem to me that the proof breaks down in the same way simultaneity breaks down with an accelerating relativistic spacecraft, because there is now a third frame of reference involved common to all the parties forced upon them by the accelerations of the observers.

What are your thoughts on this? Thanks for your time.

I would like someone to clarify some simple points I don't understand about the original example.

At Event R, both Alice and Dave are at practically the same place at the same time (though moving relative to each other) and Dave receives an FTL transmission from Carol. Dave is then able to send a transmission to Alice at Event R. But when does Alice receive the FTL transmission that Carol sent?

If Alice receives it at Event P then I'm missing a key piece of information. Why can Dave receive Carol's transmission and forward it to Alice before Alice receives Carol's transmission?

On the other hand, if Alice receives it at Event R, then if Bob and Carol both sent FTL transmissions at Event Q, Alice would receive them at different times. I keep reading elsewhere that the speed of light is relative to the observer and that the relative speed of the of the source is irrelevant except as a cause of red/blue shift. Would this not also apply to theoretical FTL transmissions? If so, Alice should receive both Bob's and Carol's transmissions at the same time (Event P), right? But if the same principle would not apply to FTL, why would it not?

I had hoped someone would have replied to my post by now... Well, I have figured it out (I think).

First, I should clarify a mistake I made in my last post. I said ,"I keep reading elsewhere that the speed of light is relative to the observer and that the relative speed of the of the source is irrelevant except as a cause of red/blue shift. Would this not also apply to theoretical FTL transmissions?".

Correction: The relative speed of the source could certainly be relevant for any form of transmission that doesn't move at the constant speed of c. But more importantly, although objects/particles traveling at c will be measured as traveling at c regardless of the observer's inertial frame, anything traveling slower or faster than c will be measured at different speeds in different inertial frames.

Though I had realized that much shortly after writing the post, I wasn't able to grasp the implications of that until I finally went and worked out the math. I was thinking that at the very least any observer would measure the sending of any FTL transmission to be before their own receipt of that transmission. This is because I was only considering speeds from 0 to ∞. The original example would have been more informative for me without using Bob or Dave.

Results of the math I did:

In Alice's inertial frame, let's say:

  • Event Q is 3 light years from Events P and R
  • Event R occurs 1.2 years before Events P and Q (Made proportional to the original examples)

In Dave's inertial frame Event Q and R are simultaneous, so:

  • Dave's speed relative to Alice is 0.4c
  • The Lorentz factor is 1/√0.84

So in Dave's inertial frame:

  • Events P, Q, and R are situated in a single line in space with R between P and Q
  • Events P and R are 0.48/√0.84 light years (~0.524) apart
  • Events Q and R are 2.52/√0.84 light years (~2.75) apart
  • Event P occurs 1.2/√0.84 years (~1.31) after Events Q and R

Let's say that in Dave's inertial frame the speed of the FTL transmission sent by Carol at Event Q in the direction of Events P and R is 1,000,000c. Meaning that Dave would receive the transmission approximately 1 minute and 26.77 seconds after Events Q and R. However, in Alice's inertial frame she would receive the transmission approximately 1 minute and 19.53 seconds after Event R (Nearly 1.2 years before it is sent in her inertial frame). The conventional concept of speed no longer applies in this case.

HI. late to the discussion.

What I don't really understand is why do you suppose that people having different time and space definition will be able to communicate instantaneously ? Meaning... how can bob give the message to carol. They are in the same time/space event for a duration so instantaneous that they can't communicate. One might even think that they can't interact.

Or that the time needed for Carol to receive the message, push on the button, and (send it instantaneously to dave) and dave hearing /relaying the message compensate the inter-event R-P. (in Carol's timeframe it is instantaneous… while in Bob time-frame, carol sent the message 1.2 years after receiving it…)

So in the end, the only conclusion I can see here is that "communication between any two different space/time causes time travel". great. something not known. (sarcasm inside). the issue here is not the ansible or the FTL. It is mainly assuming (why not, every one makes assumptions) that two different space/time inertial frame can interact.

That's one of the main principles advanced for proposing time-travel solutions: -I go in an inertial frame where time/space is sufficently different from reference spacetime. (which might work if you could easily jump between inertial frames… however you cant).

Thus this argument is so roundabout.

an inadequate image would be that you are trying to solve a two unknonw system using one equation.... and if you do that... you won't be able to solve it. It seems that you are solving it only because you make one assumption about one of the two unknowns.

To go farther. (but I won't do the maths) You are proving that a FTL "that goes Xtimes faster than light" enables such issue when two inertial frame with a Y angle of space-time can communicate (using parameter Z). I would only try to depict the relation between X and Y and the inter-frame communication parameter Z.

I suppose that the higher the value of Y the higher the difficulty to communicate. And the relativity theory doesn't seem to go against that… if I send a laser-carried message to someone that just shot by at a speed close to c, it will take them years, in my referential, to receive the message, while it will seem instantaneous to them.

For me, this means : if X0 FTL is possible, and I know parameter Z, then two inertial planes can communicate only if the angle Y is inferior to Y0.

And vice-versa. If I know Z, and I know the maximal value of Y0 for which the two planes can communicate, then I can devise a FTL that won't cause causality issues and thus is out of your choice.

juste to moderate my previous comment. I enjoyed your demonstration... 9years latter. however it is just that I feel there is something missing.

maybe special relativity gives a value of Z such that communication between any two inertial frame is always possible whatever the difference in speed between the two inertial frames.

however I've got the feeling that such communication is not as simple as that and that switching from one frame to another is not easy. Indeed one physical personne can not do it instantaneously nor without a big amount of energy. ergo I think there is a "magic hat" in the simple sentences "bob send the message to carole" and "dave send the message to alice".

But maybe my "feeling" is wrong, and maybe maths proves that suitable communication between frames is always possible and that the message from bob to carol will be the same as the message from dave to alice.. and that it will be transmitted in a form that is able to interact with alice...

I'm not good enough with such maths

To me this all falls apart as soon as you say inertial frame in a Lorentz Transformation. That is basically describing an impossible event. And at best gives us the math to describe the optical illusion of a wheel moving backwards if it is traveling faster than the frame rate. It is only a matter of time before we all fully understand that Space as well as Time are relative and that all known laws of physics hold true to their own frame of reference and that other frames of reference hold no restrictions outside their own. To me frames of reference are dimensions. So if you say something doesn't follow a known law of physics as YOU observe it. I would say your Frame of Reference is outside the governance and or measuring capability of the event.

All the space frames shown above are straight / linear. I believe that space bends under the influence of matter / gravity, possibly time can behave in a similar way under conditions as stated above. Is there room for a possible solution to the problem of causality violation when the frames of various signals are curved / bent maybe even nonlinear relative to each other ?

If this is just a stupid remark, please say so.

I'm still struggling to see how FTL communications could create causality violations.

If I phoned Earth from Alpha Centauri to say that Alpha Centauri had just exploded, then Earth called Sirius to tell them, and they pass the message on to Tau Ceti, all locations would indeed see it happening at different times.

However, how would this violate causality? All people are still receiving the FTL information in the Universal 'present', it's just that they would have to wait different times to see it from their location.

Please, people the Lorentz transformations are only valid for vc. Consider communications using entangled particles. Then transmission times are zero, and no causality contradictions occur. Only invalid use of the Lorentz transformation gives a causality contradiction.

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