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):

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):

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 quantitites. This postulate holds in classical mechanics too.
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:

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:

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):

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):

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" >>

1. Comment by Peter McArthur on September 15, 2003 1:42 PM permalink

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

2. Comment by arsaii on August 1, 2004 3:45 AM permalink

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.

3. Comment by Rich on August 1, 2004 6:28 PM permalink

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.

4. Comment by Nils on December 4, 2004 9:17 PM permalink

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.

5. Comment by Rich on December 5, 2004 7:59 PM permalink

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.

6. Comment by Igor Fedchunov on December 11, 2004 6:00 PM permalink

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

7. Comment by Rich on December 11, 2004 6:38 PM permalink

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.

8. Comment by Rich on December 11, 2004 7:17 PM permalink

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".

9. Comment by Igor Fedchunov on December 11, 2004 11:42 PM permalink

"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!

10. Comment by Igor Fedchunov on December 12, 2004 8:28 AM permalink

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 ?

11. Comment by Rakshasa on January 16, 2005 9:48 PM permalink

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?

12. Comment by Rich on January 16, 2005 10:03 PM permalink

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.

13. Comment by Benjamin Rosenbaum on May 12, 2005 4:20 PM permalink

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.

14. Comment by Benjamin Rosenbaum on May 12, 2005 7:21 PM permalink

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?"

15. Comment by Ted on May 15, 2005 10:11 PM permalink

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.

16. Comment by Rich on May 15, 2005 10:19 PM permalink

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".

17. Comment by Benjamin Rosenbaum on May 16, 2005 3:37 PM permalink

> 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.

18. Comment by David Moles on May 16, 2005 8:23 PM permalink

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.)

19. Comment by Ted on May 17, 2005 4:17 AM permalink

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}."

20. Comment by Benjamin Rosenbaum on May 17, 2005 3:17 PM permalink

(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.

21. Comment by Matt Hulan on May 17, 2005 3:40 PM permalink

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: http://www.edge.org/3rd_culture/barbour/barbour_p1.html) 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.

22. Comment by Benjamin Rosenbaum on May 17, 2005 5:43 PM permalink

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.

23. Comment by David Moles on May 17, 2005 9:23 PM permalink

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.)

24. Comment by Nicholas on June 24, 2005 12:52 AM permalink

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).

25. Comment by on June 24, 2005 12:55 AM permalink

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.

26. Comment by Shape on June 24, 2005 5:28 PM permalink

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.

27. Comment by MxM on August 29, 2005 8:37 PM permalink

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.

28. Comment by Mohd. Javed Khilji on September 27, 2005 7:07 PM permalink

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

29. Comment by a Crazy Man in a Bunny Suit on January 27, 2006 10:55 PM permalink

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?

30. Comment by Roomba on January 27, 2006 11:00 PM permalink

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

31. Comment by Jason May on January 27, 2006 11:19 PM permalink

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.

32. Comment by l33t_boi_420xxx on January 27, 2006 11:32 PM permalink

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

33. Comment by jesse on January 28, 2006 12:10 AM permalink

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.

34. Comment by Cyberdactyl on January 28, 2006 12:12 AM permalink

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. . .

35. Comment by MIKX on January 28, 2006 1:28 AM permalink

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?

36. Comment by on January 28, 2006 2:15 AM permalink

i think this report is bs

37. Comment by Chris Tayloir on January 28, 2006 3:16 AM permalink

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 apart.you 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 http://www.nerys.com/

38. Comment by Jeff on January 28, 2006 3:56 AM permalink

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?

39. Comment by Rich on January 28, 2006 11:31 AM permalink

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).

40. Comment by Rich on January 28, 2006 11:53 AM permalink

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.

41. Comment by Rich on January 28, 2006 12:03 PM permalink

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.

42. Comment by Rich on January 28, 2006 12:09 PM permalink

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.

43. Comment by Rich on January 28, 2006 12:17 PM permalink

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.

44. Comment by Ivan Minic on January 28, 2006 1:47 PM permalink

SVG usage is simply brilliant :)

45. Comment by S.O.G. on January 28, 2006 4:26 PM permalink

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!

46. Comment by John on January 28, 2006 5:17 PM permalink

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...

47. Comment by Rich on January 28, 2006 7:25 PM permalink

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.

48. Comment by Chris Taylor on January 31, 2006 5:45 AM permalink

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 http://www.nerys.com/

49. Comment by Rich on January 31, 2006 10:44 PM permalink

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.

50. Comment by David Piepgrass on February 5, 2006 9:39 AM permalink

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.

51. Comment by Allison Crawford on February 23, 2006 4:24 PM permalink

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!

52. Comment by Rich on February 23, 2006 6:36 PM permalink

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?

53. Comment by Allison on February 25, 2006 5:39 AM permalink

Hi!

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.

Allison

54. Comment by Allison on February 25, 2006 4:17 PM permalink

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

55. Comment by Mo on March 7, 2006 1:15 AM permalink

"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: http://snipurl.com/m460

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.

56. Comment by Igor on April 30, 2006 9:33 PM permalink

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.

57. Comment by on October 16, 2006 11:10 AM permalink

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?

58. Comment by me on October 18, 2006 4:38 PM permalink

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 >

59. Comment by on November 1, 2006 4:44 PM permalink

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?

60. Comment by somerandomguy on November 2, 2006 6:21 PM permalink

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.

61. Comment by hooba on November 4, 2006 3:03 AM permalink

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.

62. Comment by William Stone on December 2, 2006 6:32 AM permalink

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)

63. Comment by Bivash on December 12, 2006 7:06 AM permalink

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.

Bivash

64. Comment by Ohma on December 16, 2006 8:25 AM permalink

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.

65. Comment by Rich on December 16, 2006 9:41 AM permalink

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?

66. Comment by Gabriel on December 31, 2006 4:21 PM permalink

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.

67. Comment by Rich on December 31, 2006 4:40 PM permalink

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.

68. Comment by Az on January 5, 2007 8:01 AM permalink

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 mouth....here 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 lunch.....it 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..... :>

....here 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.... :>

69. Comment by Nathan Baum on January 6, 2007 7:53 AM permalink

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.

70. Comment by StatmanCrothers on January 10, 2007 7:12 PM permalink

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!

71. Comment by on January 22, 2007 12:21 AM permalink

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.

72. Comment by ry guy on February 16, 2007 3:46 AM permalink

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?

73. Comment by Patrick Simpson on March 11, 2007 8:56 PM permalink

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?

74. Comment by Rich on March 11, 2007 9:25 PM permalink

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.

75. Comment by Erik on March 11, 2007 10:15 PM permalink

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

76. Comment by Brandon on March 12, 2007 8:44 AM permalink

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.

77. Comment by on March 12, 2007 8:09 PM permalink

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.

78. Comment by Patrick Simpson on March 12, 2007 11:45 PM permalink

"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.

79. Comment by Patrick Simpson on March 13, 2007 1:30 AM permalink

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.

80. Comment by Patrick Simpson on March 14, 2007 12:20 AM permalink

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.

81. Comment by patrick Simpson on March 17, 2007 1:20 AM permalink

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?"

82. Comment by Rich on March 17, 2007 8:45 PM permalink

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.

83. Comment by Rich on March 17, 2007 8:57 PM permalink

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" ;)

84. Comment by Rich on March 18, 2007 1:22 PM permalink

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

85. Comment by Patrick Simpson on March 18, 2007 6:03 PM permalink

"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.

86. Comment by Rich on March 18, 2007 9:39 PM permalink

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.)

87. Comment by patrick Simpson on March 20, 2007 12:47 AM permalink

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.

88. Comment by on March 20, 2007 2:40 AM permalink

"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 t

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