Dear Richard,
Sorry, I do not understand what you mean when you say that you view what Bob is doing from Alice's frame.
What does Alice actually view? In figures 2, 3 and 4 all you show is the light transmitted and received by Bob. Nothing that is received by Alice.
So how can we view it from her frame of reference?
Maybe I am missing something. Would appreciate if you could clarify.
Many thanks, John.
Hi John,
The previous part of this series was about how Alice could attach coordinates to events in spacetime. When I say things like "how things look in Alice's frame" I mean that we should think in terms of the coordinates that Alice would assign to events using the process described in that installment. I don't mean to imply that Alice will be receiving the flashes of light used by Bob: rather, she'll be using her own flashes of light to assign coordinates to the same events but I'm not showing those flashes on the diagrams in this article or else they'd be confusing and cluttered.
You don't understand how Einstein used "practical geometry" (his term for constructivist mathematics) to formulate the relativity of simultaneity, so you don't understand how he deprived the argument of logical content by saying that one point (M in the case of the train experiment) "naturally" coincides with point M'. Below is a discussion of Einstein's mathematical orientation in its historical context. Einstein is trying to avoid paradox, but if there are no paradoxes, his arguments are unmotivated. We are just starting to understand the pernicious effect of constructivism in mathematics.
You are VERY far behind the times, very ignorant. I suggest you start by reading A. Garciadiego, BERTRAND RUSSELL AND THE ORIGINS OF THE SET-THEORETIC 'PARADOXES.' Then there is a good online article by Jose Ferreiros on the weird foundations of Cantor. Also, a good bibliographical essay on recent work in analytic philosophy, on her BU website.
Relativity, natural mathematics, constructivism, intuitionism, blah blah blah, are all OVER. Get with with it.
Search ResultsSSRN-Paradox, Natural Mathematics, Relativity and Twentieth ... Ryskamp, John Henry,Paradox, Natural Mathematics, Relativity and Twentieth-Century Ideas(June 17, 2008). Available at SSRN: http://ssrn.com/abstract=897085 ... papers.ssrn.com/sol3/papers.cfm?abstract_id=897085 - Similar pages by J Ryskamp
To help me put your example into perspective, I assigned names to Alice�s and Bob�s frames. I thought about calling the frames Alice�s and Bob�s cars on intersecting roads. I settled on Earth for Alice�s frame and moon for Bob�s frame. Both frames are moving through space at different speeds and different directions relative to each other and also relative to all other moving bodies in space. I labeled you and I as remote observers residing on the surface of the sun which is also moving through space. Allice and Bob and you and I have all the same information you show in your diagrams.
Now with all those labels, we look at your diagrams. Event T on earth begins a trip for a flash of light. Events P and Q are reflections on earth that are simultaneous. Event R is the joining of the two simultaneous reflections. That make event R represent another simultaneous event. This is similar to any and all measurements of the speed of light on earth, in Alice�s frame. Regardless of where on earth or when on earth, the speed of light is always the same and a round trip always measures the same distance between equally spaced objects on earth.
The same conditions described for earth also apply to the moon.
When bob looks at the events on earth, he sees a moving earth and the points on earth are fixed relative to earth but moving relative to the moon as well as moving relative to you and I on the sun. Bob and you and I see point T on earth when the flash first occurred. We also see point T in space. The earth moves from point T in space. Alice and Bob and you and I know that the earth and moon and sun are moving in space and time. Although Alice observes the simultaneous events at P and Q, Bob and you and I know that our observance is a false perception because we know all the facts. Using all the data, we calculate the different perceived arrival times and concur that the events are in fact simultaneous.
The same conditions apply when Alice and you and I observe the same series of events on the moon.
Remember, Allice and Bob and you and I have all the same information you show in your diagrams. We all know about your diagram with different start times and perception instead of the facts. We know that we must make calculations to adjust for false perception.
Nothing in your diagram precludes inclusion of the facts that we all know. We have different perspectives of events but we also have the ability to collect data and include that data in our calculations to show different begin and end times as well as the fact that simultaneous events are simultaneous regardless of the frame of reference where the observer resides.
Very clear illustration of the relativity of simultaneity, demonstrating the concept with easy to read diagrams.
What I would like to see is the frequently used train example, but with what observers would see( aboard the train as well as on the tracks). For instance, the case where two bolts of lightning are fired simultaneously (from the track observer's perspective) at two points on the track is often used. The illustrations are quite good at showing that the track observers deduces that the lightning strikes are simultaneous from his perspective while the train observer deduces that the lightning strike at the front of the train occured earlier than the one at the back of the train. However, what is hard to find is what both observers would actually see