Relativity of simultaneity

  1. Hello everybody,
    I know that there are a lot of questions about simultaneity, but mine is based on a specific aspect of it.
    In the book University physics ( with modern physics) they explain the train example and how the person inside of it sees the events happening non simultaneously.
    However, they say that : "You may want to argue that in this example the lightning bolts really are simultaneous and that if Mavis at O' could communicate with the distant points
    without the time delay caused by the finite speed of light, she would realize this."

    and then they add "But that would be erroneous; the finite speed of information transmission is not the real issue. If 0' is midway between A' and B', then in her frame of reference
    the time for a sigual to travel from A' to 0' is the same as that from B' to 0'.
    Two signals arrive simultaneously at 0' only if they were emitted simultaneously at A' and B'. In this example they do not arrive simultaneously at 0', and so Mavis must conclude that the events at A' and B' were not simultaneous."

    This does not really convince me, I mean I always thought that simultaneity was based on the finite speed of light (if it was infinite , the limit of the ratio of t1/t2 = 1 {t1 and t2 being the time at which the observer inside the train actually 'sees' the light after the lightning had struck}.

  2. jcsd
  3. A.T.

    A.T. 6,352
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    No, it is based on the same speed of the same light measured by every observer.
    No, relativity of simultaneity has nothing to do with signal delay due to finite speed of light. That is just a measurement problem you can account for.
  4. Thank you A.T,
    But i would appreciate it if you could elaborate more on the concepts.
    My problem is the following:
    We are saying that person A inside the moving train, is moving towards the light that was emitted at the front of the train, and away from the light emitted at the back of the train.
    Thus, person A will encounter the wave in front of him before the wave behind him. And since person A is midway between the front and behind of the train, he will think that the light coming from the front was emitted before.

    So it all seems to be that it is due to the finite propagation of light. I mean if it was infinite, then he will see both fronts in 0 time, so the times are equal.

    If my point is still not so clear, let me try to explain it with this example: Suppose there is a device that has 0 delay, attached to the back of the train, and another one attached to the front of the train. Now suppose these devices are connected to person A, and they shock him (again with 0 delay) when the lightning strikes any of the devices in the back or the front of the train, and he feels the strike with 0 delay. Does simultaneity still hold here?

    It seems to me that the event appears simultaneous or not, due to the propagation of light and speed of the observer. So the event APPEARS simultaneous or not, due to the speed of light being equal in all inertial frames, and the speed of the frame itself. But 'APPEARS' does not mean that this is the truth.
  5. A.T.

    A.T. 6,352
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    No, the signal velocity is known and can be calculated out, to yield a measurement result independent of it. Doing so in different frames yields relativity of simultaneity.
    No. The event IS simultaneous or not, due to the speed of light being equal in all inertial frames.
  6. Can you please relate it to the example that I gave, with the sensors?
  7. A.T.

    A.T. 6,352
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    Search the forum. Relativity of simultaneity and your example have been discussed many times here.
  8. Okay Thanks for your effort A.T.
    I will try to look for a similar thread, and in the mean time, I will wait for other people's useful comments
  9. bcrowell

    bcrowell 6,253
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    I would put the logical sequence the opposite way compared to the textbook that samerking quoted. The Lorentz transformation can be derived from the symmetry properties of spacetime, without even mentioning light (Morin 2008, Rindler 1979). This analysis proves that spacetime has a frame-independent velocity c, and that particles with zero rest mass travel at c. If light has zero rest mass (the current upper bound is very low), then light happens to travel at c, but this is a consequence of the theory, not an assumption.

    Now suppose that there exists some mechanism for sending signals at a velocity greater than c. Then causality would be violated, because there would exist cases where, in a certain frame, a signal propagates from event A to event B, but in another frame event B comes before event A, so the signal is received before it's sent.

    If we assume causality, it follows that light travels at less than or equal to the universal velocity c (equality holding in the case where the photon's rest mass happens to be exactly zero).

    In this logical framework c is the maximum speed of cause and effect, and therefore the assertion quoted in the textbook is exactly backwards. I'm not saying that the textbook is wrong and Morin and Rindler are right. It depends on what you take as your axioms. As a matter of taste, I think the traditional Einstein-style axiomatization is lousy, because it grants a special role to light. Light was the only fundametal field known in 1905, but we now know that it's just one of many fields, and it doesn't deserve to be singled out for special treatment.

    Morin, Introduction to Classical Mechanics, Cambridge, 1st ed., 2008
    Rindler, Essential Relativity: Special, General, and Cosmological, 1979, p. 51
  10. What the book is saying is that if the all the rules of Special Relativity applied (finite speed of light, length contraction, time dilation) and clocks are synchronised using the Einstein synchronisation method with regular finite light and if we had an alternative secret method of instantaneous communication not involving light and not subject to the rules of SR then Mavis would conclude that the strike events are not simultaneous according to her light synchronised clocks. Of course, Mavis might alternatively conclude that her light synchronised clocks are not synchronised in an absolute sense. In such a hypothetical universe, Mavis would be able to determine her absolute state of motion, because if two events are simultaneous according to light signals and according to the instantaneous transmission method, then she must be at rest with an absolute reference frame.

    Special Relativity requires that the speed of light is (1) finite, (2) independent of the speed of the emitter, (3) measured to be the same relative to the rest frame of any inertial observer and (4) is the maximum possible speed for the transmission of information. Remove any of those conditions and (I think) SR falls apart.
  11. JesseM

    JesseM 8,489
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    Here was a recent extended thread on the subject. If you read it and are still confused, perhaps you could respond to the step-by-step argument I gave in post #34 and tell me whether you agree with each step.
  12. JesseM

    JesseM 8,489
    Science Advisor

    That's only how things look in the frame of the track-observer where the train is in motion. In the train's own rest frame, the train isn't moving at all, instead it's at rest while the ground is moving past it. In SR all frames are considered equally valid, there is no objective truth about who is really moving and who is really at rest.
    "0 delay" is meaningless in relativity because of the relativity of simultaneity, which is exactly what the train example is intended to demonstrate. A signal that was moving infinitely fast in one frame (so in that frame the event of the transmitter being activated and the event of A receiving the signal would be simultaneous) would be moving at some finite FTL speed in another frame, and would actually be moving backwards in time in another frame (i.e. that frame would say A received the signal before the transmitter was activated). If you specify that you want this signal to move infinitely fast in the track frame, then in that case A will receive the signals simultaneously; but if you specify that you want the signal to move infinitely fast in the train frame, in that case A will receive one signal later than the other.
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