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B "Forced Conclusion" in Train-Embankment Experiment

  1. Mar 24, 2016 #1
    In the train-embankment thought experiment described by Einstein in his "public" version of STR, he says the following:
    “Hence the observer will see the beam of light emitted from B [the front of the train] earlier than he will see that emitted from A [the rear of the train]. Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B [front of train] took place earlier than the lightning flash A [rear of train].”
    [ REF: https://en.wikisource.org/wiki/Relativity:_The_Special_and_General_Theory/Part_I ]

    I take issue with the phrase "must ... come to the conclusion." I actually think it very unlikely that the passenger would jump to that conclusion. Here is my reasoning:

    The only way to "see" a difference in the arrival-time of these two light beams would be to detect it using sophisticated machinery. For example, assuming a 20-meter long train car traveling at 120 kph, the difference in arrival time would be around 200 trillionths of a second (if my calculations are correct). Those with access to such sophisticated machinery would already be quite aware of the hazards in jumping to any conclusion about the "real" time-origin of the two beams, especially knowing all the debates in physics that have been raging about exactly such problems. Thus, the passenger, having "observed" the phenomena on a measuring-device, would probably come up with any number of theories to explain the findings, and would withhold judgment until more definitive evidence was uncovered. Note also that anyone able to measure such beam arrival-times would probably also be able to detect a red- or blue-shift in the frequency of such light beams. Would it not be true that, in Einstein's scenario, there would be a blue-shift in the "B" (front) beam and a red-shift in the "A" (rear) beam? If so, the sophisticated passenger would have stronger (but not definitive) evidence that s/he was not standing still relative to A and B, but was actually in an inertial frame moving toward B and away from A. This color-shift example casts even more doubt on the claim that the passenger would be forced to make a specific conclusion from the observed phenomena.
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  3. Mar 24, 2016 #2


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    It's a thought experiment. All the instruments are perfect and trustworthy and all the assumptions that go into the scenario are guaranteed to hold.
  4. Mar 24, 2016 #3


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    I get a difference of ##7.4 \times 10^{-15}## seconds, which is about five orders of magnitude smaller. The difference will be ##\gamma v \Delta x / c^2##, where ##\gamma = 1 / \sqrt{1 - v^2 / c^2}##. I get ##v = 33.3## (remember that the units need to be m/s, not kph), ##\gamma = 6.22 \times 10^{-15}##, and ##\Delta x = 20## by hypothesis.

    What debates are you referring to?

    Compared to the frequencies observed by the observer on the embankment, yes.

    This is true if "A" and "B" refer to the sources of the light beams (and if we also assume that the "natural" frequencies of both beams are the same, but that's a minor point). But the sources of the light beams are objects, not events. The conclusion Einstein is talking about is about the events of the two lightning strikes--in other words, specific points in spacetime, not objects. The fact that the passenger can (correctly) conclude that the inertial frame in which he is at rest is moving relative to the sources of the light beams he sees does not change his conclusion about the timing of the events of the lightning strikes, because one cannot be "at rest" or "moving" relative to an event (as opposed to an object).

    Here's another way to look at it: the lightning flash at A happens at a particular instant at A; and the lightning flash at B happens at a particular instant at B. At the instant the flash from A is emitted, A is co-located with the rear of the train; and at the instant the flash from B is emitted, B is co-located with the front of the train. The fact that A and B move, relative to the rear and front of the train (respectively), after the flashes are emitted is irrelevant to determining the times of the flashes relative to the passenger, because the speed of the light coming from each flash is independent of the motion of A and B relative to the passenger (that is the key physical fact that was not recognized in pre-relativity physics). And the passenger, by hypothesis, is equidistant from the front and rear of the train, therefore he is also equidistant from the events at which the flashes were emitted. That is why the passenger must conclude that the lightning flashes happened at different times in his frame.
  5. Mar 25, 2016 #4


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    Einstein is describing the results of an experiment in a hypothetical universe where the speed of light is constant and independent of the motion of the source, and where this is known to the experimenters. The conclusion of simultaneity (or lack thereof) is correct in such a universe, independent of any argument over how the real universe behaves.

    Einstein then goes on to show that then-outstanding problems in physics can be resolved if this is how our universe behaves. Not so hypothetical after all.

    You are correct that the experiment isn't practical to do, but that doesn't really matter. One can always scale up the train and run it in free space instead of on the Earth. Whether there's a Doppler shift depends on details that we didn't discuss. Again we can vary the experiment slightly. Use four identical lamps, one mounted at the front and one at the rear of the train, and one at the front and one at the rear of the platform. You can arrange a mechanism so that the lamps flash as they pass each other. Then both the train and platform observers will receive one shifted and one non-shifted pulse from each end of the train and can verify that both "front" emission events were simultaneous and both "rear" emission events were simultaneous.
  6. Mar 25, 2016 #5
    Please allow me to rephrase my original question with greater clarity, and in line with your comments: the creation of the light-beams (due to the lightning strikes at A and B) are events in space-time. The instant after those events occur, each light-beam travels toward the position of the passenger. When the light-beams arrive, the passenger detects that the front beam (from the event at B) is blue-shifted relative to the rear beam (from the event at A), and that the front beam arrives before the rear beam. The passenger is free to speculate that the speed of both beams is constant and equal, in an "absolute" sense. The passenger is also free to use the clue of the color-shift differences to conclude that the two events in space-time may actually have happened simultaneously, even though the information about the event at B arrived at the passenger's location before the information about of the event at A.

    The passenger may further overcome the perplexing situation of realizing that the information about the event at B arrived "more quickly" than the information about the event at A, even though the carriers of that information (the light-beams) must be moving at exactly the same constant speed. Simply put, the passenger concludes that s/he is moving toward the information that is arriving from the event at B, and away from the information that is arriving from the event at A.
  7. Mar 25, 2016 #6


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    The passenger has no room for speculation. It is a given of the problem that the speed of both beams as measured in his rest frame is equal. The givens of a thought experiment are not debatable. They are facts of the matter and must be accepted.
    The frequency of the received light will depend on the frequency generated at the emitter and the velocity of the emitter relative to the receiver. It can not depend on any "absolute" state of motion of the receiver. That is a given of the problem. It is also completely irrelevant to the thought experiment.
    The information is carried on the leading edge of the light pulse. It moves at the speed of the light pulse.
    It is a given of the problem that no such conclusion can be reached: The laws of physics are identical regardless of one's choice of inertial reference frame.
  8. Mar 25, 2016 #7
    There is nothing in the thought experiment that says that the frequency of the light is irrelevant to the thought experiment. Moreover, this difference in frequency is entirely relevant to my questions about the thought experiment, and it is those questions to which you are, in fact, responding.

    Your statement does not overcome the fact that the information, like the light pulses, arrive(s) at different times to the passenger.

    Your statements would lead one to conclude that this is a thought experiment that precludes thought itself within the experiment. By which one could only conclude that thinking is forbidden within the world of relativity physics, and that therefore the only valid frames in which relativity physics can even be considered are those in which thinking cannot exist. Yet in reality, I think, and indeed many other people think (including you). Therefore, since thinking cannot exist within a relativity frame, relativity itself cannot exist for many people (including you). Translation: I would hope for a more thoughtful reply. To my mind, you have dismissed and sidestepped, but not actually or thoughtfully answered, my core questions about the thought experiment.

    The fact remains that the passenger could easily detect a difference in the frequency of the light beams arriving from the two different events. If allowed even a small modicum of thought, the passenger could conclude that the two events occurred simultaneously but that the information from event B arrived before the information from event A, and that the passenger is moving toward the incoming information from event B and away from the incoming information from event A.
    Last edited: Mar 25, 2016
  9. Mar 25, 2016 #8


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    The Doppler shift is incidental. Other variations of the scenario could eliminate it without changing the conclusion regarding simultaneity, like what Ibix described.

    In addition to being incidental, it is also irrelevant. Light of any frequency travels at c. The observed Doppler shift does not change the speed of propagation.

    It is a given. The passenger is required to reason based on this assumption. The question is what conclusion is required based on this assumption. Indeed, with this as a given the passenger must conclude that the flashes were not simultaneous.

    No, he isn't. The given is that light of any color or any source travels at c, so observing the Doppler shift cannot change the conclusion.
  10. Mar 25, 2016 #9
    Givens: The light moves at light speed. The passenger receives the information about event B before receiving the information about event A.
    Challenge: I propose that the passenger could perceive the color of the light beams, and that the color is relevant, because it provides a clue that could help explain, to the passenger, the reason for the sequence in the arrival-times of the light beams.

    You say that my challenge is irrelevant, but the color difference in the light beams is entirely consistent with all the terms of the thought experiment, and therefore it is entirely relevant.
  11. Mar 25, 2016 #10


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    Being consistent with the experiment and being relevant to the experiment are two different things. The light being being emitted by a ruby laser attached to the train is consistent with the experiment. The light being emitted by a strobe mounted on the embankment is consistent with the experiment. But both are irrelevant. The important thing is that a pulse of light was emitted at the time and place of the lightning strike.
  12. Mar 25, 2016 #11
    You mean: both "front" emission events were simultaneous with one another and both "rear" emission events were simultaneous with one another. This is definitely an interesting scenario, but aside from muddying the water, I do not see how they definitively put to rest the passenger's conjecture as to whether the front and rear events were simultaneous with one another.
  13. Mar 25, 2016 #12
    Dale and jbriggs444: Let me use an analogy. By your arguments, the fact that Maxwell's demon used up energy while busily opening and shutting a door between two containers of gas was "consistent with but irrelevant to" Maxwell's original thought experiment, because it did not lead to Maxwell's conclusion. Yet this challenge--that the demon must use energy to open and shut that door--allowed the second law of thermodynamics to be maintained despite Maxwell's proposed demon.

    Do you think it would have been valid for Maxwell to have done as you are proposing to do--to dismiss a constructive challenge to his thought experiment by using the term "irrelevant," without responding to the actual challenge itself?
  14. Mar 25, 2016 #13
    More simply, it is a given that the passenger is at rest in his/her frame and therefore cannot conclude that s/he is 'moving towards the information that is arriving...'
  15. Mar 25, 2016 #14


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    The challenge you pose, if correct, would contradict the givens of the experiment and prove the assumptions underlying relativity to be false. However, your challenge is not well thought out. It is not correct.
  16. Mar 25, 2016 #15
    I invite you, or others, to explain--without simply dismissing me--why my challenge is "not correct." So far, no one on this forum, in this thread, has responded in a way that seems consistent with the spirit with which Einstein's theory would have been received and discussed at the time it was proposed. Negating a serious question about a topic as "irrelevant" or "not correct" or being "not well thought out" (despite the abundance of evidence that, indeed, I have thought this out quite carefully and it is a robust argument, still waiting for an equally robust answer) is hardly educational.

    To quote Einstein himself: "I should load my conscience with grave sins against the sacred spirit of lucidity were I to formulate the aims of mechanics in this way, without serious reflection and detailed explanations." (Public STR)
  17. Mar 25, 2016 #16
    Perhaps this will clear the air. I believe all the previous posters have relied upon one assumption: that, in Einstein's thought experiment, it is a "given" that the time at which information about events are received by a receiver, requires the receiver actually to understand or conclude the timing and sequencing of the events themselves.

    All I need is for you to quote from the STR itself, to show me where the above was actually proposed as a "given" by Einstein himself, in the STR.
    Here is a source you can use:
  18. Mar 25, 2016 #17
    Just to tie up some loose ends:

    1. The challenge to Maxwell's demon was meaningful and relevant because it exposed something about the necessary nature of the demon itself. Maxwell could have said, "oh, but this is a special demon that doesn't really use up any energy," but that would have violated the laws of physics as they were at that time understood, even though those laws stood outside his thought-experiment.

    2. My challenge to Einstein's passenger is meaningful and relevant because it exposes something about the necessary nature of that passenger, in ways that refer to laws of nature that lie outside the thought-experiment but are clearly relevant to it. In order for a passenger to "conclude" anything, the passenger must be able to reason logically--clearly, the passenger is not just an inanimate object. And in order for the passenger to perceive a difference in the arrival-times of the different light-beams, the passenger must have access to extremely sophisticated equipment (as PeterDonis has pointed out, the time difference is even smaller than I had originally thought). This is a requirement within the thought experiment itself. My stipulation about the color-shift in the light beams is as consistent with the requirements of original thought-experiment, as is the stipulation about Maxwell's demon actually using up energy when it opens and shuts the door.

    3. The conclusion to the challenge to Maxwell's demon is that the second law of thermodynamics still holds. The conclusion to my challenge about Einstein's passenger would be that the passenger is NOT forced to conclude anything definitive about the actual timing of the events at A and B.

    I have raised this challenge to those on this forum, and I am still waiting for a meaningful reply that not only supports, but also lives up to the spirit of thoroughness, thoughtfulness, civility, and intellectual integrity of, the original proponent of the experiment. You may recall that Einstein himself was at times the recipient of challenges to other of his thought experiments, and he treated his challengers with respect and never doubted either their intellectual capacity, or the seriousness of the challenges themselves.
  19. Mar 25, 2016 #18


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    If you, given suitably accurate instruments, careful setup and an assurance that light always travels at a particular fixed speed were to receive a light signal that had followed a straight path and was emitted from something one light-second away, could you conclude that the time the light was emitted was one second prior to the time of its arrival?

    This is in an experimental setup that is free from smoke, mirrors or other gimmicks. You get to set it up yourself. Nobody is trying to pull the wool over your eyes.
  20. Mar 25, 2016 #19
    That's not a well-thought-out question or experimental setup. For starters, since you propose that I am within the experiment, I can tell you that I could not possibly set up such an experiment nor validate it.

    If you have a point to make, please make it, and please also make it relevant to Einstein's thought-experiment and my challenge to it.
  21. Mar 25, 2016 #20


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    In the interest of staying polite, I'm out.
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