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Einstein & Simultaneity: Two Questions

  1. Aug 24, 2013 #1
    I’ve been trying to get my brain around Einstein’s theory of special relativity, and I find I'm a bit perplexed about his thought experiment (TE) involving the speeding train and the two simultaneous lightning strikes.

    To briefly summarize, observer M is standing on a stationary “embankment” alongside the railroad tracks, midway between two points A and B. The train is about to speed by, with another observer M’ sitting in the exact middle of the train. The length of the train is identical to the distance from A to B. At the exact moment that M’ aligns with M, two simultaneous lightning strikes occur; one at A and one at B. (The complete description can be found in Einstein’s book, “Relativity: The Special and the General Theory, Chapter 9)

    Einstein then contends that whereas M will experience both lightning flashes simultaneously, M’ will NOT.
    I don’t disagree with Einstein’s contention; but I have two questions regarding his logic.

    1) As I read it, he’s trying to set the stage so that he can demonstrate the manifestation of a “peculiar phenomenon”; i.e., that because light has a universally consistent speed for all observers, the passage of “time” may be different for different reference frames.
    However, in the TE, he seems to violate, or forget about this fundamental concept. That is, he predicts that the reason M’ will see the light from B, before A, is because M’ is speeding TOWARDS the light coming from B, and AWAY from the light coming from A. In other words, relative to M’, the light from B is traveling faster than the light from A; i.e., at different speeds.

    However, if we invoke the theory of the Consistency of C (the speed of light), and define the moving train as a legitimate frame of reference, we would then view the lightning strikes as occurring TO the train, and each beam progressing down the aisle towards M’ at equal speeds, propagating through identical distances, and consequently, arriving at M’ SIMULTANEOUSLY. Ergo, no “peculiar phenomenon”.
    (We should also assume that the train has windows at both ends, and M’ either has eyes in the front and back of his head, or has some other clever contrivance by which he could make such an assessment.)

    Question 1: Am I missing something, or is there a reason that Einstein did not invoke the theory of Consistency of C?

    2) I would argue that the reason M’ (as described in the original TE) experiences the bolt from B before the bolt from A (and not in the same simultaneous manner of M) is NOT because of the train’s velocity V, but simply because M’ happens to be situated closer to B than A at the moment of interest (i.e., when the wave-front from B is passing by).

    That is, we could imagine a similar TE, with no train whatsoever. In this TE, M is again at a midpoint between A and B, but M’ is a few feet closer to B - and perfectly stationary. If we again ask the two simultaneous lightning strikes to occur at A and B, M’ will see the flash from B before M does, and experience the flash from A a short time thereafter - while M experiences both flashes simultaneously. The “peculiar phenomenon” occurs exactly the same as the original TE, even though there’s no motion involved whatsoever. And in reality, there’s nothing “peculiar” about it at all. Everything can be explained with simple math. And there’s no need to begin speculating about how we now need to reassess our understanding of time and reality.
    In other words, it seems that Einstein is trying to make it appear as if “speed” is the generator of the curious phenomenon, when it really has nothing to do with it.

    Question 2) Isn’t Einstein un-necessarily complicating things by including this speeding train into his TE? And thereby creating a “solution” for a problem that doesn’t even exist.

    In conclusion, I should say that I actually have no problem with the idea that “time” (i.e., the speed at which “physical information” is propagated between physical “stuff”) may be affected by the speed at which the stuff is plowing through space.
    A) I would think some type of “aether-like property of space” would be required to produce this phenomenon, and
    B) I’m puzzled why Einstein chose this peculiar, confusing, somewhat irrelevant thought experiment as the springboard to justify his theory.

    Any and all insights greatly appreciated.

    Thanks in advance…
  2. jcsd
  3. Aug 24, 2013 #2

    Doc Al

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    No, he's just invoking the principle of relativity: That any frame is as good as another to analyze what's going on. Looking at things from the embankment, it is clear that M' is moving towards one flash of light and away from the other. So M' will receive the light from the front of the train before the light from the rear of the train.

    Note that Einstein does invoke the invariance of the speed of light. The speed of light with respect to the embankment is the usual speed c. And the speed of light with respect to the train is the usual speed c.

    Careful. While it's true that M' views the light flashes as moving at the usual speed c with respect to him, the light flashes would only reach him simultaneously if the lightning strikes were simultaneous with respect to him--which they are not. That is the point.

    You're missing something.
  4. Aug 24, 2013 #3


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    It's best to think that of a lighting flash as something that happens to the train and the ground: There was a flash of lightning, and it left a scorch mark on the ground and on the train when it hits. Now both observers will agree that the spot on the train that now carries a scorch mark was at the same place at the same time as the spot on the ground that now carries a scorch mark.

    He is invoking that principle. Start from the point above, that the front lightning flash left a scorch mark on the front of the train and the ground when it hit; and the rear lightning flash did the same at the rear of the train; assume that the light signal from scorch mark to observer travels at a constant speed independent of the observer's speed; and you conclude that if the light from the two equidistant lightning strikes reaches one observer's eyes at the same they won't for the other observer.

    Yes, in this case M' sees the B flash a bit sooner. But - and this is the critical difference - in this case when M' calculates in the speed of light delay, he will still agree with M that the two events are simultaneous. He'll say "OK, B is 5 light-seconds away from me and light from the B flash hit my eyes at exactly noon.... Obviously the B flash happened at 5 seconds before noon. Point A is 10 light-seconds away from me and light from the A flash hit my eyes at 5 seconds past noon... Obviously the A flash also happened at five seconds before noon... seems like they happened simultaneously five seconds before noon." The observer M will be working with different distances, but as long as he is at rest relative to M' he will agree with M' that the two flashes were simultaneous (and if they've synchronized their wristwatches, they'll agree about the "five seconds before noon" part too).

    However, if M and M' are moving relative to one anther, they will not get the same results, and that's the point of the train experiment.

    BTW, it's a useful exercise to redo the thought experiment assuming that the train is at rest and the platform and the earth are moving backwards... That's a good way of seeing that relativity of simultaneity isn't just a sort of optical illusion that the train guy suffers from because he's moving and the platform isn't.
    Last edited: Aug 24, 2013
  5. Aug 24, 2013 #4

    Doc Al

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    Well, it's certainly true that by the time the light from the front of the train hits M', he is closer to point B than to point A. So what? He knows that the lightning strikes hit the ends of the train, which are equally distant from him (at A' and B'). So he must conclude--due to the constancy of the speed of light--that the lightning did not strike the ends of the train (or A and B) at the same time.

    Nothing mysterious about this, but I don't see its relevance.
  6. Aug 24, 2013 #5


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    Hi, jeffkosmo, The principles involved here are clearer if a single light source flashes when the mid points of train and embankment coincide. The light postulate says the light goes at the same speed with respect to both train and embankment.
    From the view of the bank the light goes at c in forward and aft directions and reaches the end points at the same time. But in this view the light and train are both moving, so the light reaches the train ends at different times.
    From the view of the train the light is moving at c in forward and aft directions and reaches the ends ot the train at the same time. But in this view the bank and the light are both moving, so the lingt reaches the end points on the bank at different times.
    Einsteins work was motivated in part by unsymmetries in electromagnetic phenomena in moving bodies, so you can see that his arrangement provides good symmetry between the two viewpoints.
    The ether idea was investigated and it didnt work.
  7. Aug 24, 2013 #6
    Thanks for taking the time to reply. I appreciate it.
    I've got a question about your comment:

    You say...

    As I re-read Einstein's thought experiment, he seems to go to great pains to clarify that points A and B of the train coincide with points A and B of the embankment, such that when the lightning bolts strike, they simultaneously strike A and B of the train, AND A and B of the embankment - simultaneously.

    If the strikes are simultaneous with respect to the train, and M' is ON the train (sitting directly in the middle) - how can they NOT be considered to be simultaneous to M'? Are you suggesting that the frame of reference of M' somehow lacks legitimacy, or is somehow over-ridden or trumped by the frame of reference of M? Such that, if M wasn't standing there observing, then M' WOULD report both strikes as occurring simultaneously?

    Or, are you saying that, yes, the strikes ACTUALLY OCCURRED simultaneously, but M' is justified in believing they didn't? Which I still can't buy - because according to his reference frame (not the frame of M), the light from both flashes MUST travel down the aisle at C?

    Or, are you saying that from the perspective of M, M' "should" perceive the bolts to be non-simultaneous. (regardless of what M' actually reports.)

    Thanks for your patience.
  8. Aug 24, 2013 #7
    Doc Al,

    Thanks for taking the time to reply.

    Actually, he DOESN'T know this. ALL he knows, or all he can INFER is based on when the flashes of light reach him. And since he is sitting directly in the middle of a moving reference frame, in which BOTH wave-fronts are traveling towards him at exactly C, from an equal distance apart, IMHO, he can only infer that the strikes occurred simultaneously.

    Let me ask you this (And maybe this will help clarify things for me): If M was NOT present on the embankment, and the exact same lightning strike event happened, what would M' infer?

    Thanks in advance...

  9. Aug 25, 2013 #8


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    You are the one that is promoting a “peculiar phenomenon”. You're claiming that something (anything, such as a little girl on a tricycle) can be traveling from the front towards two observers, M' in front of M, while something else (such as a little boy on a bicycle) traveling from the rear can both arrive simultaneously at M and both arrive simultaneously at M'. That's a very “peculiar phenomenon” and it's exclusively your idea, not Einstein's. Einstein is saying that if they arrive at M at the same time then obviously the girl will have already passed M' and the boy will not yet have reached M'. Or if they arrive simultaneously at M' then the boy will have already passed M and the girl will not yet have reached M.
  10. Aug 25, 2013 #9

    Doc Al

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    To avoid confusion, let's call the ends of the train A' and B' and the points on the embankment A and B. Yes, Einstein sets things up so that according to the embankment observers the lightning strikes occur at the moment that M' (the midpoint of the train) passes M (the midpoint on the embankment) and that at that moment (again, according to the embankment observers) the ends of the train A' and B' align with points A and B on the embankment. So the strikes do hit A, A', B, and B' simultaneously according to the embankment observers.

    The entire point is that both frames are perfectly legitimate! If the embankment frame concludes that the light from the strikes reaches the midpoint of the train (M') at different times, then surely the train frame must agree.

    The point is that whether one deduces that the flashes were simultaneous depends on the frame doing the observation. Simultaneity is frame dependent. In fact, based on observations made, and the fact that the train observers must agree that the light travels the length of the train at the speed of light, the train observers must conclude that the strike could not possibly have occurred at the same time. Why do you discount their conclusions, which are based on the same physics that the embankment observers used?

    Do you agree that the light hits M' at different times?
  11. Aug 25, 2013 #10

    Doc Al

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    No, it is GIVEN in the set up of the experiment that the lightning strikes the ends of the train.

    Note that you assume they are an equal distance apart, thus you must agree after all that the strikes hit the ends of the train. In any case, he can only conclude that the strikes occurred simultaneously if the light from each reached him at the same time. But we know that it doesn't.

    M is just a point on the embankment midway between the points A and B. It's purpose is to allow you do clearly define the set up. That's all. There is no need for an actual observer at that point.
  12. Aug 25, 2013 #11
    Doc Al,

    Thanks again for taking the time to comment.
    I think I may be getting closer to articulating what's bugging me about this thought experiment.

    First of all, we have to be careful to remember that this is ONLY a thought experiment (TE). To my knowledge, this specific experiment has never actually been attempted. So we're somewhat forced to deal with "reality" as it's painted by the TE's proponent, Albert Einstein.

    Second, as we read Einstein's description (in Ch 9 of his book), we necessarily make certain assumptions. And maybe this is where our interpretations may differ.

    You say, "But we know that it doesn't" (I.e., We know that the light from A and B doesn't reach M' at the same time.)

    And I guess my REAL question is, or, my contention is, this: If M was "naive", and hadn't yet read about Einstein's theory of relativity, M would be perfectly justified in conjecturing that M' SHOULD encounter the light from B before A. (Because from the perspective of Newtonian physics, M' is moving relative to the two sources of light.)

    However, if M was NOT naive, he would predict (and quite zealously) that the light approaching M' from BOTH directions would HAVE to be traveling towards M' at equal speeds, from opposite directions. Afterall, from the perspective of M', for all M' knows, it's the embankment that's passing by, and M' (and his own personal reference frame) is stationary. Consequently, M' has NO CHOICE but to expect both wave-fronts to meet him simultaneously.)

    However, for some reason, (in my humble interpretation of the TE), Einstein throws out this "straw man" (i.e., the naive M), and then asserts that because M (incorrectly) predicts that M' must encounter the wave from B before A, then it must thusly be! And moreover, because M (incorrectly) conjectures such, then M' MUST agree (that M' experienced the wave-fronts from A and B non-simultaneously.)

    Yes, it would seem from the perspective of a naive M that this is the way the TE should, or might enfold. But I think... no, I contend that this perspective, this conjecture, this "observation" of M is problematic. And in fact, um, plain wrong.

    And consequently, the entire integrity of the TE crumbles.

    As I see it, the TE "should" have gone this way:
    1) Here comes the train
    2) Two lightning strikes occur just as M and M' are immediately adjacent.
    (Technicality alert: M somehow knows the lighting strikes have already occurred, even before the light energy reaches him. Elsewise, the entire TE is even more muddled and problematic.)
    3) A microsecond later or so, M actually sees the 2 flashes from A and B, simultaneously.
    4) In the same time, the train, and M' have moved some dX towards B. But because of the peculiarities of relativity theory, M' experiences both flashes simultaneously as well... but at a position which is no longer immediately adjacent to M.
    5) The train rides into the sunset, and no laws of physics were harmed in the process.

    In other words, getting back to your quote: You say that "we know" the strikes don't reach M' simultaneously. I contend that we don't know this. All we really know is that M (incorrectly, and somewhat disingenuously, I might add) reports that they should.

    Looking forward to your thoughts about my thoughts.


  13. Aug 25, 2013 #12


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    Your point comment after (2) is wrong.

    M does not know this in advance and does not need to.

    So is this

    No. M' will not ever see the strikes be simultaneous if M has.

    You are very confused and letting your disbelief override logic. Draw a space-time diagram and the relativity ( i.e. frame dependence) of simultaneity becoms clear.

    For instance, see post#11 in this thread

    Continuously confused by Special Relativity
    Last edited: Aug 25, 2013
  14. Aug 25, 2013 #13

    Doc Al

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    This "reality" as painted by Einstein has been rigorously confirmed by experiment, many times over. You'd better get used to it!

    This is a confusing statement. M is not naive, he understands the principle of the constancy of the speed of light, so he certainly would say that the light from both ends does travel towards M' at equal speeds as measured by embankment observers. (But of course he also sees the train, and M', as moving.)

    M' has the perfect right to claim that the light from both ends travels at equal speeds towards him as measured by train observers. It does!

    A fallacious (and false) conclusion. Just because things travel equal distances at equal speeds does not mean they arrive at the same time. That would only be true if they started their journey at the same time. That's the whole point!

    Again, why do you think that the prediction that the light will reach the moving M' at different times is incorrect? Are you questioning that light does travel at speed c as seen by the embankment? Where is the mistake in the reasoning? The physics is perfectly sound.


    Clarification: The two lightning strikes occur just as M and M' are adjacent according to M. (M' will be forced to disagree!)


    Nope. Relativity predicts that M' receives the flash from the front of the train first. It's really simple! Do you not agree that it takes time for the light to reach M'? Do you not agree that, from the view of the embankment, the train and M' has moved during the time the light traveled to M'? You cannot just sweep these simple facts under the rug!

    The laws of physics were not harmed, just ignored.

    Again, show where the physics is wrong.
  15. Aug 25, 2013 #14
    Doc Al,

    Thanks again for your response, and putting up with my bull-headedness on this issue.

    In an attempt to better understand where you're coming from, let me get your thoughts about THIS thought experiment:

    M' is sitting in the exact middle of a long train, zooming along at velocity V. There's a large LED panel (B) in the very front of the train (facing back, into the cabin), and another panel (A) at the very back, facing forward.

    M' also has a control box in his hand, so that when he pushes the button, both panels will produce a short, single flash, at the exact same time.

    Question: Which flash will M' see first?

    Thanks in advance,

  16. Aug 25, 2013 #15
    Points 2) and 4) make little sense.
    2) M will know there has been a lighning strike only when the light reaches him. By what magic would he know beforehand.
    4) when the light from B reaches M', it has travelled a lessor distance of dx. When the light from A reaches M', it has travelled a greater distance of dx.
    You should note that any light from a source travels outward at the same velocity whether or not it is going to encounter a 'resting' target such as M or a 'moving' target such as M'. Since M' has moved forward the light will encounter M' before M. Similarily the light from A at the rear of the train will encounter M' after M. You can well see that M' will see the light from B before A and then M' will conclude that lightning strike B occured before lightning strike A ( if M has the light from both lightning strikes meeting him at the same time ).

    the other point with the thought experiment is in your original post
    which carries with it some problems of its own, and may be a source of some confusion.
  17. Aug 25, 2013 #16


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    M' will see the flashes at the same time. In order that the transmission events happen at the same time on M's clock, one flash is sent in each direction and reflected back. The returning light arrives simultaneosly at M's position - and all observers must agree on this. The diagrams illustrate this.

    Attached Files:

  18. Aug 25, 2013 #17

    Doc Al

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    He'll see both flashes at the same time, of course. And, as Mentz114 illustrates, everyone must agree on this fact, regardless of frame. (Just like in the original thought experiment, where everyone agrees that both flashes reach M at the same time and M' at different times.)
  19. Aug 26, 2013 #18


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    You have not adequately defined your scenario in order to get a unique answer. If both panels flash at the exact same time in the frame in which the train is zooming along at velocity V, then M' will see the flash from the front panel (B) first. On the other hand if both panels flash at the exact same time in the frame in which the train is at rest, then M' will see the flashes from both panels at the exact same time. Those are not the only two answers, there are other frames in which M' will see the flash from the rear panel (A) first.

    Your problem is that you think "at the exact same time" has the same meaning in all frames. From the very beginning when you "summarized" Einstein's train TE, you left out the very important statement that uniquely defines his scenario. Here's what you said:

    Your statement "At the exact moment...two simultaneous lightning strikes occur" has no meaning unless you specify which frame that is true in.

    If you look at what Einstein said, he included the words:

    In other words, you have to say in which frame the two remote events are simultaneous (according to Einstein's definition) in order to unambiguously define the scenario. If you don't apply Einstein's definition (or something equivalent), then your questions are meaningless.
    Last edited: Aug 26, 2013
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