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Einstein's Train Paradox

  1. Jun 13, 2004 #1
    In the following the observer at the M' locations does not know if she is moving or stationary. All data is available for analysis one week after it is acquired.

    1).
    Code (Text):


      A__________________M_____M'_____________B


     
    Light sources at A and B emit photons simultaneously both directed to M, the midpoint of the sources. A detector in the stationary frame is located at M' detects the B photon at t = M'B/c then the A photon at t = M'A/c.

    Does the observer at M' determine the lights were emitted simultaneously at A and B?

    Explain.

    2).
    Code (Text):


     A___________________M________M'B________M'A_____A
     
    Same as above only with two detectors each rigged such that the M'B detects only from the B direction, the M'A detects only from the A direction. M'B is located to the right of M.

    Does the observor conclude the photons were emitted simultaneously at A and B?

    Explain.

    3)

    Same as 2), except M' is moving in the direction of B and the light from A was pulsed on before the light from B such that each photon reached M'B and M'A simultaneously.

    Does the observer conclude the photons were emitted simultaneously.

    4). Same as 3), except the photons were emitted simultaneously when M' was at M and the M'B detected photons before the M'A detected photons..

    Does the observer at M' conclude the photons were emitted simultaneously?

    Explain.
     
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  3. Jun 14, 2004 #2

    Doc Al

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    what paradox?

    Not sure what you mean by that, since you state in each example whether she is moving or not.
    Note that in all of these examples the only thing directly measured by the observer is the time of arrival of the pulses according to her clocks. Any other conclusions drawn (for example, about whether the pulses were emitted simultaneously or not) must be based upon additional information that she is presumed to possess used in conjunction with the laws of physics.
    Yes. Based the observer's knowledge of where the lights are and their distance from her, she will conclude that they were emitted simultaneously at t = 0 according to her clock.
    Yes. No difference. (I assume that M'B and M'A are collocated, otherwise two observers are involved.)

    No she does not. What she concludes depends on where she is when she detects the lights and on her relative velocity. For example, say she intercepts the light just as she reaches B. Obviously she must conclude that the light from A was emitted before the light from B.
    When you say "emitted simultaneously" I assume you mean according to the stationary observers.

    The moving observer will conclude that the lights were not turned on simultaneously according to her clocks. If they were turned on simultaneously, just as she passes their midpoint, then she would receive the pulses simultaneously--which she does not.
     
  4. Jun 14, 2004 #3
    No problem with your answers. It is straight forward.

    No this is the same as the first, with two locations as described. The data is available one week after the photons ae detected. We will exclude this quesion.

    I agree. The light from behind is received before the light from in front, just as we rigged the experiment. Obvious, too obvious to be a trick question.

    yes simultaneously in the stationary frame as M' was at M, the stationary midpoint..

    I have been with you for the first three hypos, which weren't all that instructive. Here, though you should check your response. The question had the photons emitted simultaneously as M' passed M. How could she receive the photons simultaneously in the moving frame if the photons were emitted simultaneously when M' passed through M? Only the stationary M midpoint will receive the photons simultaneously. I don't think you intended the answer you gave. It sounds like you meant to say, if she "received the lights at the midpoint".
    Correct me if I am wrong.
     
  5. Jun 14, 2004 #4

    Doc Al

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    I meant exactly what I had said. Read it over:
     
  6. Jun 14, 2004 #5
    This is what you repeated alright. Isn't this the Einstein train experiment that you and I, among others, were arguing to death? If i misread my own post I concede, but I reread it and it is as you understand.

    here is the 4th.
    "4). Same as 3), except the photons were emitted simultaneously when M' was at M and the M'B detected photons before the M'A detected photons..

    Does the observer at M' conclude the photons were emitted simultaneously?"

    I am not arguing with you (yet) but if she ispassing through M as the photons were emittd simultaneously in the stationary frame, would not she detect the photons sequentially later as she approached B and moved away from A?

    Yet the first part of the statement said she would not conclude the lights were turned on simultaneously. Do you see where I might be a tad confused by your statement? When you conclude she would conclude simultaneity for the same condition? That is the photons were emitted simultaneously as she passed through the midpoint M in the stationary frame?
     
  7. Jun 15, 2004 #6

    Doc Al

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    Yep. You keep bringing it up, although we've discussed this many times before.
    Not sure what you mean by this statement.
    Of course she would detect the photons sequentially. I explicitly state that she does not detect the pulses simultaneously.
    Yes, that is the conclusion she would draw based upon her understanding of physics and the invariance of light speed. Paralleling Einstein's own argument, the moving observer can reason as follows: "IF the lights were turned simultaneously (according to my clocks) as I passed the midpoint, THEN I would detect them simultaneously (at a later time). But since I do not detect them simultaneously, they must not have been turned on simultaneously (according to my clocks)."
    I'm not clear where your confusion lies or what question you are asking. Are you asking, Why doesn't she conclude that the lights were turned on simultaneously? If so, see my reasoning above. If not, rephrase your question.
     
  8. Jun 16, 2004 #7
    Aha, I see the point of non-contention. When I was asking you whether she would see the lights 'simultaneusly' I was referring not to whether she would detect the lights simultaneously later, I was referring to whether she would conclude from the manner in which she did detect the lights whether the lights were emitted simultaneously in a). The statiionary frame and/or b). her moving frame.

    I wouldn't want to hold you to responding to this as I just (re)wrote it having been framed differently than in the original post. I am, however, truly interested in determining the 'official rational' for the conclusions of SRT as it applies in this case. She passes M, the midpoint of the source of lights at A and B in the stationary frame, just as the photons are emitted from A and B. She notes this time in her frame, and later detects the photons arriving first from B, then from A. She knows her velocity wrt the stationary frame.

    Does she perceive, or detect that the photons were emitted simultaneously in her frame?
    Using SR what must her conclusion be?

    Take the two cases where
    1. She knows the photons were emitted simultaneously in the stationary frame from A and B when she was at M and,
    2. She was ignorant of the time, or times, the photons were emitted from A and B in the stationary frame when she was at M.
     
  9. Jun 17, 2004 #8

    Doc Al

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    As I've said repeatedly: The moving observer will conclude that the lights were not turned on simultaneously according to her clocks.
    She reaches the same conclusion in either case. The fact that she detects the pulses from A and B at different times allows her to deduce that they were not simultaneously emitted at the moment she passed the midpoint according to her clock.
     
  10. Jun 17, 2004 #9
    Einstein's train hypothetical revisited.

    I am only asking the questions in this way so I can reduce any ambuguous understanding I have regarding simultaneity. For what it is worth I "stipulate" that SR will make the predictions you have stated here. I have my concerns regarding SR, but I do not challenge what SR will do in this case.

    First question. Does the moving observer need to make any SR calculations in concluding that the photons were not emitted simultaneously in her moving frame or is the fact of the staggered arrival of the photons from A and B sufficinent for her concluding nonsimultaneous emission of the photons in her frame?

    Second: Does her knowledge that the photons were emitted simultaneously in the stationary frame when she was at the midpoint of the A and B sources when the photons were emitted in the stationary frame have any bearing on her concluding that the photons were not emitted simultaneously in her moving frame? I would assume no, and that she is quite content to accept the "naive" contradiction based on the staggered arrival times of the photons in her frame.

    Third: You mention that she knew the time the photons were emitted in the moving frame from her clocks, which she obviously looked at at when she was located at M, the midpoint of A and B in the stationary frame. Were her clocks used in concluding the photons were not emitted simultaneously in her frame in calculations using SR Theory. Or would the calculations be redundant, or merely confirmation of the nonsimultaneous emission of the photons in her frame which she concluded from her observing the staggered arrival times?

    Fourth: Would accurately determining that the photons were emitted simultaneously in her frame be unconditionally based on the simultaneous arrival of the photons in her frame?. In other words would the simultaneous emission of photons in her frame be predicated on her observing the simultaneous arrival of the photons in her frame also?

    Five: If she knew that when the B photon arrived that M, as determined by her clocks, was at that instant the midpoint of A and B in her frame, what would she conclude about the simultaneous emission of photons in her moving frame?
    Code (Text):
    A ___________>            M             M'B'<_____________   B      
    We show M'B' the arrival point of the B photon in her frame. These conditions may be different from the previous hypotheticals above, but M is now the midpoint of A and B in her frame. Of course she would not have this information available at the instant the condition was as described by the figure until later, say the next week. However, she obviously still detects the staggered arrival of the photons.
     
    Last edited: Jun 17, 2004
  11. Jun 17, 2004 #10

    Doc Al

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    Her observation of the staggered arrival--coupled with her knowledge of the invariant speed of light--is all she needs to correctly conclude that (according to her frame) the photons could not have been emitted simultaneously at the moment she passed the midpoint. No calculations needed.
    Such knowledge is irrelevant. And, since she understands physics, she sees no contradiction whatsoever between observations made in different frames.
    See my answer to your first question.
    If you mean: "For her to conclude that the photons were simultaneously emitted (in her frame) at the very moment she crossed the midpoint, must she detect the photons arriving simultaneously?" -- Yes.
    I don't understand this question. Both frames agree that M is the midpoint between A and B.
     
  12. Jun 17, 2004 #11
    A slight difference. From the drawing M is the midpoint of the two photons when when the B photon is detected at M'B'. This may be d9ifferent from all the previous situation.
    Code:
    A ___________> M M'B'<_____________ B

    Here M is the midpoint of the photons in the moving frame at the instant the B photon was detected at M'B'.
    1. No other conditions other than the ones stated are imposed. In other words, the sources of A and B could be lightyears removed from the locality here and M need not necessarily be the midpoint of the sources of the photons, but M is the midpoint of the photons at the instance shown.
    2. As in the first situation with the added condition That M is also the midpoint of the sources of A and B in The stationary frame.
    3. The A photon arrives at where the M'B' location is at the present instant (M' has moved forward during the time the A photon was detected at the ol M'B'
     
  13. Jun 18, 2004 #12

    Doc Al

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    fifth question


    1. Is this what you are saying: A and B, at rest with respect to each other and some arbitrary distance apart, emit pulses of light at some arbitrary times (not necessarily simultaneously). A moving observer intercepts the light from B at some point and time; at that very instant (according to her moving frame) the light from A happens to be at another point. Location M happens to be midway between those two points according to the moving frame. What can she conclude?

      Beats me! It's not obvious that she can conclude anything significant.

      Was there a point you were trying to make with this example?
     
  14. Jun 18, 2004 #13
    doesn't she see the photons arriving at different tines? If so then she would preceive the photonds were not emitted in the moving frame simultaneously with the staiobary photons, I guess?
     
  15. Jun 18, 2004 #14

    Doc Al

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    Just because she intercepts the photons at different times is not sufficient for her to conclude anything about whether they were emitted simultaneously in her frame. After all, they could have been emitted simultaneously at different distances from her.
     
  16. Jun 18, 2004 #15
    Could the locations of the photons ever have been colocated at A and B in the stationary frame, or even A' and B' in the moving frame without regard to the origin of the photon's source?
    This would be equivalent to the photon 'sources' location be at A and B, correct?
     
  17. Jun 18, 2004 #16

    Doc Al

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    I really don't know the situation you are describing any longer. I thought A and B were the light sources. What are A' and B' ?

    Have you lost interest in discussing Einstein's train example? I recommend getting that one straight before adding in complications.
     
  18. Jun 18, 2004 #17

    russ_watters

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    I think there is a reason for adding the complications...
     
  19. Jun 19, 2004 #18
    No I am not trying to vary from the original experiment. I ask: if we replace the location of the sources with photons located at the same stationary frame location, are we changing any essential physical parameter of the experiment? If we neglect any source of photons A and B iinformation and define M when photons were at A and B are the physics changed?

    I intend nothing more than to minimize experimental clutter: hence, equating the 'photon source' with 'photon' we say that "M is the midpoint of the A and B photons when the moving observer M' is located at M." We define M then, not wrt to a measured physical length of the lines AM and BM in meters, rather the distance the photon moves in time t from A to M and B to M. If you disagree then please explain. [unprimed = stationary, primed = moving]

    The instantaneous locations of the essential and identifiable objects are at
    1. M'(t'0,) = M(t0)
    2. where M' = M'(t'1) when the B photon arrives at t'1.
    3. where M' = M'(t'2) when the A photon arrives at t'2.

    Hence, all previous measured events are located on the moving frames as determined by counting back from M' at t2 as: t'2 -> t'1 -> t'0 to locate the previous instantaneous locations of the photons wrt 0,0 in the moving frame.

    The frame moves as before, but all positions on the frame are determined by the positions of the detected emitted photons.

    Code (Text):
    A(t'0)_____A(t'1)>            MM'(t'0)            <B(t'1)____A(t'2)>____B(t'0)
    Figure 1
    Location scenario of the instantaneous location of MM'(t0, t'0) on the moving frame wrt A(t2).

    Determine O' conclusions regarding the simultaneous emission of the A and B photons from information of the observed arrival sequence of the A and B photons in the moving frame, starting with:
    • Simultaneity equivalence with conjectured quivalence of M'(t'0) wrt M'(t'0(M'(t'2)))? then,
    • with no consideration by O' of any of her [speculated] motion wrt A and B in the stationary platfom.
    • with consideration of any of her [speculated] motion wrt A and B in the stationary frame then.
    • what is the scenario of stationary emissions such that O' would conclude the emissions of photons in the stationary frame were emitted simultaneously in the moving frame? I ask: IF not simultaneous in moving but simultaneous in stationary, then what non simultaneous sequence in stationary produces simultaneous in moving? Assuming symmetry proper?
     
  20. Jun 19, 2004 #19
    Besides the possibility that I am trying to trick Doc Al what is the "reason" for adding complictions? Actually, I look at it as minimizing complications.

    When first learning SR did you grasp the essence and fundamentals imediately such that all SR problems and arrangments and descriptions posed were solved with ease? Isn't it a fact that at sometime in your educational process SRT stressed your logical and understanding functions?
     
  21. Jun 19, 2004 #20

    Doc Al

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    Once again, I highly recommend sticking to Einstein's original simple argument. Either your more abstract one is somehow equivalent to that, or it's not. Either way, at some point I expect you to pinpoint the flaw in Einstein's argument. There is no way around that hurdle. Note that Einstein's argument requires no understanding of relativity whatsoever except the concept of the invariant speed of light.

    Nonetheless... So both frames are observing photons heading towards each other. Let's see what happens...
    By getting rid of the light sources at A and B, which were fixed with respect to the stationary frame, you risk changing the simple scenario. M is no longer "the midpoint between the light sources A and B", which was unambiguous and agreed upon by all frames. M is also not the "midpoint of the photons A and B" since the moving frame does not agree that she is at the midpoint of the two photons when her clock reads t'=0.
    Allow me to translate:
    (1) The moving observer passes by M (the midpoint of photons according to the stationary frame at t=0) at t'=0.
    (2) She intercepts photon B when her clock reads t'=t'1.
    (3) She intercepts photon A when her clock reads t'=t'2.
    It sounds like you are assuming that the moving observer thinks the photons are at A and B when her clock says t' = 0. Not true!
    Again, I don't understand this diagram. It looks like you are assuming that the moving observer is at the midpoint of the photons when her clock reads t' = 0. That's not true.

    Just for the record, let's find out where the moving observer thinks those photons are when her clock reads t'=0.

    I will assume that in the "stationary" frame (O) at time t=0, the photons are at A (x = -L; t = 0) and at B (x = L; t = 0). (I assume that A and B are a distance L from the midpoint M, according to the stationary frame.)

    So where are these photons at t'=0 according to the moving frame?
    Photon A (at t'=0) is at:
    [tex]x\'\; = -\gamma L -\gamma \frac {vL}{c}[/tex]

    Photon B (at t'=0) is at:
    [tex]x\'\; = \gamma L -\gamma \frac {vL}{c}[/tex]

    Where, as usual, [itex]\gamma = 1/\sqrt{(1 - \frac{v^2}{c^2})}[/itex].

    Now, is your scenario really less complicated than Einstein's?
     
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