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Relativity of simultaneity explained

  1. Mar 22, 2009 #1
    Hi,
    what do you think is the best and easiest way to describe the relativity of simultaneity? The best possibilities I'm aware of are:

    a) The one of Comstock (1910), who uses two platforms. On one platform we have the endpoints A and B, and from the middle between them a signal is sent to both of them. Because of the constancy of light, the light rays will reach the points simultaneously and the clocks at A and B will start at the same time. However, from the point of view of the other platform, one ray arrives at first at A, while the second ray need longer to arrive at B, so the clocks are not synchronous.
    http://en.wikisource.org/wiki/The_principle_of_relativity

    b) And the one of Einstein (1916), who sent two light signals from A and B (the endpoints of a railway embankment and a moving train) to a point in the middle between A and B. If those signals arrive at the same time in the middle of the embankment M, then they started simultaneously in the frame where the railway embankment is at rest. However, the middle of the train M' is first hit by the signal from B. This is interpreted by an observer in the frame where the moving train is at rest that the signals were not sent simultaneously.
    http://en.wikisource.org/wiki/Relativity:_The_Special_and_General_Theory/Part_I

    I find both ways interesting and intriguing, what do you think?

    Regards,
     
  2. jcsd
  3. Mar 22, 2009 #2
    In the classic Einstein train/embankment scenario if the lightning strikes are simultaneous in the embankment frame then they are not so in the train frame and vice versa.. We have two events, lightning strikes, fortuitously simultaneous in one frame and but not in the other.

    I have only taken a very quick look at the Comstock example so I may have got it wrong, if so please correct me, but it looks like he uses a single initializing event at a point at which the centre of both systems are present. So, presumably, the events which are of interest are the arrivals of the light at the endpoints of these systems. These events are simultaneous to observers in both systems. I have not yet looked at what conclusions Comstock draws from this but his and Einstein's scenarios are, I think, not directly comparable. I have not yet read, so I cannot take issue with, anything Comstock may imply from his example, but will have a closer, longer look.

    As an afterthought, it may be, but I am not yet sure on this point, that later events arising causally from a single event that are considered simultaneous in one frame will be considered simultaneous in all frames.

    Matheinste
     
  4. Mar 22, 2009 #3
    I think the distinction between events (light emission) and perception (light detection) is ignored. Simultaneous perception of signals does not imply simultaneous events. Additional information (the distances involved) is required to determine that.
     
  5. Mar 22, 2009 #4
    Hello Histspec.

    Having read more, Comstock's approach, although diferrent from that of Einstein, is also enlightening. I think that looking at things from more than one viewpoint can only help us to more fully appreciate the theory.

    Matheinste.
     
  6. Mar 23, 2009 #5
    Hello Matheinste.

    Interestingly, Einstein's 1905-description is much more complicated... He defined a stationary system and a moving system. In the moving system he placed two clocks A and B and then sent one ray from A to B, and back the same way. Then he stated that the clocks in the "moving" system indicate the time of the "stationary" system. Now, in the stationary system B indicates tB=L/(c-v), and for the return of the signal tA=L/(c+v). If the moving observers look at their clocks, they find them not synchronous because they expect to see the times tB'=L'/c and also tA'=L'/c. So they will conclude that simultaneous events in the stationary system are not simultaneous in the moving systems. Well, it's complicated but it works....
    http://www.fourmilab.ch/etexts/einstein/specrel/www/

    A different one is from Poincaré (1904) - and his reasoning is based on an aether. Imagine two stations moving in the aether. A sends its signal when its clock marks the hour 0, and that the station B perceives it when its clock marks the hour t. The clocks are adjusted if the slowness equal to t represents the duration of the transmission, and to verify it the station B sends in its turn a signal when its clock marks 0; then the station A should perceive it when its clock marks t. The time-pieces are then adjusted.
    However, an observer resting in the aether argues that die clocks are not synchronous, because one clock travels in the direction the signal, and the other clock is moving away....
    http://en.wikisource.org/wiki/The_Principles_of_Mathematical_Physics

    Regards,
     
  7. Mar 23, 2009 #6
    Hello Histspec.

    I will take time to read these examples. Thanks.

    My quote:-
    -----later events arising causally from a single event that are considered simultaneous in one frame will be considered simultaneous in all frames.-----
    This is not correct.

    Matheinste.
     
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