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A doubt in simultaneity

  1. Jul 22, 2008 #1
    Hi everyone,

    I got interested in physics recently and started reading a book called "relativity simply explained " by martin gardener. when i was going through the book i got some doubts in relativity of simultaneity.

    my problem is described below

    o>>> ---------------------------<< 0
    ----------------C --> V
    Point 1 and 2 are light sources equidistant from observer B . There are clocks at point 1 and 2 each.The moment the light is sent from point 1 clock at point 1 is set to zero and the moment the light is sent from point2 clock at point 2 is set to zero.

    B receives the light from both point1 and point 2 simultaneously. Can he conclude that clocks at 1 and 2 are synchronized ?

    C is an observer moving w.r.t to B Can he actually see that light from both sources reaching B at same time??

    I have a few more queries

    hoping to get a reply soon
  2. jcsd
  3. Jul 22, 2008 #2

    Doc Al

    User Avatar

    Staff: Mentor

    It depends on whether those clocks are moving with respect to B or not. If the clocks are not moving, then he can conclude they are synchronized. (Assuming they are working properly.)

    If you mean will a moving observer C agree that the light from both sources reached B at the same time: Yes. All observers will agree on that.
  4. Jul 22, 2008 #3
    Doc Al thanks for the reply

    As you have mentioned the clocks are not moving w.rt to B and he concludes that clocks are synchronized.

    Observer C sees that light from both sources reaches B at the same time.

    o>>> ---------------------------<< 0
    ----------------C --> V

    the observer C is moving to the right with a speed V. He observes that light from 2 has to travel more distance and since speed of light is same in both directions he is forced to conclude that clock at 2 is set ahead of clock at 1

    is my conclusion correct?
  5. Jul 22, 2008 #4

    Doc Al

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    Staff: Mentor

    Yes, that is correct.
  6. Jul 22, 2008 #5
    Oh great!!!

    if i repeat the same experiment with two tennis balls instead of light source. ie i will release two tennis balls from both 1 and 2 with same speed say "w".

    the two balls will arrive observer B at the same moment and he will conclude that clocks are synchronized. right?

    C will see that both balls arrive observer B at the same moment.

    o--> w--------------------- w<----- 0
    C --> V

    if i take speed of ball from 1 as w-v ( relative speed . is this correct???)

    and speed of ball from 2 as w+V .

    is'nt it possible for observer C to back calculate and conclude that both clocks are synchronized??

    i know there is some error. But cant figure out

    Please help
  7. Jul 22, 2008 #6


    Staff: Mentor

    Hi novice2000,

    The error is just that you need to use the relativistic velocity addition formula, not the Gallilean one.
  8. Jul 22, 2008 #7

    Doc Al

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    Staff: Mentor



    No, as DaleSpam already pointed out, this is not correct. You must combine speeds relativistically to get the correct answer. (That's why relativity thought experiments always use light beams--they always go at the same rate in any frame. Much easier to switch from one frame to another.)

    The transformation of velocities that you used to get w-v and w+v is only true in Newtonian physics, not Einsteinian. (That transformation is called Galilean relativity, after Galileo.) Using that transformation, you would be able to conclude both clocks are synchronized: But that's no surprise--in the Newtonian world time is the same for any frame.

    If you used the proper relativistic transformation (see DaleSpam's link), you'd find--once again--that simultaneity is relative.
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