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Simultaneity in Special Relativity

  1. Nov 13, 2006 #1
    How do I derive the equation for Simultaneityfrom one of the lorentz transformation.

    If you can help me with that, please help with time dilation as well.

    The textbook focused mainly on the mathematically derivation without using the lorentz transformations, and I cannot find any answers online.
     
  2. jcsd
  3. Nov 13, 2006 #2

    robphy

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    Take two spatially-separated events A and B that are simultaneous in one frame: So, x_A=/=x_B and t_A=t_B. After a Lorentz Transformation, you'll find that in another frame t'_A=/=t'_B.
     
  4. Nov 13, 2006 #3
    simultaneity

    Please have a critical look at

    arXiv.org > physics > physics/0511062
    Physics, abstract
    physics/0511062

    Illustrating the relativity of simultaneity

    Subj-class: Physics Education

    We present a relativistic space-time diagram that displays in true magnitudes the readings (date times) of two inertial reference frames clocks. One reference frame is the rest frame for one clock. This diagram shows that two events simultaneous in one reference frames are not compulsory simultaneous in the other frame. This approach has a bi-dimensional character.

    Full-text: PDF only
     
  5. Nov 14, 2006 #4

    pervect

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    Try the wikipedia article on the relativity of simultaneity

    http://en.wikipedia.org/wiki/Relativity_of_simultaneity

    Basically, events are simultaneous if they have the same t coordinate.

    Suppose we have two frames: S1, with coordinates x and t, and S2, with coordinates x' and t'.

    Then two events are simultaneous in frame S1 if they have the same t coordinate, i.e. t(event1) = t(event2).

    Two events are simultaneous in frame S2 if they have the same t' coordinate, i.e. t'(event1) = t'(event2).


    The two sets above are not the same.

    Because the Lorentz transform gives t' and x' in terms of t and x, one can determine the equation of a 'line of simultaneity' in S2 in terms of x and t.

    Let us find the set of events simultaneous with the origin. Then we have

    t' = gamma * (t - v*x/c^2) = 0

    This means that the equation of t'=0 is t = vx/c^2 , which defines the equation of the "line of simultaneity" of events in S2 in terms of the coordinates (t,x) of S1.

    If you work out a more general example, you'll find that all lines of simultaneity have the same slope on the space-time diagram, which by the example above is slope = dx/dt = c^2 / v.
     
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