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Question concerning the relativity of length

  1. Oct 30, 2006 #1
    let K' = a stationary rigid rod. let its length be AB (the length 299,792,458 meters between the two ends A and B of K'). the axis of K' is lying along the x-axis of a stationary system of coordinates K.

    let there be a stationary red clock and an observer stationed at A.

    let there be a stationary blue clock and another observer at the origin of K.

    let the red clock and the blue clock synchronize.

    let t = the time values of events as measured by the observer stationed at the origin of K using the blue clock.

    let T = the time values of events as measured by the observer stationed at A using the red clock.

    let a ray of light depart from A at t0 = T0 in the direction of B, and let the ray of light be reflected at B at t1 = T1.

    the observer stationed at A measures the time (T1 - T0 = 1 s) required by the ray of light to travel from A to B.

    the observer stationed at the origin of K measures the time (t1 - t0 = 1 s) required by the ray of light to travel from A to B.

    c = AB/(T1 - T0) = AB/(t1 - t0).

    c is the velocity of the ray of light as measured by the observer stationed at the origin of K, whether K' is stationary or moving at a constant speed v in the direction of increasing x.

    let a constant speed v in the direction of increasing x be imparted to K'.

    let a ray of light depart again from A at t0 = T0 in the direction of B, and let the ray of light be reflected at B at T1 and at t1.

    the observer stationed at A measures again the time (T1 - T0 = 1 s) required by the ray of light to travel from A to B.

    according to the relativity of time, the observer stationed at the origin of K is expected to measure the time [t1 - t0 = (1 s)/sqrt(1 - v^2/c^2)] required by the ray of light to travel from A to B. therefore, T1 is not equal to t1.

    since c is the velocity of the ray of light as measured by the observer stationed at the origin of K, whether K' is stationary or moving at a constant speed v in the direction of increasing x, c = rAB/[(1 s)/sqrt(1 - v^2/c^2)], where rAB is not equal to AB.

    What is the value of rAB, such that c = AB/(T1 -T0) = rAB/[(1 s)/sqrt(1 - v^2/c^2)]? thanks!
     
    Last edited: Oct 30, 2006
  2. jcsd
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