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Relativity of L, (t'A - tB), and (tB - tA)

  1. Sep 18, 2006 #1
    i think i finally understand. i also think that Einstein's derivation in his 1905 paper is very clear, simple, not at all confusing, and not at all ambiguous.

    the principle of the constancy of the velocity of light states the following: any ray of light moves in the stationary system of coordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body.

    for example, if K is the stationary system, and K' is the stationary body by which the ray is emitted, the ray of light moves in the stationary system K (as seen by an observer in K') with the determined velocity c = L / (tB - tA) = L / (t'A - tB), where L is the value of the length of the light path from one end of K' (A) to the other (B), tB - tA is the value of the time interval required by the ray of light to travel from A to B, and t'A - tB is the value of the time interval required by the ray of light to travel back from B to A.

    in essence, i think, the observer in K' is asking himself (or herself), "with what speed would the ray of light (the one that moves from point A to point B and back to point A in my system of coordinates K') move in the system of coordinates K (in all respects resembling mine) if k' and K are at rest relatively to one another?

    if, on the other hand, K is the stationary system, and K' is the moving body (in uniform translatory motion with velocity v) by which the ray of light is emitted, the ray of light moves in the stationary system K (as seen by the observer in K') with the determined velocity c = [rAB / (tB - tA)] + v if the direction of the motion of the ray of light is the same as the direction of the motion of the moving body K', and c = [ rAB / (t'A - tB)] - v if the direction of the motion of the ray of light is opposite the direction of the motion of the moving body K', where rAB is the value of the length of the light path from a point x1 (which corresponds to A at tA) to a point x2 (which corresponds to B at tA) in the stationary system K, tB - tA is the value of the time interval required by light to travel from A to B, and t'A - tB is the value of the time interval required by the ray of light to travel from X2 to X1. note that rAB is determined by c = [rAB / (tB - tA)] + v, where the only unknown is rAB. and t'A - tB is determined by c = [rAB / (t'A - tB)] - v, where t'A - tB is the only unknown.

    in essence, then, the observer in K' is asking himself, "with what speed would the ray of light (the one that moves from point A to point B and back to A in my system of coordinates K') move in the system of coordinates K (in all respects resembling mine) if k' and K are in uniform translatory motion v relatively to one another?

    in both cases, the ray of light moves in the stationary system K with the determined velocity c, whether the ray of light is emitted by the stationary or the moving body K'.

    the principle of the constancy of the velocity of light, thus is consistent with the principle of relativity, which states the following: the laws by which the states of physical systems undergo change, are not affected, whether these changes of state be referred to the one or the other of two systems of coordinates in uniform translatory motion.

    in other words, the laws by which the ray of light moves with the determined velocity c in the stationary system K are not affected, whether the motion of the light is referred to the stationary body K' or the moving body K' in uniform translatory motion with velocity v.

    consequently, L, (tB - tA), and (t'A - tB) are relative, in other words, they depend on v, or they are not absolute; they are not independent of v, since the only invariant is c.
     
    Last edited: Sep 19, 2006
  2. jcsd
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