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Why there can be only one invariant speed

  1. Jul 4, 2009 #1
    I've just come across the following argument as to why there can be only one invariant speed for massless particles. It's from Applications of Classical Physics by Roger Blandford and Kip Thorne. But I don't understand. Obviously, it's a contradiction to say that the hypothetical speed c_0 is both invariant and not invariant, but why must this contradiction arise if such a speed existed? Or to put it another way, why does this argument for the non-existence of two invariant speeds not apply to the existence of one invariant speed? I thought that there was no rest frame defined for a photon moving at c. Wouldn't it be equally meaningless to assume one for any other hypothetical invariant speed?

    Must these [hypothetical massless particles] travel at the same speed as photons? The answer to this question, according to the principle of relativity, is yes. The reason is simple. Suppose there were two such waves (or particles) whose governing laws led to different speeds, c and c_0 < c each the same in all reference frames. If we then move with speed c_0 in the direction of propagation of the second wave, we would bring it to rest, in conflict with our hypothesis. Therefore all signals, whose governing laws require them to travel with a speed that has no governing parameters must travel with a unique speed which we call c".

    http://www.pma.caltech.edu/Courses/ph136/yr2004/0401.1.K.pdf
     
  2. jcsd
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