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Re: Variable speed of light (was: Relativity conundrum)



Bob LaMontagne wrote:

Pentcho Valev wrote:


There is a version which could be a thought experiment and which unequivocally
shows that the speed of light is not constant. In the rest (railway) frame the
beam approaches the train at a right angle so that, in the train frame, it moves
obliquely. Consider two events - the beam entering the train and the beam
leaving the train - registered in both frames. Obviously x < x', where x is the
distance the beam travels between the two events in the rest frame and x' is the
respective distance in the moving frame. The time measured in the rest frame for
the travel x is t, and that measured in the moving frame for the travel x' is
t'. If there is time dilation, t' < t and, accordingly,

c = x/t < x'/t' = c'


Just for the sake of the argument, assume that the numerical value of the speed of
light is the same in the two frames. then, in the frame where the light moves
obliquely, the light must travel a longer distance, x', and hence must take a
proportionately longer time, t', to travel that longer distance. The ratio x'/t'
would therefore remain the same as x/t (because x' > x and t' > t). Time dilation
really is not a consideration here, and t' is definitely not less than t. Even if
time dilation was applied (which would also require considering a length contraction
of the component of obliqueness parallel to the train's motion), t' > t still holds.

Your assumption of t' < t is what's leading to the differing values for c and c'.

This is not "my assumption" - rather, this is the famous corollary of Lorentz equations
- on the moving train clocks go more slowly.. In fact, your argument amounts to reductio
ad absurdum. You assume that the speed of light is constant and this leads you to a
result inconsistent with the Lorentz equations. Therefore you should reject the
assumption "speed of light is constant". Also, considering the length contraction of the
component of obliqueness paralell to the train motion would not change drastically the
analysis - in the train frame, the oblique path is always greater than the perpendicular
path, and the perpendicular paths are EQUAL in the two frames for a train moving along
the x-axis, according to Lorentz equations. (My notation x and x' is a bit misleading -
light in this experiment mainly moves along the y axis so I should have used some
neutral notation - e.g. D and D').

Pentcho