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



Bob LaMontagne wrote:

Pentcho Valev wrote:

Michael Burns-Kaurin wrote:

I find that the best solution to relativity conundrums is to apply the
Lorentz transformations.

Let the light enter the train at the origin in both reference frames. The
train moves in the +x direction according to the track frame. The light
moves across the track in the +y direction in the track frame. The width
of the train is w, same in both frames.

In track frame, time of light leaving train is simply w/c. Location of
that event is x=0, y=w, t=w/c.

Now plug those numbers into the Lorentz transformations to find the
spacetime locations for the leaving-train event in the train frame.

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

You obtain t' > t so your argument could be regarded as reductio ad absurdum.
If clocks on the train run slower, as textbooks say, then t' < t.

Pentcho

t' > t is actually correct in this case - if you correctly interpret t' and t.
They measure the time between the same to events, light entering the train and
light leaving the train. That interval has to be greater for the person in the
train because the light travels a longer distance.

Still this is reductio ad absurdum since, by using the same method, we can obtain
contradictory results. In another experiment, the events are again "light enters
train" and "light leaves train". However in the rest frame the beam approaches the
train obliquely so that, in the train frame, it runs perpendicular to the train. In
this case Lorentz equations give

x' = 0 ; x = vt ; t' = (1 / gamma)*t

Clearly, t' < t whereas in the original experiment the analogous time intervals were
found to obey t' > t. These are absurd results in my view. Lorentz equations predict
that, in the train frame, some processes are slower than in the rest frame whereas
others are faster. To call this "time dilation" is both wrong and misleading.
"Absurd time deformation" seems to be the most suitable name.

Pentcho