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

[Bob LaMontagne <rlamont@POSTOFFICE.PROVIDENCE.EDU>]

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.

The "textbooks" are applying t' and t to an entirely different situation, i.e.,
the comparative rates at which a clock on board the train and a clock on the
ground will run.

There is no reductio ad absurdum because identical quantities are not being
compared. I think that Michael is entirely correct in asserting that the Lorentz
transformations offer the clearest analysis.

Bob at PC