Re: Relativity conundrum

[Ken Caviness <caviness@SOUTHERN.EDU>]

Pentcho Valev wrote:

> The analysis of the following situation may prove instructive. The person on
> the train measures the speed of light by sending the beam crosswise - from one
> side to a mirror on the other etc. There are two possibilities:
>
> 1. The person DOES NOT KNOW that the train is moving with a speed v with
> respect to the railway. So he/she obtains c' = x'/t, where x' is the distance
> between the sides of the train and t is the time measured.

This is all the person can do, using distance & time as measured by meter
sticks & clocks at rest in her own reference frame.

> 2. The person KNOWS that the train is moving with a speed v with respect to the
> railway and accordingly determines the "real" distance x the beam has gone
> through:
>
> x^2 = (x')^2  +  (vt)^2
>
> Eventually he/she calculates the "real" speed of light:
>
> c = x/t = gamma.c'
>
> where gamma = [1 - (v/c)^2]^(-1/2)

This is in incomplete, mixed-reference-frame treatment of the problem.  If the
person on the train insists on using distances (*) as measured by observers on
the platform, why is she so inconsistent as to use _time_ as measured by _her_
clocks (*)?  She could use time as measured by clocks at rest with respect to
the station platform, and will then again find that light travelled at speed
c.

(* Neither distances nor times measured by observers at rest with respect to
the station platform turn out to not agree with distances/times measured in
her own reference frame.)

Ken Caviness