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

[Michael Burns-Kaurin <mburns-k@SPELMAN.EDU>]

The point of the exercise is, "moving clocks run slow" is an incomplete
picture of special relativity.  In certain restricted situations, you can
understand situations using "moving clocks run slow", but as you have seen
you quickly run into problems.  I disagree with your statement in another
post that the full story should not be taught to students.  Rather, unless
special relativity is properly presented, students will be left confused as
to how everyone can see moving clocks run slow.

I suggest you look at this book:  A Traveler's Guide to Spacetime by Thomas
Moore.  A very early version of this book cleared up a lot of confusion for
me.  It is written at an introductory level; a revised version is published
as Unit R of Moore's Six Ideas textbook series.

Michael Burns-Kaurin
Spelman College





                      Pentcho Valev
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                      Sent by: Forum           cc:
                      for Physics              Subject:  Re: Variable speed of light (was: Relativity
                      Educators                 conundrum)
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                      04/29/2003 11:02
                      AM
                      Please respond to
                      Forum for Physics
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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