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Re: Variable speed of light



Thanks for this - I've learnt on this list to do what I'm always telling my
students to do: provoke a clarification by stating that which you
understand partially.

On the idea of proper time I'm quoting A.P. French "Special Relativity" p106.


At 07:34 29/04/03 -0400, John S. Denker wrote:

The way to deal with virtually all problems of this
ilk is to DRAW THE SPACETIME DIAGRAM.

The fact that this is not my first reaction is probably why I get confused...

...

> The proper time interval between two
> events in a given reference frame must be measured with one clock only,

Not true.
The conventional wisdom is diametrically opposite.
You want a "lattice of rods and clocks" in each
frame. (The clocks are of course synchronized in
that frame.) This allows the observers in that
frame to measure the time of an event _at_ that
event, using the colocated clock and no other.

OK... referred to the same clock rather than with the same clock. The
process of referring the measurement on the distant clock to the local one
will involve the corrections detailed.

...
> Your setting is more complicated (and
> therefore probably unsuitable as a thought experiment designed to clarify
> the situation)

More complicated than what?
The stipulated setting isn't complicated in any
absolute sense, and is 100% suitable as a thought
experiment.

More complicated than the case proposed using the mirror to enable
measurements to be made with a single clock, as used widely in relativity
textbooks to illustrate the time dilation.

There is however no notion of proper time involved.
The proper time for a photon to go from point A to
point B is zero, if the concept can be defined at all.

I don't get why we must go to the photon's frame when using the term proper
time. Is French's usage of "proper time" at variance with the rest of the
world?

That the difficulty comes down to the relativity of simultaneity of
separated events is what I had in mind, and you've clarified nicely how it
should be applied. Not sure that PV would agree, though, since the
relativity of simultaneity is derived from the constancy of c, which is
what he is testing.

Mark