Re: [Phys-l] Relativity Question

[John Denker <jsd@av8n.com>]

On 05/15/2009 06:17 AM, Philip Keller wrote:
> I believe that the point is that the scientists on the train have NOT
> been lied to.  In their reference frame, their clocks ARE
> synchronized.  

OK, I must have guessed wrong about what story was being told.
Sorry.

> To take things further, you can consider a procedure that the
> scientists could use to ensure that the clocks on their own train
> were synchronized.  Suppose that there is a star that is known to
> occasionally emit a burst of light at a specific frequency.  And
> suppose you could design clocks that start running when exposed to
> that frequency.  You could preset your clocks but with each clock set
> further ahead than the one before it.  Then when the light from the
> star reached the individual clock, it would start the clock.  The
> preset time differences would be to allow for the additional time it
> takes for the light to reach that train car.

You don't need a star.  You can generate your own pulse.  Using
the star is actually very tricky, because the star is in one
frame and your train is in another, so you have to assume you
know the speed of light and assume that it is frame-independent
et cetera.

You can get along just fine without the star, if you are able to 
send a signal up and down your train in a way that is independent
of the state of motion of the train.  A sound signal suffices,
if your sound is very very accurate, and the medium is comoving
with your train, and you invoke Galilean relativity.  In practice
people often use electrical pulses.

> If both sets of train scientists performed this procedure, they could
> each argue that their own clocks were in fact synchronized. And they
> would each argue that the other train performed the procedure
> incorrectly because that other train was in motion relative to the
> light source -- but we weren't.  So in the final analysis, it is
> simultaneity that is relative and it leads to the other weird things
> about clocks and lengths.

No, that is not the "final" analysis.  It's just a slightly eccentric
way of skinning the cat.  There's lots of additional ways.

This is a phase that people go through, trying to find the minimal
set of axioms that allow them to deduce all of special relativity.

Eventually you realize that there are about a dozen things we know
about special relativity, and roughly speaking any three (sometimes
two) of them can be taken as "the" axioms, because they are sufficient 
to deduce all the rest.

If you are going to take non-simultaneity as one of your foundational
axioms, you need 20/20 hindsight or you need to invoke some additional
principle to tell you _how much_ non-simultaneity is needed.