Re: Relativity conundrum

[Ken Caviness <caviness@SOUTHERN.EDU>]

Brian Whatcott wrote:

> [debate labeled in time sequence]
>
> > > Pentcho Valev wrote:
> > ...
> > > > 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.
>
> Ken Caviness responded:
>
> > > This is all the person can do, using distance & time as measured by meter
> > > sticks & clocks at rest in her own reference frame.
> /snip/
> > > 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 (*)?
> /snip/
> > > She could use time as measured by clocks at rest with respect to
> > > the station platform,
>
> At 07:22 PM 4/21/2003 +0200, Pentcho, you wrote:
>
> > How could she do this? She would have to leave her frame and move to
> > the other one - I am not sure this is unproblematic with respect to
> > the conventional theory (if time is constant this is unproblematic).
> /snip/
> > Pentcho
>
> To address only this question, a train observer who requires a stationary
> associate to mail in the results of a time interval determination taken
> in the stationary frame resolves the concern - only the observation need
> be specified in space time.
>
> Brian Whatcott

In fact, a message from a confederate on the platform is the only way our
observer on the train can be sure of the "real distance" the light travels or
the "real time" it takes.

I put the expressions in quotes, because actually the distance and time as
measured by any observer are equally valid, although special relativity
predicts that such measurements will vary for different observers in relative
motion.  (Some things just depend on one's point of view!  Others, such as the
speed of light in vacuum, don't:  they're the same for everyone.)

An alternative scenario is to have the train stop at the station and let all
the observers check that their clocks run at the same rate and that their
meter sticks are the same length.  Then as the train accelerates and then
reaches some constant speed with respect to the station, the train observer
might (incorrectly) assume that her clocks and meter sticks were still in
agreement with those on the station platform.

But in any case it would not be logical for her to trust her own clocks as
giving "real time" but the station observer's distance measurements as giving
the "real distance".  It is my impression that most apparent paradoxes in
relativity turn out to be due to such a mixed-reference-frame treatment of
some problem.

Ken Caviness