Re: Question: Lorenz' interpretation of SR v. Einstein's

From: Benno Muilwyk (benno_at_muilwijk-met-wyk.nl)
Date: 08/12/04 

Date: Thu, 12 Aug 2004 23:13:00 +0200

"Harry" <harald.vanlintel@epfl.ch> schreef in bericht
news:411b4c88$1@epflnews.epfl.ch...
>
> "Benno Muilwyk" <benno@muilwijk-met-wyk.nl> wrote in message
> news:411a9822_1@news3.prserv.net...
> >
> > "Harry" <harald.vanlintel@epfl.ch> schreef in bericht
> > news:3bff5641.0408080700.28a5be7f@posting.google.com...
> > > Andrew Dabrowski <dabrowsa@indiana.edu> wrote in message
> > news:<4115DDDA.1030307@indiana.edu>...
> > >
> > > As a logician, what do you think of the Einsteinian concept that when
> > > A sees B moving, both A is right to say that its own clock is truly
> > > unaffected by speed but B's clock runs slow, *and* B to say that its
> > > own clock is truly unaffected by speed but A's clock runs slow? Thus
> > > what do you think of the relativity of logical truth? Thanks in
> > > advance!
> > >
> > > Harald
> >
> > This is comparable to the following situation:
> > A and B are both driving a car. They started from the same point at the
> > same time at the same constant speed, but in different directions. Not
> > opposite directions, but rather at a sharp angle, e.g. like this:
> >
> > A B
> > | /
> > | /
> > | /
> > |/
> >
> > Although A and B are both travelling with the same speed, each will
> observe
> > that the other is staying behind. What's so strange about that?
> >
> > Benno
>
> It's often a question of definitions and references. As I see your
> illustration, it depends where one wants to go, and what the end result
is!
> In this case, if they are traveling at the same speed, and they started
> together and travel the same path lenght between the same two points, then
> they will agree that they both traveled at the same speed if they arrive
at
> the same time. They will take into account that each made a mesurement
error
> about the progress of the other due to their own deviation. But if one
moves
> on a straight path and the other on a curved path:
>
> A __/\__
> B______
>
> while the one on the curved path ignores its own deviation, the truth
about
> who took the curved path comes out when they meet. For this case it is
> incorrect to state that the angles A chose didn't affect its progress.
> It's certainly erroneous to claim that the angle we choose DOES NOT affect
> our own progress AND that the angle someone else chooses DOES affect the
> progress of the other.
>
> Harald

In the first case A and B both follow straight paths and there is only an
angle between their paths.
The observation that the other stays behind is indeed a matter of
references. Just as in SR!

In the second case A's path is no longer straight and A will feel (sideways)
accelleration while changing the direction of his path.
This accelleration is always perpendicular to the (curved) path when the
speed along the path is constant.

Both cases can be mapped almost directly to SR.
The path maps to the worldline in spacetime.
The path length maps to elapsed proper time of the object following the
world line.
The acceleration is perpendicular to the world line (time): a spatial
direction.

Benno

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