Re: A mixture of time dilations and constrictions

[Ken Caviness <caviness@SOUTHERN.EDU>]

Stephen's answer below really is the best one to the questions in this
thread.  I second his high recommendation of Taylor and Wheeler's
"Spacetime Physics".  I read it and worked through the problems in the
first edition when I was a senior in high school, the math is not at all
onerous.  It's worth the expense and time spent to study this book, which I
believe is now in the second edition.

But since I've already said a few words about the "complex analysis" of
Pentcho's latest question, let me add one more thing:

It's not hard to apply the Lorentz transformations and find the speed of
the tip of the clock arm in any inertial observer's reference frame.  But
that doesn't say anything about the nature of time in the different
reference frames, nor identify time dilations nor indicate "time
constrictions" at all.  It was precisely to separate out the behavior of a
moving object (the tip of the clock arm) from the actual passage of time
that I introduced the minute and second hands (and in principle, as many
more as we want).  But the same effect is achieved by achieved by using a
simpler clock, such as the light-clock I mentioned.  In any case, the main
misunderstanding is dealing with the tip of the clock arm without taking
into consideration that it is an accelerated object even in the clock's
rest frame, adding up the speeds without even using the Lorentz velocity
transformations (!), and then expecting to get meaningful insights about
time.  One doesn't.

Over and out,

Ken



At 10:24 AM 01.07.03 -0700, Stephen Speicher wrote:

> On Tue, 1 Jul 2003, Pentcho Valev wrote:
>
> > Stephen Speicher wrote:
> >
> > >
> > > I do not know what you have been told on other lists, but special
> > > relativity is a geometric theory with the notion of a point-like
> > > event as a fundamental concept.  Clocks are idealized to be
> > > present at any given event, not as an extended object but as a
> > > point-like particle. One can deal with a clock as an extended
> > > object in relativity, but such techniques are _vastly_ more
> > > complex than standard analysis.
> >
> > Still let us try.
> >
>
> No, let us not. There is no point to complex analysis when there
> is a lack of understanding and agreement of basic principles upon
> which such an analysis is based.
>
> >
> > I would be grateful if you could stop hinting at my ignorance ...
> >
>
> I have not been "hinting" at anything. I have stated outright
> that _before_ one can presume to be critical of relativity
> theory, one must first learn about what one intends to criticize.
> It has been my experience with others that, in almost all cases,
> a proper education in the basics of the theory dispels the more
> complicated "concerns" which they have.  There is nothing wrong
> or shameful with ignorance per se, as long as one makes an effort
> to replace that ignorance with knowledge. To that point I again
> suggest Taylor and Wheeler's "Spacetime Physics" as an excellent
> non-technical yet conceptual introduction to the theory.
>
> --
> Stephen
> speicher@caltech.edu
>
> Ignorance is just a placeholder for knowledge.
>
> Printed using 100% recycled electrons.
> -----------------------------------------------------------