Re: A mixture of time dilations and constrictions

[Chuck Britton <britton@NCSSM.EDU>]

At 1:26 PM +0300 7/7/03,  pvalev wrote:

> Just a question. When a clock is idealized as a point-like particle,
> the analysis is standard and simple, as you say above. When one deals
> with a clock as an extended object (i.e. with a real clock), the
> analysis is vastly more complex and we should not discuss it since
> there is a lack of understanding between us. But something is amiss.
> The lack of understanding has nothing to do with the existence or
> nonexistence of techniques dealing with a clock as an extended
> object. So please describe these techniques in simple terms and give
> references where it is proved that results for a clock as an extended
> object are essentially the same as results for a "point-like clock".
> I wonder why the comparison between "extended clocks" and "point-like
> clocks" is not even mentioned in the literature I have had access to.
> Sometimes idealizations prove wrong and a lot of investigation is
> needed to show they are not.
>
> Pentcho

Two points, from a total non-'expert' in the field. But I DO remember
some brief discussions with our Freshman physics professor back in
the old days.

1)      An example of a 'real' clock that is straightforward to
analyze, is presented in many intro texts. Instead of a 'pointlike'
clock, it is a 'one-dimensional' apparatus that is carefully aligned
to be perpendicular to the axis of relative motion. If we accept the
result that dilation only occurs along this axis (a separate question
- but easily addressed) the extent of the clock perpendicular to this
axis should introduce problems.
       This is the clock that has a photon bouncing between two
mirrors. The 'clock holding frame' sees the 'beam' of light bouncing
a given distance in a given time that is unaffected by relative
motions.
       Does this satisfy the nature of the clock requirement?


2)      Our professor set up the two reference frames with an
INFINITE number of clocks along the direction of motion. There were
Frame#1 clocks and Frame#2 clocks whizzing past each other. All the
clocks in a given frame are synchronized with each other. (an
interesting but not difficult exercise in engineering).
       Now-a-days I replace the string of clocks with a string of
video cameras which have time-stamps included with their current
image.
       TWO sets of video cameras, TWO sets of time/space.

Helpful?


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Chuck Britton                                   Education is what is left when
britton@ncssm.edu                       you have forgotten everything
North Carolina School of Science & Math         you learned in school.
(919) 416-2762                                  Albert Einstein,        1936