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Re: [Phys-l] how to explain relativity



On 06/17/2010 02:51 PM, Jeffrey Schnick wrote:
Let me limit my argument to the class of
cases for which, for some times, there is a comoving reference frame
that both crews can agree on. For the case of an acceleration profile
a(tau) in which the acceleration is non-zero for a period of time tau_c
and after that it is zero, at times for which all parties agree that the
acceleration of both spaceships is zero, the rest frame of either
spaceship is such a co-moving reference frame.

Thanks. That works. I'm convinced.

Some tangential observations:

1) The important point is that in the class of cases defined
above, given ships A and B, a contour of constant t_A will
also be a contour of constant t_B (during the unaccelerated
"rest phase").

A less-important point is that they will disagree as to
what time it is. If at t=0 their clocks were synchronized,
then during the later rest period they will be offset by a
constant. This offset does not affect the dynamics during
the rest phase; we can just pretend they are living in
different "time zones". This is, however, a reminder of
some tricky dynamics that happened earlier, during the
acceleration.

2) During the acceleration phase (not the rest phase) their
is, in general, no such thing as the "rest frame" of the
rope. In any frame that is chosen to be comoving with part
of the rope, at any given time other parts of the rope are
in motion (relative to this chosen frame).

Therefore the following definition of "proper length" is
not usable in such situations:

On 06/17/2010 09:17 AM, John Mallinckrodt wrote:
The
proper length of an object is determined by finding the interval
between two events that take place at the endpoints of an object *at
the same time* in the rest frame of the object.

Alas I do not at the moment have a better definition.
I suspect we can define it locally, and then integrate
along the rope to find the total length. This is
important for understanding the general case, as
opposed to the restricted class considered above.

3) In addition to knowing the right answer, I would like
to understand what went wrong in my incorrect analysis.
I think it can be described roughly as a pole-in-barn
mistake. I correctly calculated the length of the barn,
but wrongly passed that off as the length of the pole
(i.e. rope) that was passing through the barn.