From: ram@zedat.fu-berlin.de
Sylvia Else writes:
>Yet if we perform an experiment that doesn't accelerate anything, but
>instead transfers clock readings between observers travelling in
>different directions, we still get a "twin paradox" style result.
The crucial thing is that two macroscopic systems that are
localized at each point in time, but also moveable (the
twins), meet /twice/.
They meet at an event A. Then they both travel to a later
event B where they then meet again. (An event being
determined by a certain place and a certain time.)
The proper time passed between A and B can depend on the
path taken from A to B. It is given by the integral of all
infinitesimal differences of proper time ds from A to B,
where, IIRC,
ds² = dx² + dy² + dz² - dt²
. This integral is determined for each twin by the worldline
taken between A and B. This integral might differ between
the twins. (But, of course, this is not a contradiction
["paradox"].)
So, the proper time passed between A and B might differ for
the twins. But the proper times passed can only be compared
when they meet again. And therefore, it is crucial that they
meet twice.
This integral is not changed by someone calling some parts
of that wordline "accelerated". The word "acceleration" is
not needed to describe what is happening here.
To a traveller, acceleration by a field of gravity (i.e.,
free fall) feels just like resting in spaces without
gravity. (As long as tidal forces are small.) However, being
accelerated by a push by another body (e.g., a rocket floor)
can feel totally different because this force does not apply
to all points of the traveller with the same intensity. So
acceleration can have totally different effects on
macroscopic bodies depending on how it is applied.
--- SoupGate-Win32 v1.05
* Origin: you cannot sedate... all the things you hate (1:229/2)
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