Re: the heart of a paradox
From: Tom Roberts (tjroberts_at_lucent.com)
Date: 07/31/04
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Date: Sat, 31 Jul 2004 01:00:17 GMT
Ken and Vicki wrote:
> So you have this exactly symmetrical, albeit unlikely, binary star system
> out in no-man's land. Or they could be two heavy spacecrafts likewise
> circling about one another, out where other gravitation is negligible. What
> evidence leads the pilot inside one of those crafts from presuming his is a
> non-inertial FoR? so that he can therefore *justify* the denial/dismissal of
> SR mutual Lorentz transform as the end-all-be-all ciphering of the situation
> (which would lead to a contradiction).
First, the pilot in spacecraft A can not only assume but also measure
that the inside of his spacecraft is an inertial frame to a given
accuracy; for ordinary tools this accuracy will probably exceeds his
measurement accuracy. But he cannot do so to infinite accuracy -- with
accurate enough tools he can detect the time variation in tidal forces
due to the other spacecraft.
Second, if pilot A watches the position of spacecraft B over time he
will observe that it does not move in uniform rectilinear motion, and
from the absence of any non-gravitational force on either spacecraft he
can conclude that gravitation is influencing the motion, and that his
spacecraft does not sit at rest in a GLOBALLY-inertial frame --
therefore SR is not valid.
This last implies that there is no need whatsoever to "deny/dismiss" the
"SR mutual Lorentz transform", as that is valid only in SR, and SR is
known to not apply here. <shrug>
> no hypothetical machine aboard the inner cabin of either of these
> aforementioned mutually encircling stars or heavy crafts could sense any
> pseudo force or witness any local bending of light
Not true. For sufficiently-accurate measurements the time variation of
tidal forces could be measured inside the cabin of either spacecraft.
Ditto for bending of light (which requires fantastically more accuracy,
but is measurable at least in principle).
> -- so where, oh where,
> does the necessary inference of any GR effect derive... in their view?
From the fact that SR is not applicable to this situation. Because
neither spacecraft moves in uniform rectilinear motion wrt the other.
> How would
> those pilots know to differentiate their's from an inertial frame?
See above. Each cabin can be considered a locally-inertial frame to
reasonable accuracy, but cannot be considered a GLOBALLY-inertial frame.
This can be determined by watching the position of the other spacecraft
over time.
> Without
> application of GR, an SR paradox results.
An invalid application of a theory outside its domain of applicability
does not constitute a "paradox", it is an ERROR.
Tom Roberts tjroberts@lucent.com
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