Re: relativistic centrifuge
From: RP (no_mail_no_spam_at_yahoo.com)
Date: 10/24/04
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Date: Sun, 24 Oct 2004 14:01:09 -0500
Edward Green wrote:
> RP <no_mail_no_spam@yahoo.com> wrote in message news:<2srr9tF1nt4aaU1@uni-berlin.de>...
>
>>RP wrote:
>
>
>>>>In SR, the rate of a moving clock is slowed by sqrt[1 - v^2/c^2], or
>>>>
>>>> sqrt[1 - aR/c^2]
>>>>
>>>>expressed in terms of acceleration and radius for a centrifuge.
>>>>
>>>>In GR, the rate of a clock on the surface of a planet is slowed by
>>>>
>>>> sqrt[1 - 2aR/c^2]
>>>>
>>>>where a == g, the acceleration of gravity, R the planetary radius.
>
>
>>>http://www.beyondweird.com/einstein/contents/ap03.htm
>>>
>>>Read the original.
>
>
> Thanks for the link!
>
>
>>After reading Einstein's version of the same argument, do you agree with
>>Al's statement?
>>Obviously in this derivation the gravitational clock rate reduction is
>>exactly the special relativistic reduction, or IOW, it is in fact just
>>the special relativistic transverse doppler effect, as Al claimed, but
>>it is also simultaneously held by Einstein to be a gravitational clock
>>rate reduction.
>
>
> The (relativistic) "tranverse doppler effect" should in fact be a
> compound of time dilation at the source and effect calculable purely
> from motion of the source in the rest frame of the observer, sans
> relativity -- just as the (relativistic) longitudinal doppler effect.
> But maybe just at the crossing point there are no effects on the
> received frequency beyond time dilation at the source? Is the
> transverse doppler effect is a strict synonym for what I have in mind,
> or a first cousin?
>
> As for what was held by Einstein in the linked material, let me offer
> the great man a fig leaf, and say that this was intended as a
> heuristic derivation, guided by the equivalence principle. I say this
> because I think a modern point of view would be that the argument is
> in fact heuristic, since it is an overextension of the said principle.
>
> Anyway, as has been said before, once the scaffolding falls away, it
> doesn't matter what arguments were used to construct the equations --
> only that they stand under experiment. There is no way to rigorously
> derive a new theory from accepted results, obviously!
>
> Let me get this right, though: are you saying that if we don't state
> the results in terms of acceleration, but in terms of potential, that
> the discrepant "2" goes away!? I like that. It ought to be correct,
> and I ought to have guessed that: I knew somewhere that gravitational
> potential was the Right Stuff in predicting gravitational time
> dilation. Presumably the 2 then reflects the very different shape of
> the "gravitational field" of a centrifuge vs. a gravitating sphere --
> and the different relation of a to phi.
>
> Nice.
>
>
>>IOW, in this derivation it is implicit that GR and SR are just alternate
>>descriptions of this effect, rather than superposed effects.
>
>
> Now I don't know that _that_ follows at all. Recall what I said about
> scaffolding and heuristics. However he got there, GR contains
> fundamentally new physics: curved spacetime. SR then becomes a
> special case which GR reduces to locally, or globally in the case of
> flat spacetimes.
>
>
>>IMHO,
>>there are entirely too many ifs in this derivation, and no basis
>>whatsoever provided for them, seeing as there is no such angular
>>velocity of a mass at rest on a nonrotating gravitating body to
>>correspond the special relativistic clock rate adjustment to, and thus
>>an absence of the equivalence principle entirely in this derivation. If
>>a frog had wings, then.....well....it must follow that frogs do indeed
>>have wings and do not in fact bump their ass every time they jump.
>
>
> You're right about the logical quality of the "derivation", but wrong
> I think about its significance. GR is born and stands by test alone.
>
> Anyway, thanks immensely for the reference -- so the mystery sharpens.
> Einstein built the theory precisely ensuring that "concidences" like
> this would hold. But is the world similarly constructed? Orbiting
> atomic clocks do not disagree.
>
> [You gave me a chance for self-observation regarding prejudice and
> authority, and the utility of humor: I'll be honest with you. At
> first I didn't follow the link because I thought it was to _your_
> material, not Einstein's! Then you gave me a good laugh with your
> comment about getting a moderator to filter out the non-cranks in this
> group, so I thought you weren't such a bad sort, and went back to
> check it out -- but I'm _still_ thinking it's your material! So
> oriented, my first reaction was you are taking entirely too long to
> come to the point. ;-)]
I can appreciate your sentiment towards my posts. I admit that I tend to
dispute what may seem to you to be "just about every orthodox stance in
existence". ;) OTOH, I am sometimes unambiguously correct, as in this
instance. Your interpretation is correct -- the discrepant 2 vanishes
when the ticking rate is derived in terms of potential.
(Not that I'm wrong as often as commonly thought, though some of the
arguments may be difficult for one trained in the orthodoxy to
appreciate, having been reared in traditional modes of thought, but I
digress...
There is no logical connection between potential and clock ticking rate
from the standpoint of special relativity. Moreover, Einstein's
derivation in the appendix is not a heuristic argument, it is in fact
the very basis that he used in the development of general relativity.
There simply is no other means of deriving gravitational clock rate effects.
Regardless of its success, or forced success, as the case may be, either
the general relativistic interpretation of transverse doppler effect is
incorrect, or the special relativistic interpretation is incorrect,
since in the former case the ticking rate is supposed to be due to the
potential in which the clock finds itself, and in the latter it is
supposed to be due to the relative velocity wrt inertial frame. If we
insert another clock, comoving in a given instant with the centrifuge
clock, but we then allow the second clock be moving uniformly along a
straight line, then the original clock's rate will be gravitationally
affected and the other clock's ticking rate will not be gravitationally
affected, even though from the special relativistic stance, both clocks
are ticking at the same rate. Thus, if indeed there is a link to the
EP in this derivation in any guise, then it must follow that an inertial
frame is immersed in a gravitational well by virtue of nothing more than
its relative motion to anther frame. Thus for the purposes of
relativistic clock rate changes we derive velocity == acceleration. The
only other alternative, is that the derivation was baseless and bogus.
Now do you understand the basis of my objections?
Almost all orthodox theory that I've examined is based upon
insupportable speculation, and almost all contain logical contradictions
such as this. Of course I don't have all the answers, I'm just a human,
but I have derived at least a few of them, and directly from the
empirical data in order to ensure their empirical consistency, and
empirical consistency, as you noted, is the bottom line de facto
requirement of any useful theory. Logical integrity is secondary, but
it is likewise a necessity, that is, if the theory is to make valid
predictions about a given outcome, then it is imperative that it predict
only one outcome.
Richard Perry
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