🚀 go-pugleaf

Edward Green wrote:

> Wolfgang G. Gasser wrote:
> 
> 
>>Two distant observers with each a (transversal) LIGHT CLOCK orbit at a
>>constant distance around their common center (assumed at rest).
>>
>>Special relativity postulates that the light beams in both light clocks
>>propagate at c relative to both (almost inertially moving) observers.
> 
> 
> This needs to be reworded, I think.
> 
> 
>>This requires that for each observer the clock rate of the opposite clock
>>CAN be lower than the clock rate of his own clock.
>>
>>Because of symmetry and unchanging distance, clock rate CANNOT differ.
>>
>>The impossibility of mutual time dilation in this situation entails the
>>impossibility of a constant speed of light as a general law.
> 
> 
> Of course you haven't "disproven special relativity", but I think it's
> a good conundrum.  I'm not really happy with "non-inertial observers"
> as the full rebuttal.  That's the answer at the old transatlantic cable
> rates -- words are now cheaper.

I like your answer best. I looked at situations like this one a lot a 
few years ago, including one where a spaceship orbits the Earth, and 
sees time passing faster, not slower, for the Earth, even though 
acceleration has been proven to have no relativistic effects whatsoever. 
It turns out that yes, things like this can happen, but they don't 
violate the laws of SP. Two INERTIAL observers will always see each 
other as having a slower time-rate (well, as long as they don't travel 
around the universe), and that is indeed the prediction of SP, but under 
SP, non-inertial observers will not see the same thing.

However, although people often claim that we need GR to solve such 
problems, GR is only necessary if large gravitational fields are 
involved. As long as only acceleration is invovled, including large 
acceleration, we can use the laws of SR to correctly predict the 
results. In fact, using GR's technique of replacing an acceleration with 
an equivalent gravitational field will only work if the acceleration is 
constant. Varying acceleration, such as found in the normal clock 
paradox, cannot be solved using this "GR substitution," as Wolfgang 
Rindler pointed out in his book, "Special Relativity" a long time ago.

Phil

> 
> Obviously the situation is fully symmetric, but then, so is the
> situation of inertial observers passing each other at constant
> velocity: why bother with the rotation, when we could already argue
> that "each clock is running slower with respect to the other, which is
> obviously impossible".  That's already a fairly piquant paradox, which
> I have no ready glib answer to, and one of the special charms of SR!
> 
> Roughly, the dependence of t and t' on x' and x, respectively, is what
> enables the math to weasel out of this seeming contradiction; also,
> "running slower with respect to the other" may not be operationally
> well characterized.  Ask any concrete empirical question, and we get a
> single answer -- if we accept the implied operational characterization
> of "running slower with respect to the other", then we have extended
> the sense of the phrase in a new situation to exclude one of its
> expected properties (non-reflexivity).
> 
> Standard concept-splitting.
> 
> The "non-inertial observer" thing seems cheap to me, and possibly off
> the mark.  Rotating rings force SR to show its cards by allowing
> movement in a closed path, but acceleration is not necessarily crucial:
> it can be made as small as we like for fixed speed of the circumferance
> by choosing a large enough ring.  Both clocks are running slow as
> according to an inertial observer at the hub.  How do they describe
> each others behavior?  They had better be careful to make some
> empirical predictions!  Then they will agree.  Distrust glib language.
>