BIESEL@RUTGERS (02/15/83)
Recently an acquaintance popped this on me, and I was unable to answer his questions satisfactorily. General Relativity states that no experiment performed within non-inertial reference frames can distinguish between 1) Acceleration due to a gravitational field 2) Constant acceleration due to propulsion, for example. (Of course, an outside observer can always distinguish between these two cases) assume two identical closed boxes, each containing an observer and an electrically charged sphere. One of the boxes resides in a constant gravitational field, the other is undergoing constant linear acceleration in 'flat' space. Now Maxwell's equations predict that an accelerationg charge will generate an electromagnetic field, and will radiate energy ( which presumably comes from the energy supplying the acceleration). General Relativity would seem to demand that the charged sphere in the gravitational also radiate energy. If so, where does the energy come from; if not, how does this square with General Relativity? Where is the fallacy? Regards, Pete. -------
JGA@MIT-MC (02/16/83)
From: John G. Aspinall <JGA @ MIT-MC> Well, to start with, neither observer will detect any electromagnetic radiation from their respective charges. To detect a radiated field an observer has to have a relative acceleration w.r.t the charge. This doesn't cover all the energy arguments though, but be careful here too -- an outside observer would see acceleration going on, so there would have to be some form of energy input to the system to account for the acceleration.
ltn (02/17/83)
Paradox: General relativity says that an observer in a box cannot tell if he is
undergoing uniform acceleration, or is sitting in a gravitational field. A
charge carried in the box would radiate if accelerated. But if the box and
charge are in a gravitational field, then either:
A) The charge radiates, in which case, where does the energy come from?
B) The charge doesn't radiate, in which case there is a difference between
a gravitational field and uniform acceleration.
Resolution: The charge in the gravitational field does *not* radiate.
However, the observer in the box undergoing uniform acceleration (with the
charge that *does* radiate) will *not* see any radiation. This is because
he remains at rest with respect to the charge. A magnetic field is generated
by a moving electric field; since he is at rest, there is no motion, hence
no magnetic field and no radiation (in the observer's frame).
(Maxwell's equations are relativistically correct, despite having been
developed 40 years before Einstein came along.)
Thus in either case, the observer sees no radiation from the charge, and thus
cannot tell if he is undergoing acceleration or is sitting in a magnetic
field. An outside observer, can of course, tell which is the case.
Les Niles, Bell Labs Murray Hill (aluxz!ltn)rb (02/17/83)
Since the observer is in the box with the charged particle, the observer and the particle are at rest with respect to each other. The observer sees a charged particle at rest, so he detects an elecrostatic field, with no magnetic field. As far as the observer is concerned, there is no radiation. -Ronen
rhm (02/18/83)
Hey, this is great physics. An observer sees a photon emitted from a box; an observer travelling with the box doesn't see it. Wow! I'm told that I can't tell the difference between uniform acceleration, and gravitational acceleration, despite the enormous tidal effects from the latter. That's not the way my third grade teacher told it to me.
jfw (02/18/83)
Relativity states that gravitational acceleration is indistinguishable from any other form of acceleration. The tidal effects are a matter of a vector field, not of acceleration.
thomas (02/18/83)
There was a very good article by Forward in a recent Analog(? I think) about tidal effects and nulling them out for doing "0 gravity" work. =Spencer
gjphw (02/21/83)
Most of the comments of late about General Relativity (often called
Einstein Theory to distinguish it from other relativity theories) mention
what GR says. The equivalence between mechanics in a gravitational field
and in accelerating reference frames is an assumption in Einstein Theory and
not a consequence of it. And, since Einstein Theory has received only
three significant tests (passing them all quite well, though), this
equivalence assumption may still not be valid.
Patrick Wyant
Bell Labs IH
*!iheds!gjphw