act@pur-phy.UUCP (Alex C. Tselis) (12/02/84)
I have a question concerning the apparent paradox between electromagnetic theory and the equivalence principle. I hope those who know about these sorts of things can resolve this paradox in an easy way. The question concerns the behavior of electric charges in a gravitational field. Suppose that I were to take an electrical charge (a point charge or a distributed one; it makes no difference), put a force on it and accelerated it. It would then radiate electromagnetic waves. Now suppose that I were to place this charge on a table in my office. The charge is in a gravitational field (due to the earth). But according to the equivalence principle, a gravitational field is equivalent to an acceleration (at least locally; I can always make the distribution of charge so that it is confined to a small enough spatial region so that the earth's gravitational field can be taken to be uniform over it.). However, this charge does not radiate, even though it is in a situation which is equivalent to an acceleration. How is this resolved?
gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (12/08/84)
> ... Suppose that I were to take an electrical charge ..., put a force on > it and accelerated it. It would then radiate electromagnetic waves. Now > suppose that I were to place this charge on a table in my office. The > charge is in a gravitational field ... However, this charge does not > radiate, even though it is in a situation which is equivalent to an > acceleration. I think it would, if you were in free-fall. Similarly, if you had been attached to the charge's rest frame in the first example, I don't think it would appear to radiate. However, it has been a long time since I was up on this stuff...
ethan@utastro.UUCP (Ethan Vishniac) (12/08/84)
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I've never thought about this before, and I suspect that
working out the full answer is quite time consuming. However,
I think I know what the resolution must be. The equivalence
of gravity and acceleration (for an object on the surface of
the Earth) is a *local* equivalence. On the other hand, the
radiation of electromagnetic waves necessarily involves the
application of boundary conditions at infinity (i.e. no incoming
waves in the Minkowski frame, something more complicated but
along the same lines when curvature is invoked). Therefore there
is not necessarily a paradox involved here. On the other hand,
it would be nice if someone worked this one out. Any volunteers?
The above will not be the official opinion of the University of Texas
until such time as it can be reliably ascertained that hell has frozen
over to a depth of at least 10 meters.
"I can't help it if my Ethan Vishniac
knee jerks" {charm,ut-sally,ut-ngp,noao}!utastro!ethan
Department of Astronomy
University of Texas
Austin, Texas 78712berry@zinfandel.UUCP (Berry Kercheval) (12/10/84)
Charges radiate EM when accelerated. If a charge is resting on a table (as I believe the original query was phrased) in a graviataional field, then (ignoring rotation of the Earth) it is at rest, NOT being accelerated. Gravity pulls down, the table pushes up. Acceleration of a charge WILL cause it to radiate, whether said acceleration is due to gravity, magnetic fields, fusion rockets or telekinesis. You don't need to drag Minkowski into it. -- Berry Kercheval Zehntel Inc. (ihnp4!zehntel!zinfandel!berry) (415)932-6900