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Re: EM Radiation Without a Source



At 04:04 AM 11/30/00 -0500, Ed Schweber wrote:

Do Maxwell's equations preclude the existence of electromagnetic
radiation that at some time in the past has not originated from an
accelerating charge (besides any vacuum fluctuations)?

No, that is not precluded.

Here's how the argument goes:

First, to illustrate why the answer is not trivial, consider a different
problem, namely the orbital dynamics of the moon. We start by treating the
earth/moon system in isolation. We know that due to tidal effects, angular
momentum is being transferred from the daily spin of the earth into the
monthly orbit of the moon. If you run this process backwards in time, at
some definite point in the past you find that the moon was inside the Roche
radius, and the hypothesis that we have an isolated earth/moon system
breaks down -- there _must_ have been something else going on.

Now, let's see what happens with EM waves. Start with some present-day
pattern of EM waves. Run the equations back in time. There is _no_ time t
in the past where the equations break down (provided t>0). The fields will
get very large, but Maxwell's equations _per se_ are linear, so there's no
problem. If you allow pair production, these large fields will cause pair
production. OTOH in an imaginary universe without pair production, the
large fields will just be large fields. (Pair production can be thought of
as EM waves interacting with vacuum fluctuations.)

You can run t back to a value as small as you like, provided
t>0. Questions about what happens right at t=0 are not physics. They need
not be asked and can not be answered in terms of physics.

Could EM have been created at the big bang without having first been
"radiated" from a source.

This picture is not only allowed by our current understanding of physics,
it is the starting point of many models. In such models, cosmologists
don't start by saying "at some early time t we have X amount of hydrogen
and Y amount of energy." Instead, they just assume there was nothing but
EM energy and let everything else be created in due course as the universe
evolves according to the laws of physics.