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Re: superposition




It should be pointed out explicitly that superposition breaks down
for the electromagnetic field also at sufficiently extreme limits.
That field, too, exhibits nonlinearity, and a consequence of that
is that high energy gamma rays cannot be seen from great distances
in the universe because they collide with other radiation (the
microwave background) in otherwise free space.

Do tell! What are the other facets of this observation. I.e. how do we
know that there should be high energy gamma rays coming from great
distances, and how is it known that their absence is due to E&M
non-linearity?

Of course we don't know that high energy gamma rays should be coming
from great distances, but quantum electrodynamics wouldn't let them
travel long distances if they tried because of the cosmic microwave
background. I don't quite understand your question, however. If
the process were linear (i.e. if superposition held) electromagnetic
waves would not interact at all they would pass through one another
in free space without interaction, as indeed they do at lower energies.


Sorry, I was making assumptions. I really wanted to ask what the
background for your statement was, and I erroneously assumed that it was
experimental. If David Bowman's note correctly describes the phenomenon to
which you were referring, then it answers the question I was trying to ask.

David Bowman's explanation is correct, but incomplete. There is reason
to expect that whatever these high energy gamma sources are, they are
uniformly distributed throughout the universe. That is called the
Copernican principle, or the principle of mediocrity. It says we aren't
located anywhere special. That uniform distribution won't be apparent
to us, however, because we can't observe the universe "now". Our
observations of very distant objevts are of objects at a very much
earlier time in the universe's evolution, and the Copernican principle
does not say that we don't live at a special time. (The principle that
does say that is called the perfect cosmological principle, and it is
currently in bad odor because the universe appears to be expanding.)

Gamma ray bursters (GRBs) are distributed in space in a way which seems
to indicate that there are relatively fewer of them at longer distances
than there are at shorter distances. The energies at which gamma rays
are finding the CMBR opacity challenging are higher than those at which
the GRBs exhibit this apparent inhomogeneity, and the conventional
explanation is that whatever GRBs are (no one knows), they were likely
less common in the early universe than they are now.

Leigh