From: ted@physics.Berkeley.EDU (Emory F. Bunn)
Newsgroups: sci.physics
Subject: Re: Redshifted light wonders
Date: 31 Aug 1992 05:27:14 GMT
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Distribution: world
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In article <1992Aug30.224446.25468@hellgate.utah.edu> tolman%asylum.cs.utah.edu@cs.utah.edu (Kenneth Tolman) writes:
>  If the universe is expanding merrily away, and photons fly across this,
>there are some peculiar things that result.... how can these things be 
>resolved?
>
>  1) Is there some minimal energy state that a photon can be redshifted to?
>Is there some minimal energy which a photon can have before it effectively
>ceases to exist?  (read next question to make more sense of this)

Photons just keep losing energy forever; there is no minimum energy a 
photon can have.

> 2) Is there a continuous energy change for a particular photon, or does
>it get redshifted across jumps?  Does not quantum mechanics imply that
>there are only certain meaningful energy values, and as such would not a 
>photon move from one to the other?  If not, this would imply that there
>would be undetectable photons- high energy photons which did not correspond
>to any absorption frequency of any detection device.  Unless of course, the
>detection devices were somewhat forgiving.... is this the case?

Not everything in quantum mechanics comes in discrete units; some quantities
are allowed to vary continuously.  The energy of a photon (at least in an
infinite Universe) is one of them.  In a finite Universe, there are discrete
allowed energy values, but they are extremely closely spaced.  Furthermore,
a redshifting photon in such a Universe does not lose energy by jumping from
one level to another; rather, each energy level gradually shifts downwards
as the Universe expands.

But if you ask me (which you didn't), our Universe is infinite anyway,
so it doesn't matter.

> 3) Are these photons losing energy for the whole universe?  Is energy not
>being conserved, or is it?

This is a tricky one.  Let me come at it indirectly.  If you fire a photon 
upwards in the Earth's gravitational field, it loses energy and redshifts.
You can get away with viewing this phenomenon in the same way as the
more commonplace phenomenon that if you throw a massive object up in the
air, it slows down and loses energy.  That is, you can say that kinetic
energy is being transformed into gravitational potential energy.

Now, the redshift of a photon due to the expansion of the Universe can
be viewed as a gravitational redshift, and so you might hope to use the
same explanation here:  Energy is conserved as the photon's energy gets
converted into some sort of gravitational potential energy.  The problem
is that there is no consistent way to define "gravitational potential
energy" within the context of general relativity.  You can do it in
certain special cases; specifically, if the massive objects in your spacetime
are located within some finite region, and spacetime asymptotically
approaches flat spacetime far from that region, you can define the total
energy in a sensible way, and it's conserved.  The spacetime near the
Earth fits into that class (to a good approximation), and so you can
get away with talking about gravitational potential energy near the Earth.
But you can't for the Universe as a whole.

So the answer I would give to your question is that non-gravitational
energy is definitely NOT conserved in the expanding Universe, and
there's no way to sensibly define the gravitational energy, so the question
"Is total (gravitational and non-gravitational) energy conserved?" is
not well-defined and has no answer.  Pretty unsatisfying, but life's
sometimes like that.

I should make the disclaimer here that I am not a general relativity 
expert, and so what I say might be wrong.  I'm pretty confident about
the general picture, although some of the details might be mixed up.

-Ted

Newsgroups: sci.physics