[Physltest] [Phys-L] Re: expansion of gases

[John Denker <jsd@AV8N.COM>]

Anthony Lapinski wrote:
> My physics colleague brought a puzzling idea to me today regarding
> cosmology. We all know that when a gas expands, it cools. By conservation
> of energy, the expanding gas cools and its surroundings warm up.
>
> But what happens when a gas expands in a vacuum? If it cools, is the total
> energy still conserved? More specifically, what about the Big Bang? If the
> Universe was very hot in the beginning and expanded (into a vacuum), then
> it should cool. And it has -- to 2.7 K. But does this violate conservation
> of energy? We were both baffled. Can anyone help us with this apparent
> dilemma?

That's truly a deep question.

You have to know quite a lot about how "the expansion of the universe"
works in order to figure it out.

To cut to the chase:  The expansion does *not* consist of little cracks of
vacuum opening up within the gas, whereupon the gas expands into the
vacuum.

Instead, please visualize something like this:  Imagine a waveguide that
closes on itself to make a racetrack-shaped path for the microwaves.
Set up some sort of standing wave in it.  Now imagine that the
racetrack can expand, trombone-wise.  The waves will get adiabatically
red-shifted, assuming the expansion is done reasonably smoothly, as
opposed to ridiculously suddenly.  The result is nothing like free
expansion into a vacuum.  The result is more like adiabatic expansion
against a piston, i.e. expansion against a slowly-moving constraint.

Now, when you try to apply this analogy to the whole universe, you have
to be careful.  You cannot ask "where in the universe is the piston" or
"in what direction did the trombone-slide move".  To the extent that
those things exist at all, they exist in the embedding dimension, and
move in the embedding dimension, not in any real dimension.

The physical reality is that the waves do cool.  You can to a fair
approximation say that they "do work against the embedding dimension".
There are also more-sophisticated (harder to visualize) descriptions
that do not rely on any embedding.

Mathematically, it isn't hard to formulate the conservation laws so
that this contribution to the energy budget is elegantly accounted for.
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