Rambling morning note and Chuck Britton's comment

[Leigh Palmer <palmer@SFU.CA>]

At 18:08 -0700 8/5/99, Chuck Britton wrote:

> I just sat through the AAPT's Klopsteg Memorial Lecture delivered by
> Michael S. Turner of the U. of Chicago, entitled Cosmology: From
> Quantum Fluctuations to the Expanding Universe.
>
> He points out that in GR, the gravitational attraction has its
> 'source' in rho + 3p, with rho being the usual mass density and p is
> the 'pressure' of local space. (His analogy, if space is a stretched
> sheet, then its p is negative.)

This is one of those guys who likes to work in reduced units, even
when he talks to physics teachers. I certainly understand why a
theoretician, thoroughly familiar with the problem he is working
on, would want to use reduced units. They both simplify and clarify.
However when a theoretician talks to a nonspecialist (and we physics
teachers are mostly nonspecialists) I believe it gets in the way of
understanding. For me this source term is demystified a bit if it is
written as rho c^2 + 3p. The familiar c^2 makes the units come out
right in the systems we teach in and alerts us to the fact that this
is an energy density term. It could also be written as rho + 3p/c^2,
of course, to make it come out in mass units.

I don't use c = h = 1 every day. I chide students for failing to
check their solutions for dimensions and dimensional consistency.
Then some theoretician comes along and dazzles me with his working
convenience and the distraction of trying to keep up with what he's
saying while making the units consistent makes me lose the thread.
Top that off with the added distraction some of them use, setting
pi = 1. This is an astrophysicists' convention (called the "small
circle approximation by some wags) used when they only want to keep
track of orders of magnitude!

There. I've always wanted to express that peeve in public; I've
never done so before, but Chuck gives me a good opening. I served as
colloquium organizer for our department during the spring semester
(and I will do so again next spring). I try to select good speakers
who recognize that a colloquium is supposed to be directed to the
nonspecialist physicist. I really feel disappointed when I attend a
talk by a world reknowned physicist and the only people who ask
questions after the talk are specialists in the speaker's field. It
means that the rest of us, the majority, have probably wasted a
microcentury and come away with nothing of value.

> This overall NEGATIVE gravity source is used to 'explain' the
> recently verified ACCELERATION of the expansion of the universe.

"Explain" is, in my opinion, an exaggeration. It would be more
proper to call this pressure a *parameterization* of the theory to
make it fit the observations. I think it is the same thing as the
cosmological constant lambda which parameterizes the universe
together with its mass term omega. It was in the not so distant past
that theoreticians confidently told us that omega = 1 and lambda = 0
since they *had* to have those values if they were even close
observationally. (That's a Platonic ideal.) Add to this the fact
that omega is really a reduced mass density, leaving off not only
the c^2 , but expressing the density in terms of the critical
density for an asymptotically flat universe. No longer do the
theoreticians point to the Platonic ideal values 1 and 0. They've
now freed *both* to fit the new Type Ia supernova study data (which
are, admittedly, compelling). Such is the current fad, alas!

Bottom line: don't put cosmology on the list of closed questions
just yet.

> I dunno if this is relevant to the current 'discussion' of energy but
> it seemed relevant to Leigh's post.

It is relevant. The pressure p involved here is only of order of
magnitude comparable to the critical energy density of the universe.
It is insignificant on, say, a galactic scale, and absolutely
undetectable on the scale of the solar system mass density, where GR
works so well with lambda = 0 that it (GR) is considered to be above
question. Thus the pressure term plays no role in my claim that the
gravitational field energy density (and, I believe, the associated
gravitational mass density, the source term) associated with this
field, is negative. The field energy is a very small fraction of the
gravitational source term in this case anyway, the dominant term
being that due to the "real" masses themselves. I'm afraid I'm way
out of my depth here in discussing GR - since I don't even know the
theory! The business of the scale of significance was explained to
me by (the late) William Kaufmann. It is the answer to my question
to him: "Why does the universe expand while the galaxies don't?" He
answered by email and followed up with printed material that I
could understand. He must have been a fine teacher; his sense of
impedence matching was excellent!

I must go lower my canoe. Can't leave it precariously high while
I'm at school.

Leigh