Re: Gen. Relativity

Dear Tom Roberts:

"Tom Roberts" <[EMAIL PROTECTED]> wrote in message
news:[EMAIL PROTECTED]
> On 12/1/2003 6:53 PM, [EMAIL PROTECTED] (formerly) wrote:
> > "Tom Roberts" <[EMAIL PROTECTED]> wrote in message
> > news:[EMAIL PROTECTED]
> >>On Mon, 1 Dec 2003 07:25:24 -0700, [EMAIL PROTECTED] (formerly) wrote:
> >>>>How about this.  Take all the energy in the Universe (converting all
> >>>> other
> >>>>matter), and stick it into a single neutron, so that it is going like
a
> >>>>"bat out of hell".  Since it is the only particle in the Universe, it
> >>>> is no longer moving, is it?
> >>>
> >>Impossible assumptions lead to impossible conclusions. In GR it is not
> >>possible to do that. Becuase locally both energy and momenum are
> >> conserved.
> >
> > I understand that the only way we could transfer momentum to an object
is
> > by hitting it with something, which would leave at least two particles
in
> > the Universe.  But I don't see what you see when you say "both energy
and
> > momentum are conserved" in a single body system (whether or not a
neutron
> > could "take" it).
>
> It is the "take all the energy in the universe and stick it into a
> single neutron" that is the problem. This is well known in
> thermodynamics (c.f. the Second Law of Thermodynamics, and more
> particularly Gibbs Free Energy). The same notion applies, and it is
> impossible to "get it all". You could (in principle) start with a
> universe containing just a single particle, but you cannot in general
> get there from a universe that initially has more than that.
>
> I put "get it all" in quotes because it is so poorly
> defined. I mean nothing unusual.

And here I was expecting metaphysics!  Well reasoned.  Thank you.

> > The net angular momentum in the Universe is possibly
> > non-zero.  The net linear momentum of the Universe is zero(?).
>
> Doesn't matter. The problem is with the impossibility of "getting it
> all", not non-zero values for momentum or angular momentum.
>
> Questions about the "total angular momentum" and/or "total
> momentum" of the universe are wrapped up in the "boundary
> conditions at infinity". In general such "totals" do not
> make sense (due to difficulties of doing integrals over finite
> regions of a curved manifold), but there is a large class of
> manifolds for which this does make sense. Within that class
> there is no inherent requirement for either total to be zero
> (but zero is the most natural and obvious choice). This is the
> same issue as that of "radiation zooming in from infinity"
> -- consistent with the theory but quite unreasonable.

Thanks, Mr. Roberts.  I do have some "logical" concern about a one-body
Universe having any net angular momentum, but that is because I don't know
any better!

David A. Smith