RE: [asa] (Planck limits) Thermodynamics & Eternal Universe - A Question

---- Ted Davis <TDavis@messiah.edu> wrote:
> I heard recently from someone knowledgeable that the first law of
> thermodynamics does not actually apply to relativistic cosmology.
> Apparently something of a "secret," in terms of the general public, though I
> understand that physicists do talk about this and are concerned about fixing
> the problem. They are also not at all confident that it can be fixed.
>
> That's what I am hearing. Can anyone who actually knows about this fill in
> the details for me? Is this in any way related to Hoyle's claim in the
> steady state theory that hydrogen atoms can just sort of pop into
> existence?
>
> Ted

Ted -
 
I'm not sure just what "secret" you're referring to but it's true that there are
problems with energy conservation (aka 1st law of thermo) in general relativity
- & not just with cosmology.
 
The root of the problem is that the conservation laws for energy, momentum &
angular momentum are consequences of certain symmetries of space-time & a
space-time that is a solution of Einstein's equations will, in general, have no
symmetries. Energy conservation in particular is a consequence of invariance
under time translation (i.e., space-time will be the same tomorrow as today) &
if that invariance doesn't hold - as in a general expanding universe - then
energy conservation won't.
 
Then a distinction has to be made between local & global conservation laws.
Unlike the case with, e.g., E & M, we can't define a unique energy density -
energy per unit volume - for the gravitational field. That's a consequence of
the equivalence principle which says, among other things, you can get rid of
gravitational acceleration locally by an appropriate choice of coordinate
system.
(Technically, the 1st derivatives of the metric can be made to vanish along a
worldline.)
 
For isolated physical systems (like a single particle or cloud of particles)
space-time is "asymptotically flat" (i.e., Euclidean at large distance from
matter) & a conserved _global_ energy can be defined as an integral over a large
sphere surrounding the matter & this has the appropriate properties. (For a
mass m, the energy is mc^2.) But a cosmological model is _not_ asymptotically
flat. (3-D space is, it now seems, close to being flat but space-time isn't.)
 
The there's another phenomenon in expanding universes. In general a particle
will have a "peculiar motion" - i.e., be moving relative to the expanding space
(to speak crudely). But this peculiar motion dies out & eventually the particle
is in effect "swept along" with the general expansion. That means that if you
use just that peculiar velocity to calculate its kinetic energy, that energy
decreases with time. (Schroedinger discussed this at some length in his book
_Expanding Universes_.) Humphreys tried to use this phenomenon to get rid of
the excess energy produced by accelerated radioactive decay at the time of the
flood (I say, trying to keep a straight face) but it doesn't work. See the NCSE
paper that Glenn Morton & I did, & especially the appendix - it's included with
Randy Isaacs' critique of the RATE claims at the ASA website.
 
None of this has anything directly to do with Hoyle's "creation field." It's
worth noting, however, that the steady state folks argued correctly that while
energy is created locally in their model, the total energy in the _observable_
universe is conserved, which isn't the case in big bang models.
 
I don't know if this answers your question but hope it's of some use.
 
Shalom,
George

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Received on Sat Oct 4 12:22:55 2008