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Re: Law of conservation a fraud?



Merlin wrote:

Recently in my reading of PJE Peebles Principles of Physical Cosmology I
came across an intersesting if not inadequately explored issue.

I quote:

"...since the volume of the universe varies as a(t)3 (cubed), the net
radiation energy in a closed universe decreases as 1/a(t) as the universe
expands. Where does the lost energy go? Since there is no pressure gradient
in the homogeneously distributed radiation (Cosmic Background Radiation,
CBR) the pressure does not act to accelerate the expansion of the
universe...The resolution of this apparent paradox is that while energy
conservation is a good local concept and can be defined more generally in
the special case of an isolated system in asymptotically flat space, there
is not a general global energy conservation law in general relativity
theory."

There is a similar discussion in the Chapter 11 of the concise book,
_General Relativity, A First Course for Physicists_ by J. L. Martin,
Prentice Hall, London, 1996. In sec. 11-9, entitled "The
non-conservation of energy," Martin writes out a classical equation for
the adiabatic change of volume V of a gas, stating that it represents
conservation of energy:

d(rho*V) = -p*dV ..... d(rho)/dt + (rho + p)*[(dV/dt)/V] = 0 ,

where rho is the energy density and p is the pressure.

From the Einstein equations of GR as applied
to the Robertson-Walker metric (One case is worked out) he arrives at
an equation of exactly the same form as the classical adiabatic equation
expressing conservation of energy. Interestingly, he comments:

"Oddly, this does not represent cosmological conservation of energy,
since there are no cosmological boundaries for the pressure to work
on. An expanding universe loses energy, but it loses it to nowhere in
particular. However, there is really no reason to expect energy
conservation on two counts: conservation of energy is always associated
with systems in a static environment, and such an environment is not
provided by an expanding cosmology; and, in any case, integration of
the matter tensor to yield a total energy is an ill-defined procedure in
curved space." Sections 11-4 and 11-11 of Martin's book also have
discussions which seem to tie in with that of Peebles.

Hugh Logan