Re: law of conservation

[Hugh Logan <hlogan@ix.netcom.com>]

Ninduk wrote:
> to mr. logan and mr. merlin
> well your arguments regarding conservation laws were exciting. if energy is not conserved in the universe then
> where does the lost energy go to? is the total energy of the universe >not constant? 

In the first place, what do you mean by the total energy of the
universe? In particular, how do you sum the infinitesimal contributions
over the entire universe? This is possible in Newtonian physics and in
the flat spacetime of special relativity, where one has conservation
of the momentum-energy 4-vector. In either of these cases it would only
be possible to refer the total energy (or momentum-energy) to a single
inertial reference frame. Even in Newtonian physics, it would not
make sense to sum energies if they were not referred to the same frame
of reference. If a 1 kg object is sliding across the floor of a train
with a velocity of 1 m/s relative to the train along the direction of
motion of the train which, in turn, is moving uniformly at 20 m/s
relative to straight tracks on the ground, the kinetic energy of the 1
kg object relative to the train is 1 Joule, but is 441 J relative to the
tracks. If you wanted the total energy of the train and the object, it
would be 1 J relative to the train frame of reference, but relative to
the tracks it would be 441 J plus the KE of the train relative to the
tracks. But it would not make sense to combine the KE's in different
reference frames.
   According to my intuition, it would no more make sense to combine the 
energies of two very distant infinitesimal regions of spacetime in an
expanding universe. According to the article that Bob Sciamanda referred
to (http://math.ucr.edu/home/baez/physics/energy_gr.html), some attempt
has been made to arrive at a total energy. However, this can only be
done using questionable mathematical entities called pseudotensors. 
This seems to lead to inconsistencies in the theory, and there appears
to be controversy about whether or not this should be done. There are
further questions about the role of gravitational energy in GR, since
gravitational potential energy is done away with in favor of the
introduction of the curvature of spacetime. But this is complicated by
the possibility of gravitational waves that can interact owing to the
nonlinearity of the Einstein equation. With regard to energy loss in the
red-shift of the cosmological background radiation, Michael Weiss and
John Baez state, "Cosmologists model the expanding universe with
Friedmann-Robertson-Walker (FRW) spacetimes.
(The familiar "expanding balloon speckled with galaxies" belongs to this
class of models.) The FRW spacetimes are neither
static nor asymptotically flat. Those who harbor no qualms about
pseudo-tensors will say that radiant energy becomes
gravitational energy. Others will say that the energy is simply lost." 
I think the Weiss-Baez article is definitely worth reading. 

> if energy is not conserved then it will be easy to create energy/mass uot of nothing at anywhere in the universe - but this sounds
> inconsistent.

How would this be possible if energy is lost by the universe? The only
thing like creation of matter out of nothing that I have heard of is the
continuous creation theory of Bondi,Gold and Hoyle in which particles
are spontanously created so as to keep the particle density of the
universe constant. I will leave the explanation of this to others more
expert in the field.

Hugh Logan