Zero Energy Universe: Examining Conservation of Energy in Cosmology

[Naty1]

I was looking for some information on the total energy in the universe:
Crowell said: How does conservation of energy apply to cosmology?

General relativity doesn't have a conserved scalar mass-energy that can be defined in any spacetime.[MTW 1973] It only has certain definitions that work in special cases, including stationary spacetimes and asymptotically flat spacetimes. Cosmological solutions aren't stationary or asymptotically flat. Therefore there is no way to define the total energy of the universe (regardless of whether the universe is spatially finite or infinite). There is not even any way to define the total energy of the observable universe. There is no way to say whether or not energy is conserved during cosmological expansion.

(oops. I lost the thread where this appeared...ok, post #12 here: https://www.physicsforums.com/showthread.php?t=453837&highlight=zero+energy+universe)

Yet I turned up this which seems to say it's zero:


http://arxiv.org/PS_cache/gr-qc/pdf/0605/0605063v3.pdf

(and Wikipedia...http://en.wikipedia.org/wiki/Zero-energy_universe)

ON THE ZERO-ENERGY UNIVERSE
Marcelo Samuel Berman1

We consider the energy of the Universe, from the pseudo-tensor point of view(Berman,1981).
We find zero values, when the calculations are well-done.The doubts concerning this subject are
clarified, with the novel idea that the justification for the calculation lies in the association of the
equivalence principle, with the nature of co-motional observers, as demanded in Cosmology. In
Section 4, we give a novel calculation for the zero-total energy result.

in which he says:

(Guth, 1981), as an accelerated expansion of the Universe, immediately after the creation
instant,while the Universe, as it expands,borrows energy from the gravitational field to
create more matter. According to his description, the positive matter energy is exactly
balanced by the negative gravitational energy, so that the total energy is zero,and that
when the size of the Universe doubles, both the matter and gravitational energies also
double, keeping the total energy zero (twice zero).

It has been generally accepted that the Universe has zero-total energy. The first such claim, as far as the present author recollects, was due to Feynman(1962-3). Lately,
Berman(2006, 2006 a) has proved this result by means of simple arguments involving
Robertson-Walker’s metric for any value of the tri-curvature ( 0,−1, 1 ).

Are these views complementary or contradictory?

 

[Chalnoth]

Are these views complementary or contradictory?

The first point was talking only about the energy in the matter fields. The second was using the Hamiltonian formalism, which defines a potential energy for gravitational fields, and essentially enforces energy conservation by hand. When this is done, the total energy for a closed FRW universe turns out to be zero.

 

[Chronos]

It would be logically inconsistent for the total 'energy' of the universe to be anything other than zero [or very, very close] due to the laws to thermodynamics. It would otherwise be highly unstable. The trick is in how you define 'energy'. Personally, I prefer the information theory definition.

 

[bcrowell]

General relativity doesn't have a conserved scalar mass-energy that can be defined in any spacetime.[MTW 1973]

We consider the energy of the Universe, from the pseudo-tensor point of view(Berman,1981).

Are these views complementary or contradictory?

Complementary. Note the word "scalar" in my quote and the word "pseudo-tensor" in the Berman quote.

-Ben

 

[Naty1]

aw. c'mon guys/girls, this is physics forums...where controversey reigns supreme! I don't believe I have ever seen three "expert" posters in such agreement...that ruins the fun, but I guess aids understanding, so thanks...

"such a big place, so little time to learm."

 

[bcrowell]

aw. c'mon guys/girls, this is physics forums...where controversey reigns supreme! I don't believe I have ever seen three "expert" posters in such agreement...that ruins the fun, but I guess aids understanding, so thanks...

We could still probably get in a good rip-roaring argument about whether pseudo-tensors are good or evil. It would be fun for me to watch that one from the sidelines, since I know nothing about pseudo-tensors :-)

 

[mrspeedybob]

Along these same lines I came across this article...

http://www.science20.com/hammock_physicist/square_root_universe

I follow their logic right up to this point...

And now comes the key point: if we associate with a black hole horizon an energy equal to its HHR or half-radius, then we have to associate a similar energy to the cosmic horizon.

That statement needs some justification to me. What is that justification?

 

[Chalnoth]

That statement needs some justification to me. What is that justification?

That's the mass-energy of a black hole.

 

[mrspeedybob]

That's the mass-energy of a black hole.

Yes but how do we justify the assertion that the inside event horizon of the universe has anything to do with its energy content?

 

[Chalnoth]

Yes but how do we justify the assertion that the inside event horizon of the universe has anything to do with its energy content?

Ah, sorry, I misread. This sounds like just another way of wording the fact that in a closed universe, the total energy works out to identically zero in the Hamiltonian formalism of General Relativity.