Gravitational Energy: Is it Really Zero?

[maximus]

is it not true that the total energy of the universe is zero? i heard somewhere that the gravitational attraction between objects is exactly canceled by the electromagnic force required to keep them apart at close ranges. this might only mean gravitational energy is zero. but gravity still is observed and has a very apparent effect so this is a sort of worthless thread.

 

[Alexander]

Rest mass energy mc² of universe is equal to its negative gravitational energy.

 

[pellman]

The total energy of the universe is an undefined quantity, from a General Relativity point of view. Even from a Newtonian point of view, it all depends on which inertial frame you are measuring from.

 

[jeff]

Originally posted by pellman
The total energy of the universe is an undefined quantity, from a General Relativity point of view.

It is defined for asymptotically euclidean spacetimes.

 

[marcus]

any idea how relevant, if at all?

Originally posted by steinitz
It is defined for asymptotically euclidean spacetimes.

I've often heard statements like this but never heard it claimed that these special cases are at all realistic. I have heard, although haven't gone thru the proof, that one can define
a total energy in "assymptotically hyperbolic" or "assymptotically Minkowski" cases. But these seem to have no connection with reality. The expanding space time we have as given does not fit these cases, or so it seems to me.

BTW assymptotically "euclidean" does not immediately make sense to me---I would have expected you to say "assymptotically Minkowski" or "assymptotically flat spacetimes". Clarify if you wish.

 

[marcus]

Originally posted by pellman
The total energy of the universe is an undefined quantity, from a General Relativity point of view. Even from a Newtonian point of view, it all depends on which inertial frame you are measuring from.

Pellman! Where did you drop in from! I've been wanting some corroboration for my assertion that no global energy conservation theorem has been proved in General Relativity.

Can you confirm this? I know there are special souped up versions with "pseudo-tensors" that have some kind of energy conservation law but they are not the common GR we know and love. I just have never heard a responsible person claim that ordinary GR has global energy conservation. But people here seem determined to believe it does! Can you help? sort of summarize the situation?

At issue is, for example, where did the CMB energy go? I say it did not have to go anywhere---space expanded, the wavelengths got longer, the CMB photons lost 999/1000 of their energy, and it just went away. But it seems to outrage people to be told that .
Any words of wisdom?

 

[Alexander]

it still is there. Called potential energy of futher separated parts of system. Move two rocks away from each other - their gravitational potential energy increases.

Enegy "wents away" only for some who does not know that gravitational field has energy and momentum too (called GR, by the way ) or who just parrot somebody's wrong statements or cite shaky web sites without analysing .

 

[jeff]

Originally posted by marcus


BTW assymptotically "euclidean" does not immediately make sense to me---I would have expected you to say "assymptotically Minkowski" or "assymptotically flat spacetimes". Clarify if you wish.

Confusingly, the term "euclidean" is sometimes used to indicate a positive definite metric while at others to indicate flatness. Here it's being used in the latter sense.

Interestingly, total energy can be defined for spacetimes satisfying the even weaker condition of being asymptotically static.