Redshift from space expansion, & conservation of energy?

[CosmicVoyager]

Greetings,

When a photon travels through expanding space, it's frequency decreases and it has less energy.

The energy of photons of the cosmic background radiation have decreased dramatically.

Where does the energy go? Is it lost?

Thanks

 

[bcrowell]

FAQ: How does conservation of energy apply to cosmology? What is the total mass-energy of the universe?

Conservation of energy doesn't apply to cosmology. General relativity doesn't have a conserved scalar mass-energy that can be defined in all spacetimes.[MTW] There is no standard way to define the total energy of the universe (regardless of whether the universe is spatially finite or infinite). There is not even any standard way to define the total mass-energy of the *observable* universe. There is no standard way to say whether or not mass-energy is conserved during cosmological expansion.

Note the repeated use of the word "standard" above. To amplify further on this point, there is a variety of possible ways to define mass-energy in general relativity. Some of these (Komar mass, ADM mass [Wald, p. 293], Bondi mass [Wald, p. 291]) are valid tensors, while others are things known as "pseudo-tensors" [Berman 1981]. Pseudo-tensors have various undesirable properties, such as coordinate-dependence.[Weiss] The tensorial definitions only apply to spacetimes that have certain special properties, such as asymptotic flatness or stationarity, and cosmological spacetimes don't have those properties. For certain pseudo-tensor definitions of mass-energy, the total energy of a closed universe can be calculated, and is zero.[Berman 2009] This does not mean that "the" energy of the universe is zero, especially since our universe is not closed.

One can also estimate certain quantities such as the sum of the rest masses of all the hydrogen atoms in the observable universe, which is something like 10^54 kg. Such an estimate is not the same thing as the total mass-energy of the observable universe (which can't even be defined). It is not the mass-energy measured by any observer in any particular state of motion, and it is not conserved.

MTW: Misner, Thorne, and Wheeler, Gravitation, 1973. See p. 457.

Berman 1981: M. Berman, unpublished M.Sc. thesis, 1981.

Berman 2009: M. Berman, Int J Theor Phys, http://www.springerlink.com/content/357757q4g88144p0/

Weiss and Baez, "Is Energy Conserved in General Relativity?," http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

Wald, General Relativity, 1984

 

[Tanelorn]

Bcrowell, Am I understanding this right; Dark energy is responsible for the expanding space? Is this the same as saying new space is being created from nothing or just stretch existing space? Am I understanding correctly that Dark energy and the expansion of space do not need to obey any laws of conservation of energy or mometum or anything else? Does this mean that something is acting on the universe from beyond the universe or is it something else?

 

[bcrowell]

Bcrowell, Am I understanding this right; Dark energy is responsible for the expanding space?

I don't think the answer to Cosmic Voyager's question really has much to do with dark energy. The same question arises even if the cosmological constant is zero. The FRW model has a zero cosmological constant, but it still has expanding space.

Is this the same as saying new space is being created from nothing or just stretch existing space?

The Einstein field equations don't make a distinction between those two verbal descriptions.

Am I understanding correctly that Dark energy and the expansion of space do not need to obey any laws of conservation of energy or mometum or anything else?

There simply isn't any general, global law of conservation of energy in GR.

Does this mean that something is acting on the universe from beyond the universe or is it something else?

It just means that there isn't any general, global law of conservation of energy. No law of physics is being violated. There just isn't any such law.

-Ben

 

[Tanelorn]

Thanks Ben!
Chris

 

[Subluminal]

It just means that there isn't any general, global law of conservation of energy. No law of physics is being violated. There just isn't any such law.

OK I'm catching on a little bit, good to find this thread. I was convinced that if energy is lost by photons, then it had to show up somewhere else, and all that prevented our following it was an observation problem. Giving up for now on the "was energy lost and if so then where did it go?" search, I had another lonely thought but no luck searching the www or pf for "tired neutrinos". It's probably hiding in the many pages of homework I've been given on here (mostly thanks to marcus and yourself) but couldn't wait.

Do neutrinos lose energy while crossing expanding space? Photons are constrained by c and suffer an increase in wavelength instead as I understand it. Neutrinos from a supernova arrive hours before the photons emitted by the same event, so they must not go slower than c, (and therefore cannot be more massive than photons according to GR?) To see if they lose energy some other way, analogous to the stretching of EM wavelength, what do we look for? I was thinking temperature, but without a mass to be heated I had trouble seeing how temperature is meaningfully converted to units of energy.

As always, thanks for your patience. If you find the answer to this already on PF, please clue me in on the search term used to find it.

 

[cosmik debris]

According to Noether's theorem energy conservation is a result of time symmetry of the Lagrangian. This is really a local law in flat spacetime. In curved manifolds this gets difficult. Globally total energy is a problem since you have to do volume integrals and in a curved manifold the integral depends on the path taken.

 

[cosmik debris]

According to Noether's theorem energy conservation is a result of time symmetry of the Lagrangian. This is really a local law in flat spacetime. In curved manifolds this gets difficult. Globally total energy is a problem since you have to do volume integrals and in a curved manifold the integral depends on the path taken.

Hmmm, after sleeping on this I should say that it is not only in flat spacetime that this holds, it is any spacetime with a time symmetry.

 

[bcrowell]

Hmmm, after sleeping on this I should say that it is not only in flat spacetime that this holds, it is any spacetime with a time symmetry.

Noether's theorem just doesn't produce any useful results when applied to GR. GR's symmetry group is the group of diffeomorphisms, and Noether's theorem doesn't give conservation of energy when you apply it to that group.

 

[Chronos]

Keep in mind redshifted photons are also time dilated.