# Violation of conservation of energy by expansion of the universe

1. Jan 26, 2010

### marthkiki

I was watching this video, and it was saying that because the universe is expanding, the wavelengths of light waves were elongating, and therefore the energy of radiation throughout the universe is decreasing. They said that this defies the conservation of energy, but Einstein's general theory of relativity defies Noether's theorem and says that we don't have to have energy as a conserved state because we don't live in time invariance.
Is the first part true? Does the expansion of the universe elongate wavelengths and violate conservation of energy?

2. Jan 26, 2010

### torquil

It is true that the expansion causes the wavelength of a freely travelling ray of light to increase. Think about the cosmic background radiation. In the beginning, it was a high frequency radiation. Now, it has a much lower frequency (longer wavelength) because the universe has expanded. This is described well by Einsteins gravitational theory. I'm sure you can find mathematical derivations of this on the internet.

I don't know if this constitutes a violation of the conservation of energy or not. I think this is a more of a subtle question in gravitational theory than otherwise. It would seem that the energy contained in the electromagnetic field itself has decreased, since I don't think the field strength will increase.

Maybe someone else can comment on this?

3. Jan 26, 2010

### nicksauce

Here are multiple ways to think about it.

1) There should be no conversation of energy globally in our universe because there is no timelike Killing vector in the FRW metric. That is, there is nothing we can identify as energy and say that it is conserved.

2) GR automatically forces a kind of energy conservation $\nabla_{\mu}T^{\mu\nu} = 0$, where T is the energy-momentum tensor. This is enforced by the Bianchi identity and the Einstein field equations.

3) Newtonian perspective: The redshifted light is compensated for by a change in volume. That is, there is a pressure, so PdV work is done to expand the universe, exactly compensating for the redshift. In fact,using Newtonian arguments of energy conservation, you can derive the Friedmann equations, which describe the expansion of the universe.

4. Jan 27, 2010

### Chronos

I like option 3, Nick. i think the Newtonian approach is fundamentally correct and GR is a scale factor correction.

5. Jan 29, 2010

### herbert

Interesting, but in option 3 when a gas expands the work (PdV) done is done in 'pushing back' the surrounding atmosphere.
If there is nothing outside the expanding universe, then why should work be done in order for it to expand into nothing?

6. Apr 19, 2010

### inflector

This is really interesting. Might one liken the "pressure" here in the Newtonian perspective to dark energy?

Wouldn't the work be performed against the gravity of the universe? When space expands, this should be performing work because of the larger gravitational potential energy of the galaxies because of the increased distances between them. Or am I missing something?