Photon Red Shift Energy losses in expanding universe theories

[alexjbuck]

The evidence points to an expanding universe, we tell this by looking at the redshift/distance relationship, objects further away are receding faster, with their redshift and distance at an almost linear relation.

My question is, the photons emitted by those objects that we are just now observing were emitted at significantly higher frequencies (and thus higher energies!) than we are seeing them, so where did the energy go?

E=hf

So a photon emitted at f1 and received at f2, ( f1 > f2 ) has energy E1 > E2 unless something is happening to Planck's constant...

 

[nicksauce]

In the Newtonian point of view, the energy lost of redshifting photons goes into PdV work in expanding the universe.

In the relativistic point of view, because the FRW metric doesn't have a timelike Killing vector, there doesn't exist a conserved energy, and there is thus no reason to expect photons to conserve their energy.

 

[alexjbuck]

so... on a cosmic scale there is no such thing as conservation of energy? What explains why we do observe conservation effects on smaller scales then?

 

[nicksauce]

As a consequence of Einstein's equations, the stress-energy tensor is divergence-less, which implies local conservation of energy-momentum.

 

[eloheim]

I recall a Scientific American article about exactly this question not too long ago (surely within the year). I don't have the qualifications to judge the merit of the article, but I'll tell you what I (vaguely) remember.

I think the author's viewpoint was that, no, they do not lose energy in violation of the 2nd law. The reasoning involved something to do with the observers (relativistic) perspective; that just as the whistle of a train flying past you changes pitch without gaining/losing energy, light changes color in the same fashion. Although I wouldn't put too much trust in my memory if I were you...

 

[Chalnoth]

so... on a cosmic scale there is no such thing as conservation of energy? What explains why we do observe conservation effects on smaller scales then?

Well, sort of. You can recover conservation of energy if you include gravitational potential energy (which is not usually done). For the most part, though, in General Relativity energy is simply not a conserved quantity. This comes out by necessity from two facts:
1. The energy of a particle is a coordinate-dependent quantity.
2. General Relativity allows you to use any coordinate system you like.

These two statements mean that no matter your physical system, you can write down a set of coordinates where energy changes in time, or where energy doesn't change in time. Whether or not energy changes in time, then, is completely arbitrary in GR.

What we have instead is the conservation of the stress-energy tensor, which contains energy, momentum, pressure, and twisting stresses. This tensor as a whole is conserved in a particular fashion, a fashion which takes into account the possibility of coordinates changing from place to place (for example, one degree of longitude near the pole of the Earth represents a very different distance than one degree of longitude near the equator).

Anyway, for a more detailed look into energy conservation in General Relativity, this is a great read:
http://www.xs4all.nl/~johanw/PhysFAQ/Relativity/GR/energy_gr.html

 

[Chronos]

IMO, photon energy is conserved. I agree EC is not required by GR, but, I think that is a mathematical artifact. Photons in an expanding universe are time dilated, hence, must appear to lose energy. On the other hand, given enough time, they eventually balance the energy budget.

 

[Chalnoth]

IMO, photon energy is conserved. I agree EC is not required by GR, but, I think that is a mathematical artifact. Photons in an expanding universe are time dilated, hence, must appear to lose energy. On the other hand, given enough time, they eventually balance the energy budget.

How do they eventually balance the energy budget? They redshift away to zero...

 

[Jorrie]

How do they eventually balance the energy budget? They redshift away to zero...

Do I have it right that photon density is already very close to zero, less than some 0.01% of overall lambda-CDM energy density?

 

[Chalnoth]

Do I have it right that photon density is already very close to zero, less than some 0.01% of overall lambda-CDM energy density?

Depends upon what you mean by near zero, but yes, less than 0.01% of the overall energy density is correct.

 

[Chronos]

A photon never gives up its energy until it interacts with matter. So, who you going to believe, the clock bound perspective of a receeding observer, or the photon? Time is meaningless from the perspective of a photon.

 

[Chalnoth]

A photon never gives up its energy until it interacts with matter. So, who you going to believe, the clock bound perspective of a receeding observer, or the photon? Time is meaningless from the perspective of a photon.

This makes no sense to me. Photon energy is only conserved in flat space-time.