Redshift from space expansion, & conservation of energy?

In summary, when a photon travels through expanding space, its frequency decreases and it has less energy. The energy of photons of the cosmic background radiation have decreased dramatically. There is no standard way to define the total energy of the universe, and conservation of energy does not apply to cosmology. The expansion of space and dark energy do not need to obey any laws of conservation. Neutrinos may lose energy while crossing expanding space, but this is difficult to detect due to the lack of mass and other factors. In curved manifolds, global energy conservation is a problem as the integral depends on the path taken.
  • #1
CosmicVoyager
164
0
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
 
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  • #2
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
 
  • #3
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?
 
  • #4
Tanelorn said:
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.

Tanelorn said:
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.

Tanelorn said:
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.

Tanelorn said:
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
 
  • #5
Thanks Ben!
Chris
 
  • #6
bcrowell said:
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.
 
  • #7
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.
 
  • #8
cosmik debris said:
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.
 
  • #9
cosmik debris said:
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.
 
  • #10
Keep in mind redshifted photons are also time dilated.
 

1. What is redshift and how does it relate to space expansion?

Redshift is a phenomenon observed in light where the wavelength of light appears to be stretched out, causing it to appear more red. This is caused by the expansion of space, where as the universe expands, the light traveling through it also stretches out, resulting in a longer wavelength and a redshift.

2. How does the redshift of light support the theory of the expansion of the universe?

The redshift of light is one of the key pieces of evidence supporting the theory of the expansion of the universe. It shows that galaxies and other objects in the universe are moving away from each other, and the further they are, the faster they are moving. This is consistent with the idea that the universe is expanding.

3. How does the conservation of energy apply to the redshift from space expansion?

The conservation of energy is a fundamental law in physics that states that energy cannot be created or destroyed, only transformed. This applies to the redshift from space expansion in the sense that the energy of the light traveling through space is not lost, but rather transformed into a longer wavelength due to the stretching of space.

4. Can redshift be used to determine the age of the universe?

Yes, the redshift of light can be used to estimate the age of the universe. By measuring the redshift of distant galaxies and using the known rate of expansion of the universe, scientists can calculate how long it would have taken for those galaxies to reach their current distance from us. This provides an estimate of the age of the universe.

5. Is there a limit to how much redshift can occur due to space expansion?

Yes, there is a limit to how much redshift can occur due to space expansion. This is known as the cosmological redshift limit and is determined by the distance of the object from us. The further away an object is, the more redshift can occur. However, there is a point where the redshift becomes so extreme that the light can no longer be detected, making it impossible to measure the distance or redshift accurately.

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