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Gravitational redshift, energy and the EP

  1. Sep 11, 2011 #1
    It is common knowledge that of the classical tests of GR, gravitational redshift is normally considered to be testing the Equivalence principle and conservation of energy rather than the full GR theory. So it is considered a more fundamental test of our basic principles of GR and physics in general.
    Actually in some GR books it's stressed that what gravitational redshift experiments prove is E=hf (planck equation) when energy is conserved. But at the same time it is claimed that energy conservation in GR doesn't apply to cosmology, does this mean that gravitational redshift doesn't apply to cosmological distances? Let's imagine a supermassive Black Hole with an event horizon radius of cosmological size, would there be no gravitational redshift in that case?
     
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  3. Sep 11, 2011 #2

    tom.stoer

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    Cosmological redshift is a well-known effect in large-scale cosmology and can be interpreted as an effect of "stretching of space" and therefore "stretching of light waves". It is true that in GR there is no general principle of conserved energy.In the case of redshift it is rather simple: the emitted photon as detected by a co-moving observer closed to the source has frequency f and therefore energy E=hf; the photon as detected by a distant, co-moving observer has a different frequency f' and therefore energy E'=hf'. There is no way to attribute a conserved energy to this photon.
     
  4. Sep 11, 2011 #3
    Read carefully, I never mentioned cosmological redshift, I'm only referring to gravitational redshift. I just introduced an imaginary situation where that redshift would be significative at arbitrarily long distances.
     
  5. Sep 11, 2011 #4

    PeterDonis

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    As I understand it, the reason "energy conservation in GR doesn't apply to cosmology" is that the spacetimes used in cosmology (the FRW models) are not stationary, and nobody has figured out a definition of conserved energy that works for a non-stationary spacetime. It has nothing to do with size; an FRW spacetime the size of the Earth would still not be stationary and so there would still be the same issues with defining a conserved energy. A black hole spacetime (at least if you mean an idealized Schwarzschild or Kerr black hole, with nothing else in the universe) is stationary, so a conserved energy can be defined, regardless of its size.
     
  6. Sep 11, 2011 #5

    tom.stoer

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    Oh, sorry, may mistake.

    I can't remember exactly, but somewhere I saw an attempt to "split" the observed cosmological redshift into a "gravitational redshift plus Doppler effect".

    Of course there is "something like gravitational redshift at cosmological distances", but usually it is not taken into account b/c the simplest models are homogeneous and isotropic, so there is nothing like a "varying gravitational potential". If you study inhomogeneous spacetimes you will get "something like gravitational redshift" as well, but I am not sure if and how these two contributions can be seperated and interpreted uniquely.
     
  7. Sep 11, 2011 #6
    Ok, nevermind size.
    According to what you are saying then non-stationary universe means coe doesn't apply to cosmology, but where exactly does conservation cease to apply, everyone seems to accept at least it applies "locally", but how far is locally in this context?
     
  8. Sep 11, 2011 #7

    PeterDonis

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    Technically the statement that "conservation of energy doesn't apply to cosmology" is usually taken to mean that there is no way to calculate a conserved "total energy" for the universe as a whole, because the universe is non-stationary, whereas for a stationary spacetime one can define such a "total energy". I don't know that it is intended to mean that conservation of energy does not apply *within* the spacetime past a certain distance.

    However, let's consider a thought experiment. Suppose we did a gravitational redshift experiment by shining light from a lab on Earth out to a point a billion light-years away (let's assume for simplicity that we can find a point that far out such that we could have a light path to it that would be unaffected by any other gravitating body, even though that's unrealistic in practice), and then dropping the massive object back to Earth from a billion light-years away. Since that distance is far enough away for the worldlines of both the light and the dropping object to be measurably affected by the expansion of the universe, would conservation of energy be violated in this experiment because of the non-stationarity of the spacetime?

    I don't know if anyone has actually tried to calculate an answer to this type of question. Off the top of my head I'm not sure how it would turn out; the photon would experience some extra redshift as a result of the expansion (the target point which was a billion light-years away when the light was emitted from Earth would be somewhat further than a billion light-years when the light is received there, hence greater redshift), but the falling massive object would also be falling from a greater distance, hence would gain a greater amount of kinetic energy, so that may turn out to be a wash. However, the fact that the universe continues to expand while the falling object falls back to Earth has to be taken into account too. I need to think about this some more.
     
  9. Sep 11, 2011 #8
    I agree with this, but I have problems equating the fact that a "total energy" can't be meaningfully quantified within GR and the ambiguous statement that energy is not conserved in cosmology. I don't think these two are one and the same.
     
  10. Sep 11, 2011 #9

    PeterDonis

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    I agree that the simple statement "energy is not conserved in cosmology" is ambiguous as it stands. Every time I've seen something like that asserted, it has turned out, on examination, to mean that a "total energy" for the universe can't be defined because it's non-stationary. Do you have any specific examples where "energy is not conserved in cosmology" appears to mean something else?
     
  11. Sep 12, 2011 #10
    This is an interesting reflection on this issue:
    http://blogs.discovermagazine.com/cosmicvariance/2010/02/22/energy-is-not-conserved/
     
  12. Sep 12, 2011 #11

    PeterDonis

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    The following excerpt from that article states the point of view I have been taking better than I stated it:

     
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