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Energy conservation paradox?

  1. Feb 14, 2007 #1
    Not able to really find an already existing thread where my question could fit in very well, I am starting this new thread which I hope is not too much confusing.

    Conservation of energy of photons in an expanding vacuum part of the universe?
    The wavelength of a photon travelling through the expanding universe increases linear with the expansion. The energy of the photon goes inversely with its wavelength, so the radiation energy density goes down with the fourth power of the expansion.
    Now I am confronted with the following paradox.
    The decrease of the energy density of a universe only containing particles (baryons) goes down with the third power since stars etc don’t take part in the expansion.
    Let’s assume an “elongated” photon hits an atom and brings it to a long term exited state.
    If after a while the universe starts shrinking (a possibility in an FRLW universe I suppose), then the travelling photons increase their energy density with the fourth power again and the energy density of the particles goes up with the third power again. But then at a certain moment our exited atom falls back to its original state and a photon will leave it at a frequency different from the frequency of the photons that never excited an atom. It looks like as if energy is not fully conserved. What is wrong in my thinking, is it just a bad way of energy book keeping?
  2. jcsd
  3. Feb 16, 2007 #2


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    You are right that there are problems with conservation of energy in an expanding space. A great online reference that discusses this issue is this one: Is Energy Conserved in General Relativity?. See the section "Expansion of the universe leading to cosmological redshift".
  4. Feb 17, 2007 #3


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    Not all that difficult to resolve. As the universe expands, it dilutes the energy of the photons transversing it - usually referred to as redshift.
  5. Feb 17, 2007 #4
    Dear Hellfire,
    Thank you for your answer an the link. I already printed the article and I am trying to understand it.
    Kind regards,
  6. Feb 17, 2007 #5
    Dear Chronus,
    Yes (if I understand your answer right?) that is what I already understood some time. But to me the problem is in the simultaniety of photons and massive particles in the universe while having interactions (with delay times)
    Kind regards,
  7. Feb 18, 2007 #6


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    What 'simultaneity' are you talking about? Last time I checked photons had no reference frame wrt time. I'm slightly amused by your attempt to toss GR under the bus.
    Last edited: Feb 18, 2007
  8. Feb 18, 2007 #7
    Could it be the "lost" momentum is really dark energy? The momentum lost by the photons is somehow transferred/regained/recovered back to its source creating a "pressure" forcing apart all objects which emit electromagnetic radiation.

    Hmmm???? Not sure that works?
  9. Feb 18, 2007 #8
    While our universe is expanding, photons are travelling through it end are elongated if I may say so, leading to the well know redshift. This is certainly not what I need too explain yo you. Photon density in this space goes then with the inverse third power and because of stretching of its wavelenght, foton energy density falls down with the fourth power. Simultaniously, as an average, the density of starclusters (which are fixed in the universe and thus do not travel) goes down with the third power.

    I'm slightly amused by your attempt to toss GR under the bus.[/QUOTE]

    My english might be not good enough to understand what you mean by this expression. Certainly I have great respect for GR. Maybe I did not express myself not clear enough or to stupid so that it slightly amused you. But I suppose there is only one autonomous reality. If we find paradoxes within a well established physical theory then in the first place we have to check whether it is a real paradox . But if the paradox is real then we have to review our theory. (I will study the article Hellfire indicated and see what I personnally can find. I very much doubt my own paradox.) But if you can and will show me where I went wrong I will be happy to learn.

    Many thanks in advance and kind regards,
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