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What operator acting on vacuum gives a box of cosmic background radiat

  1. Sep 21, 2013 #1
    What operator acting on the vacuum state (vacuum state of the box?) gives a m^3 box of cosmic background radiation at 2.7K?

    As the temperature 2.7K slowly drops (wait a million years) must our operator above change in time?

    Do photons scatter via gravitions so that their energy changes (very slowly) in time ? We have a box of photons that over time has fewer and fewer photons (?) and their average energy over time decreases (?). Does energy change in jumps or continuously? Something is going on in my box?

    Thanks for your help!
  2. jcsd
  3. Sep 21, 2013 #2

    Simon Bridge

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    You sound confused there. Are you trying to ask about the QCD vacuum?
    I think we need more context to be able to answer your questions properly.
    Perhaps if you described the thought experiment more carefully - how are you preparing the "box"? What is ti supposed to be modelling?
  4. Sep 22, 2013 #3
    The photons of cosmic background radiation lose their energy continuously due to continuous expansion of space. No scattering off gravitons is involved.

    I'm not sure I understand why you need an operator to fill your box with photons.
  5. Sep 22, 2013 #4
    "lose their energy continuously", that does not sound quantum mechanical to me.

    Is there not an operator that operates on the vacuum state and results in a state ( or wave function?) that describes the cosmic background radiation in any box you choose in empty space?

    Would a quantum theory of gravitation change your answer?
    Last edited: Sep 22, 2013
  6. Sep 22, 2013 #5
    I guess it is the "quantum optics vacuum state", [0>, where we only worry about light.

    The box is any box say in empty space that contains "light", the CMB. I'm guessing there is a quantum mechanical description of the black body radiation photons in the box.

    It seems a quantum theory of gravitation might include scattering of both matter and radiation. Less confusion is better!

    Thanks for your help!
    Last edited: Sep 22, 2013
  7. Sep 22, 2013 #6


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    No because the CMB is a thermal ensemble of photons and cannot be described by a unique state vector. It's entropy is high while the entropy of the vacuum state is zero. You have to use density matrices to describe such a mixed state.

    Questions about quantum gravity belong in the "Beyond the Standard Model" forum. The answer to your graviton question may depend on which theory candidate you use.
  8. Sep 22, 2013 #7
    Mixed state, right, thank you. So there is a quantum mechanical description. That description must change in time (if however slowly)?
  9. Sep 22, 2013 #8

    Simon Bridge

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    What is it that you are trying to understand?
  10. Sep 22, 2013 #9
    The proper (I guess we need a quantum theory of gravitation?) time dependent quantum mechanical description of the CMB in some small (say m^3) matter free region of our Universe. The CMB changes in time if only exceedingly slowly and any proper quantum mechanical mixed state that describes it must also change in time?

    Thanks for the help!
  11. Sep 22, 2013 #10

    Simon Bridge

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    OK - so you are not thinking of a "box" is the usual sense of an isolated system then?
    You want to set aside a volume - say, one cubic meter (your example, but presumably the exact volume does not matter as ling as it is small compared to, say, a star cluster, or something cosmological right?) and find a QM description of what happens there, considering only the cosmic microwave background?

    You only need an operator for interactions and measurements.
    The mixed state would be described by the density matrix. In general these things time-evolve ... but that's not saying very much.

    AFAIK you don't currently need quantum gravity to understand the CMB - but it's been a while.
    Its not generated by vacuum fluctuations last I looked. But certainly CMB is different depending on which direction you point your detector and presumably would vary over time too.

    You are constantly coming back to the state changing in time. Where are you going with this?
    (I am reluctant to go into detail without knowing what you think it means, in case I accidentally reinforce a misunderstanding.)
  12. Sep 23, 2013 #11
  13. Sep 23, 2013 #12

    Simon Bridge

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    Oh all right
    ... there is nothing conflicting about "continuousness" and QM. You have continuous wavefunctions for eg.

    Photon energies are not, in general, quantized ... so far as we can tell.
    Perhaps the boundary box for the Universe is so large that individual energy states are too close together for us to measure? Whatever - free-space energies have a continuous variation. If you haven't learned about continuous "eigenvalues" before, you will.

    Therefore you can have continuous changes in, say, photon energies. i.e. through gravitational shifting.
    Distributions of energies can also be continuous - and that is pretty much what the CMB is known by.

    We observe the CMB coming from all directions at once. I don't know what you mean by "all mixed up".
  14. Sep 24, 2013 #13
    So the CMB photons loose a little energy everyday, minute, second? Again that does not sound quantum mechanical? Maybe I should try and find some basic notes on quantum fields in curved space time. The study of quantum fields in curved space time includes curved spaces whose curvature changes in time? Sounds complicated!

    Can I think of it this way, the redshifted photons of distant starlight or the CMB continuously lose energy, but the redshifted photons total energy (include gravitational potential energy if General Relativity allows something like that) remains constant?

    By "all mixed up" I was kind of shooting down my thought that the CMB photons ( or ancient redshifted starlight) scattered off "something" to loose energy, if those photons did scatter to lose energy they could not change direction or otherwise distant objects in our universe would be a blur or worse? Can you scatter, lose energy, and not change direction for billions of years?

    Have a good day!
  15. Sep 24, 2013 #14

    Simon Bridge

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  16. Sep 25, 2013 #15
    I feel better now about continuous energy loss of red-shifted photons. I guess at this point I would still like to see a quantum mechanical time dependent description of the CMB in terms of creation and annihilation operators and mixed states.

  17. Sep 26, 2013 #16

    Simon Bridge

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    I think thermalized statistics for photons is covered in quantum optics courses.
    You may also find a treatment if you read around the subject: "photon gas".

    Hmmm... maybe:
    (lecture slides I'm afraid - but should give you a quick overview of where to look next.)

    If you can model stuff like Compton Scattering in terms of creation and annihilation operators, then you should be able to manage CMB photon thermalization.
  18. Sep 27, 2013 #17
    Will give that a look, thank you.
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