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

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## Main Question or Discussion Point

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!

## Answers and Replies

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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?

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.

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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.
"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?

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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?
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!

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kith
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?
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.

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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.
Mixed state, right, thank you. So there is a quantum mechanical description. That description must change in time (if however slowly)?

Simon Bridge
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What is it that you are trying to understand?

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What is it that you are trying to understand?
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!

Simon Bridge
Homework Helper
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.
http://en.wikipedia.org/wiki/Density_matrix

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.)

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Simon Bridge; ..... 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 said:
The temperature and also the energy density of a box of CMB changes with time if very, very slowly. I was told that the energy changes continuously and I remarked that did not sound quantum mechanical. How quantum mechanically do you describe the CMB as it changes very slowly in time? I would like to think there is a quantum exchange of energy between the photons and whatever that allows the CMB photons to slowly loose energy?

If there is such a process the CMB photons can't change direction or otherwise the CMB we observe would be all scrambled up?

Thanks for you efforts in trying to reduce my confusion!

Simon Bridge
Homework Helper
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".

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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".
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!

Simon Bridge
Homework Helper
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Conservation of energy is not trivial in GR.
See other discussions.
http://physics.stackexchange.com/questions/2597/energy-conservation-in-general-relativity

Why does it matter whether something sounds quantum mechanical to you or not?
Are you expecting energy to change in discrete jumps for absolutely everything? Why?
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.

Thanks!

Simon Bridge
Homework Helper
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:
http://indico.cern.ch/getFile.py/access?contribId=21&sessionId=8&resId=1&materialId=slides&confId=78565
(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.

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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:
http://indico.cern.ch/getFile.py/access?contribId=21&sessionId=8&resId=1&materialId=slides&confId=78565
(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.
Will give that a look, thank you.