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Do two photons traveling in opposite directions emit gravitational waves? If so, does it mean that any volume filled with photon gas will eventually degrade into graviton gas?

In other words, if flat non-expanding universe is filled with photon gas, will the photons over time annihilate into gravitons? Or will photons and gravitons somehow reach equilibrium?

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    $\begingroup$ Partially related $\endgroup$ – Trimok Jan 3 '14 at 12:32
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This is a very hypothetical question.

a) we do not have a quantized theory of gravity working in conjunction with elementary particles ( the photon is an elementary particle).

b) we have not detected a graviton in the way we detect photons

If we forget a) and assume for b) that if gravitons exist they are the 0 mass carriers of the gravitational interactions the way the photon is the carrier of the electromagnetic interactions and also assume that what we know of quantum mechanics and kinematics of elementary particles pertains to the graviton too then

no, the photons cannot radiate gravitons and vice versa because both are moving at the velocity of light and cannot be accelerated or decelerated in order to give up radiation in the classical way.

In this hypothesis, as elementary particles, they can interact by scatterings, with a very very low probability due to the smallness of the gravitational interaction. Through higher order diagrams in the scattering crossection, they may change form and produce other elementary particles depending on their energy, or just photons and gravitons of different energies. There will be an equilibrium of sorts.

Without a solid theory of everything all this is speculation.

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    $\begingroup$ Photons can't be accelerated in the classical sense, but they can be "accelerated" in the sense that their momenta can be affected by gravitational fields. Is it obvious that two photons can't redshift each other through gravitation (which would result in emission of gravitational radiation)? $\endgroup$ – Brian Bi Jan 3 '14 at 8:09
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    $\begingroup$ @BrianBi You have to think of feynman diagrams when you think of elementary particles. Of course one could write a compton like diagram where gravitons are exchanged, but the interaction is higher order and the numbers would probably be out of the lifetime of the universe. Gravitons may come out from all the possible diagrams of photon photon interactions, with very low probabilities. Actually for the mass energy equivalence gravitons have to be exchanged all the time with the gravitational field but they will be virtual ones . $\endgroup$ – anna v Jan 3 '14 at 8:24
  • $\begingroup$ continued: Take gravitational lensing of light passing a strong gravitational field. In the above framework, the individual photons are exchanging virtual gravitons with the gravitational field, changing their polarization and orientation parameters in the ensemble so as to observe the classical behavior of bending. $\endgroup$ – anna v Jan 3 '14 at 8:29
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In short, photons perfectly interact with gravity (or, if you like it more, with still hypothetical gravitons). It includes planar EM waves (i.e. photons traveling in parallel directions), because the stress–energy tensor is non-zero. Even a single photon must have, theoretically, its gravitational field.

But it is not clear, why an equilibrium gas should give most of its energy to gravitational field, depriving photons of it. IMHO it depends on exact conditions (how hot and dense is the gas and in which cosmology is it supposed to exist).

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"Do two photons traveling in opposite directions emit gravitational waves?"

Does virtual graviton count as gravitational waves? for sure there are gravitational effects so call it gravitational field. And two photons can interact indirectly through other fields.

"If so, does it mean that any volume filled with photon gas will eventually degrade into graviton gas?"

How are the photons contained in this volume? With perfects mirror? a black hole? ... It seems that in any case there will be some radiations escaping.

"In other words, if flat non-expanding universe is filled with photon gas, will the photons over time annihilate into gravitons? Or will photons and gravitons somehow reach equilibrium?"

the whole universe is filled with photons and nothing else, and it's flat...To give an answer I think the problem should be defined more precisely. For example how do you define the state of the vacuum here?

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Photons can not emit gravitons, only mass (matter) can. If the photons are energetic enough, some of them will be changed into matter (which will emit gravitons), so you would end up with a mixture of "weak" photons, particles with mass, and gravitons. The ratio of each, depends on how much energy the initial photons have. If they are weak, no mass will be created and therefore no gravitons. If this is the case, you end up with nothing but the photons you started with.

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