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Question 1. Can virtual particles, in particular gravitons, interfere?

Virtual particles are created and annihilated in a distance too small and a time too short to be measured. Their existence is allowed by Heisenberg's uncertainty principle, which allows a transitory violation of energy conservation in processes that endure a short enough time.

The electromagnetic interaction has a single force carrier, the photon. The weak interaction has two force carriers, the W and Z particles (with 2 signs for W). The strong interaction has 8 force carriers, the gluons.

The quantum carrier of the gravitational force is the graviton (a massless spin 2 particle). Gravitons act together in such vast numbers that there is a scant hope to seeing evidence for just one or a few.

I think that it is established that the less energetic the force carrier, the stronger is the force mediated. If gravitons can interfere, then it is likely that they would interfere destructively (chance dictates that both constructive and destructive interference are present, but destructive interference is more likely, that we can prove). From Planck's relation from quantum mechanics, that means that these gravitons will be less energetic, thus increasing the strength of the force of gravitation, over large scales.

I emphasize that the probability of graviton interference increases for large scale systems (galaxies, clusters of galaxies), and it is very small for small scales, due to the ephemeral character of the virtual particles, in this case the graviton.

Here is my second question.

Question 2. Could this lead to a solution of the dark matter problem (a more accurate analysis than sketched here, of course)? Is it possible that the accumulated tiny effects of graviton interference in the Planck region could lead to an observable deviation from the known laws of gravity at very large scales (galaxies, clusters of galaxies), thus solving the dark matter problem?

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3 Answers 3

Question 1. Can virtual particles, in particular gravitons, interfere?

Gravitons are the hypothetical carriers of gravity, corresponding to the photon for electromagnetism, with a very weak coupling to matter in comparison to all other forces:

With the strong force coupling at 1, the electromagnetic is at 1/137 , the weak 10^-6, the gravitational 10^-39.

Supposing for a valid quantization of gravity, the graviton graviton interaction will go through loops of other matter particles, making the interaction between two gravitons practically infinitesimal, 10^-78 .

So the answer is no. Consequently the answer to the second section is no.

You might be interested in reading the wiki entry on the graviton.

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This is wrong. In a quantum theory, gravitons would interfere. I don't even think the meaning of interference is correct here. Interference isn't an interaction between particles; its a cancellation between Feynman diagrams contributing to an amplitude. –  innisfree Mar 22 at 20:30
    
@innisfree I am sure the OP is asking about interference in the sense of interaction. Do photons interfere other than with higher order diagrams? the same should be true with gravitons. –  anna v Mar 22 at 20:42
    
Diagrams with only single photons do interfere! Look at the cancellation of IR divergences from soft-photon emission and a corrected vertex. It happens and it's very important! –  innisfree Mar 22 at 20:44
    
@innisfree But internal lines in diagrams are not measurable, so what you call interference is a mathematical construct . Dark matter is measurable, as it has been measured. It can have no input from mathematical internal lines. You are calling interference mathematical cancellations and I am using interference as "interference patterns in waves" for example. –  anna v Mar 22 at 20:47
    
"I am using interference as "interference patterns in waves" for example" - this is identical to a mathematical cancellation between Feynman diagrams (though i do not consider the wavefunction etc to be a real wave). i have no idea what you are talking about. –  innisfree Mar 22 at 21:00
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You first ask whether there could be interference effects between virtual gravitons. Assuming something like the standard theory for particle interactions (quantum field theory) would apply to a quantum theory of gravitons, there would indeed be interference between virtual gravitons.

The total probability of a scattering event involving gravitons, say $ee\to ee$ with intermediate gravitons, would be a sum of all possible intermediate states involving gravitons. There would be interference between these intermediate states.

It's unlikely, however, that the effects of quantum gravity could solve the dark matter problem (your second question). The effects of quantum gravity are thought to be important only for incredibly large energies (energies similar to the Planck mass). Large energies are equivalent to very small distances (because of the de Broglie wavelength).

The evidence for dark matter is from experiments testing a few different distance scales, but all of them are much much bigger than the small scale (the Planck length) at which quantum gravity should be relevant.

A minority of physicists think the dark matter problem could be solved by modifying gravity (e.g. Modified Newtonian Dynamics), but their theories don't involve quantum gravity, just modified but classical gravity.

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Thank you anna v and specially, thank you innisfree, your discussion is very interesting to me. I will rephrase question 2. Is it possible that the accumulated tiny effects of graviton interference in the Planck region could lead to an observable deviation from the known laws of gravity at very large scales (galaxies, clusters of galaxies), thus solving the dark matter problem? –  Cristian Dumitrescu Mar 23 at 18:27
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As i see it a gravitons would interfere if gravity waves interfere. And I certainly think that a gravity wave would interfere. I guess that they are transverse waves that can interfere like any other waves.

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i looked up how gravity waves behave in the perpendicular plane to motion. z compresses, while y expands. Then y compresses while x expands. I would think that a graviton would have energy hf. Why they are not created in accelerators is beyond me. –  user43953 Apr 7 at 1:12
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