In QED the carrier for electromagnetic interaction is a photon, while macroscopic forces are due to electromagnetic interaction (by macroscopic forces I mean: normal force, object collision, friction etc..).

But for example, in the collision of two billiard balls, if 1 kgm/s of momentum is exchanged between the balls, the amount of Energy required in the form of photon virtual particles would be enormous (3E8 J). And while they do not necessarily obey the mass-shell relation, still the farther off shell interactions are, the less they should contribute to the actual phenomena.

For least action to be satisfied it seems like some other type of exchange interaction would occur. Is there some kind of larger scale decoherence type interaction going on?

  • $\begingroup$ Could you explain what do you mean with your question? What do you mean with "larger scale decoherence type interaction"? In any case, for macroscopic solids like the billiard balls, there should not be virtual photons exchanged. But it can be said that their deformation should lead to internal forms of energy, like electromagnetic oscillations of their structure (phonons or molecular vibrations). $\endgroup$
    – rmhleo
    Jul 30, 2014 at 16:28
  • $\begingroup$ So then what particle mediates the initial deformation, as phonons propagate within the bloch wave of whatever material they are made of and not as external particle. Perhaps the balls could exchange phonons through some coupling of the oscillations of their molecules? $\endgroup$
    – BearMan
    Jul 30, 2014 at 17:16
  • $\begingroup$ The collision process of two billiard balls has almost nothing to do with QED. The QED part will actually make the balls attract one another while a more subtle mechanism owing to Pauli principle will be responsible for the actual non penetration and momenta exchange of the particles. $\endgroup$
    – gatsu
    Jul 31, 2014 at 8:27

1 Answer 1


Until an expert in this field gives a rigorous answer to your question, I will give you my view.

If I understand correctly your questions, you are on the one hand asking about other types of existing exchange interactions between virtual particles and real particles, and on the other hand you claim that using the usual virtual photon picture for the momentum exchange between two billiard balls, would undermine Feynman's least action principle.

In all the Feynman diagrams I have seen so far, virtual photons are the element of choice and not phonons (as you ask in comments), as the idea is to use electromagnetic fields to describe repulsion/attraction forces, momentum exchange, charged particle interactions and so on. Furthermore, in case of a simple momentum exchange between two objects, one doesn't deal with interatomic modes of oscillation, so phonons do not really fit our case here anyway.

As for the least action principle, it does not actually matter how large the energy exchanged between the two objects is, because what the least principle action tells you, is that only paths (here for the virtual photons) close to the least action contribute to the final probability amplitude of paths, whose modulus squared here corresponds to the probability density of the virtual photons being absorbed in the shell x that would require the least action. This then means that for any amount of total energy in terms of virtual photons that has to absorbed for the momentum exchange to take place, the frequency of the constituent virtual photons is then defined based on the shell-energy that has contributed most to the overall paths' amplitude (which will also dictate the number of virtual photons needed).

So following this logic, the further off shell interactions are most likely to contribute least because of the least action principle, without the need of another type of exchange interaction.

It may help to make contrast between this scenario and that of the electron-nucleon interaction, where long wavelength virtual photons will only see the whole nucleon and shorter ones will be able to see and interact with the quarks inside.

Anna v's answer in an older post also contains relavant bits of explanations that you may want to check out. One other source would be this.


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