The clack of two billiard balls signifies the transference of their momentum and the mathematics of resulting vectors is fairly straight forward. At the quantum level, I understand that the transfer of momentum is carried out by photon interactions. This would mean a lot of photons interacting and somehow, in sum, conserving of the classical momentum vectors. If there are no red flags in the above, I would appreciate guidance to a reference that explains the process in more detail, particularly the conservation of momentum. I would guess that each photon interaction must somehow convey vector information.
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Each scattering process conserves momentum individually -- which would result in a bunch of processes conserving momentum as a whole as well. For example, a typical interaction in which two electrons interact via a virtual photon and come out of the interaction having exchanged some momentum (called Moller scattering) does conserve momentum -- simply by virtue of the fact that the physics of such scattering, i.e., the theory of quantum electrodynamics, is a translationally invariant theory.
Of course, in an actual collision of two objects, much more complicated scattering processes would be involved because we are not only talking about free electrons colliding but about electrons in the bound states of atoms. However, as far as your question goes, the same basic principle applies: each scattering process that contributes to the perturbative expansion of the amplitude of a given transition conserves momentum.
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$\begingroup$ Thanks for the your comment, helpful. Sometime ago I read that things don't actually touch, come into direct contact, but are always fended off through photon, or more properly virtual photon interactions. Be that as it may, it is difficult to give credence to the idea that such a multiplicity of very subtle individual events could integrate into a single vector determinate to very many significant digits. Would the vector be within a probabilistic range? $\endgroup$ Commented Aug 3, 2022 at 14:31
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$\begingroup$ And, this discussion reminds me of recent reading on work by Nicholas Gisin to the effect that “real numbers are not real”, that is, physically real. There is this paper, <a href="arxiv.org/abs/2011.02348"> Indeterminism in Physics and Intuitionistic Mathematics </a> and a <a href="youtube.com/watch?v=gqLIfCkorRc">video</a> that makes a simple case. That said, while it makes sense to me, I don’t know how well regarded his work is and physics proper is still proceeding according to precedent. Perhaps tangentially related to discussion. $\endgroup$ Commented Aug 3, 2022 at 19:26
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$\begingroup$ Well did not do well with the mark up, hope you can decipher. $\endgroup$ Commented Aug 3, 2022 at 19:29