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How is it possible that for example, a point-like fermion interacts with a point photon in one point in space? I mean, how is it possible that two points can "hit" each other?

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  • $\begingroup$ Time to study string theory? $\endgroup$
    – user137289
    Commented Dec 28, 2016 at 19:33
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    $\begingroup$ You're thinking classically. In QFT particles are not localised; it makes no sense to state that particles interact "at a point". $\endgroup$ Commented Dec 28, 2016 at 19:36
  • $\begingroup$ @Pieter What do strings say about this? AccidentalFourierTransform's point has nothing to do with strings and it's how I think about this too. When the wave functions of particles overlap, there is an amplitude for there to be an interaction which is proportional to the overlap. $\endgroup$ Commented Dec 28, 2016 at 20:10
  • $\begingroup$ @AccidentalFourierTransform Wave functions do not need to overlap to interact: electrons in orbitals with $\ell > 0$ have no overlap with the nucleus. In QED, zero-dimensional particles interact at vertices. QED is already beyond me. But if one does not like point particles, strings may be something to look into. $\endgroup$
    – user137289
    Commented Dec 28, 2016 at 20:20
  • $\begingroup$ The particles' wavefunctions are spread out and can overlap. $\endgroup$
    – tparker
    Commented Dec 28, 2016 at 21:54

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Two point particles can, purely mathematically, be at the same point of space. Of course, in an imagination of a collision experiment of real point particles, such coincidence, while possible, should be assigned zero probability unless there is specific reason to assign non-zero.

Collision of point electron with point photon at one point of space is not a real event, since there are no "point photons" as real point particles. It is rather a metaphor that describes properties of certain mathematical objects - Feynman diagrams - as if there were point electrons and photons running around in space.

Feynman diagrams in turn are just a convenient way to denote and order certain complicated integrals from the theory of EM interaction. Although wavy lines in the Feynman diagrams look like representations of spacetime trajectories of some point particles different from electrons, there are no such particles in the most fundamental EM theory.

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  • $\begingroup$ Then how should we imagine what the objects we call elementary particles "look" like? I know the vertices of a Feynman diagram just correspond to a mathematical expression and do not represent the point in space where the interaction takes place, but that doesn't mean elementary particles are not considered as point-like. Not localized, because of the wave function, but nevertheless. Also, virtual particles (with no relation between their energy and momentum), are considered point-like. I don't think it's just a mathematical construction. Non-point-like particles solve many problems. $\endgroup$ Commented Dec 29, 2016 at 1:30
  • $\begingroup$ @descheleschilder a universal way to imagine elementary particles is not known, sometimes it is helpful to imagine them as microscopic grains of matter (when detecting them), sometimes as macroscopically extended waves (when calculating probabilities). I prefer the view where particles like proton, electron are microscopic grains of matter, in some cases (electrons) with zero size (points); I do not try to imagine "photons" as I think description of EM interaction is better done without this nebulous concept. I imagine EM field as vector field in space. $\endgroup$ Commented Dec 29, 2016 at 21:59

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