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For example, an electron, it has mass and charge, but is considered to have point mass and point charge, but why? Why are they assumed to have charge and mass in a single infinitely small point in space? Doesn't QFT show us that point like particles aren't really points rather extended excitations of fields?

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  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/41676/2451 , physics.stackexchange.com/q/137541/2451 and links therein. $\endgroup$ – Qmechanic May 12 '16 at 19:21
  • $\begingroup$ But I'm also asking why are they considered point charges and point masses. $\endgroup$ – user86072 May 12 '16 at 19:26
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    $\begingroup$ This assumption explains almost all known interactions and processes known to date. Therefore, it is a good assumption. $\endgroup$ – Prahar May 12 '16 at 19:37
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    $\begingroup$ To emphasize one point beyond @garyp's excellent answer: what physicists mean by "point particle" is that the commutators of the field theory are trivial (0) anywhere but for operators defined at the same spacetime point. It doesn't mean that tiny little balls are flying around. The field theory is simply local, just like Maxwell's equations are local. String theory challenges that assumption and gets extremely interesting, albeit so far physically not very useful, results. Keep in mind that even a point-like fundamental theory produces non-point-like objects like nuclei and atoms! $\endgroup$ – CuriousOne May 12 '16 at 21:10
  • $\begingroup$ "It doesn't mean that tiny little balls are flying around." - Indeed; why not flesh that out in the form of an answer? $\endgroup$ – Alfred Centauri May 12 '16 at 22:35
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Scattering experiments can be used to determine the size of a particle. The results for an extended object are different than that of a point particle. But all of these scattering experiments depend on getting the probe particle "close" to the scattering object. In the case of electrons, that means launching the probe with enough energy to overcome the Coulomb repulsion ... and get "close". How close depends on the energy of the probe particle. But there's a limit on the energy that can be given to the probe, so there's a limit to how "close" the probe can get. Consequently, we can't know what happens at distance shorter than some value.

The best scattering experiments done on electrons to date show a scattering pattern identical to that of a point particle.

That doesn't mean that it actually is a point particle, it just means that to the best of our knowledge it is. No experiment to date, scattering or otherwise, has shown any sign of a size for the electron. Our theory and our experiments are both happy ... for now ... with the notion that the electron is (more accurately: behaves exactly like) a point particle.

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    $\begingroup$ Just for fun, do you know the current state of the art for scattering from electrons? I lost track a long time ago... $\endgroup$ – Jon Custer May 13 '16 at 0:14
  • $\begingroup$ @JonCuster Afraid I don't. I asked Google, and she reported $10^{-18}$ m. Thats $1/1000$ the size of a proton. $\endgroup$ – garyp May 14 '16 at 15:02

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