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Is there anything about the implications of the "early" quantum theory of Schrodinger equation, wave-particle duality, or the two slit experiment that conflicts with the idea of a point charge? Did the realization that electrons and protons have size emerge from a conflict of principle between classical E&M and foundational ideas of quantum theory? Or did the realization of size of subatomic particles emerge from developing the best model from later experiments, perhaps with accelerators, nuclear reactions, ...?

I'm sure that there is a more precise way to describe the issue I'm asking about but I only have a very superficial understanding/awareness of quantum theory and modern physics. My question is motivated from my studying E&M from Purcell and Griffiths.

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closed as unclear what you're asking by ZeroTheHero, John Rennie, Buzz, FGSUZ, Cosmas Zachos Jan 27 at 22:55

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    $\begingroup$ Can you give an example of somewhere saying that electrons etc do have size? $\endgroup$ – jacob1729 Jan 24 at 21:48
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    $\begingroup$ String theory is the first serious departure from the notion of particles as not being points, everywhere else in physics one fundamentally models particles as points, indeed special relativity prevents us from treating particles as rigid bodies, and so this unavoidably leads to the concept of renormalization, e.g. the classical electrostatic energy of a system of charges involves the $1/r_{aa} = 1/0$ self-energy, whichis divergent, but this infinity can be absorbed into the mass of the electron and so is a flaw of the mathematics rather than the physics, with the problem persisting into QFT. $\endgroup$ – bolbteppa Jan 24 at 21:55
  • $\begingroup$ @jacob1729 I've only read on wikipedia about the classical electron radius and the electron has a volume of 10^-30 m. I did read that electrons are understood to be point charges, but honestly I don't know enough/understand how a point charge can have volume. Please regard these comments as me only reporting what I've read, I don't understand any of it. $\endgroup$ – lamplamp Jan 24 at 22:04
  • $\begingroup$ Related: physics.stackexchange.com/q/41676/2451 and links therein. $\endgroup$ – Qmechanic Jan 24 at 22:17
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The sizes of subatomic particles have been measured by studying how beams of other particles bounce off them in different directions, using particle accelerators to form the beams.

Those experiments show that electrons have no size to them; as far as can be presently detected, they are zero-dimensional. Protons have finite size, an experimental fact which has been known for decades, but the quarks inside them are point particles like the electron.

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