The Casimir effect is usually derived for parallel plates, with the pressure going as the inverse fourth power of the separation. It strikes me that this implies that a tiny spherical shell of charge (approximating opposite walls to be parallel) will feel an attractive force that goes roughly as the inverse square of the radius (since the area goes as the square of the radius). This seems like a suggestive coincidence that would hint that the Casimir effect would provide the attractive force necessary to hold the charge of the electron together. Is this idea trivially ruled out or has it been explored?

Edited to add: I asked a distinct but related question a couple years ago that I think got a nice answer: link.

  • $\begingroup$ Explanation of the Casimir effect requires consideration of boundary conditions on the surface of the plates. Resulting attraction depends on the kind of material of the plates. Why would one introduce such concepts as boundary conditions and material for composite electron ? This would just make charged parts that make up the electron more elementary than the electron itself and description of these parts seems hugely more difficult than description of the single electron in the first place. $\endgroup$ – Ján Lalinský Mar 17 '14 at 20:29
  • $\begingroup$ @JánLalinský, maybe you aren't familiar with the classical problem of electron self-energy? I agree with your statements, but I think that normally you would consider how much energy it takes to "assemble" the electron. Even though the electron is considered elementary, there is no explanation for what "holds it together." $\endgroup$ – user1247 Mar 17 '14 at 21:31
  • $\begingroup$ I am familiar with the problem, but I do not think it is an actual problem. If there are no parts, there is no need to explain how they hold together. $\endgroup$ – Ján Lalinský Mar 18 '14 at 21:42
  • $\begingroup$ @JánLalinský, I tend to think it is a problem given that Feynman dedicates a few pages to it in his Feynman Lectures and seems genuinely perplexed by it. $\endgroup$ – user1247 Mar 18 '14 at 22:54
  • $\begingroup$ Many people who thought about it were perplexed. One possible solution that does not require introduction of any electronic parts is known at least from 1925: J. Frenkel, Zur Elektrodynamik punktf¨ ormiger Elektronen, Zeits. f. Phys., 32, (1925), p. 518-534. dx.doi.org/10.1007/BF01331692 Feynman most probably knew about this paper since he and Wheeler cite it in their paper on their version of this approach, but they did not realize that Frenkel's paper already contains most parts of a solution: if electron is a point, it has no parts and does not act on itself. $\endgroup$ – Ján Lalinský Mar 19 '14 at 22:11

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