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It occurred to me that if the radius of an electron was bigger than its wavelength this might pose a problem. If a particle's radius exceeded its wavelength how would you describe this situation? Would it create a crisis of some kind or could it be understood somehow?

Derek Seabrooke
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    What do you mean by radius of an electron? According to the standard model the electron is a point-like particle, i.e. it has radius zero. – Thomas Fritsch Dec 10 '22 at 23:26
  • The radius cannot be zero or it would collapse into a blackhole. Any energy must have a finite density. – Derek Seabrooke Dec 10 '22 at 23:36
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    There are no black holes in the Standard Model… it doesn’t include gravity! Furthermore, there is no accepted theory of quantum gravity. No elementary particle in the Standard Model has a radius. However, quantum effects make the electron not appear to be a point particle; in a naive description, it is surrounded by a halo of virtual electrons and positrons, and this “virtual cloud” has a characteristic size on the order of the Compton wavelength of the electron. The effect of this vacuum polarization is measurable. See Wikipedia. – Ghoster Dec 10 '22 at 23:59
  • @Ghoster that is very interesting. I had long suspected something that might be possible, but it ignores one philosophical question. The electron only has so much energy and so it is limited to how much it can squeeze a charge. It cannot squeeze it all the way to a zero-radius point! – Derek Seabrooke Dec 11 '22 at 05:17
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    It cannot squeeze it all the way to a zero-radius point! Maybe, maybe not. I don’t like to think I know what Nature “cannot do”. I’m not concerned about your issue, since my view of the Standard Model is that it’s a great theory for now but almost certainly wrong, and we will eventually have an even better theory. I’m just trying to explain to you what current mainstream physics has to say about the size of the electron: its “bare” size is zero, and its “dressed” size is on the order of its Compton wavelength. – Ghoster Dec 11 '22 at 05:33
  • Haha @Ghoster I truly appreciate your input. On the other hands I cannot ignore conservation of energy! The classic electron radius says it's a certain size and I guess for a reason? – Derek Seabrooke Dec 11 '22 at 05:38
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    I’m fairly confident that we know from experiments at particle accelerators that the electron does not have a bare radius equal to the classical electron radius. That’s bigger than a proton! The bare radius, if there is one, has to be several orders of magnitude smaller. – Ghoster Dec 11 '22 at 05:42
  • @Ghoster I will take your word for it, but it seems to me to create a crisis to squeeze a charge into such a small space without using energy to do so. – Derek Seabrooke Dec 11 '22 at 05:45
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    In mainstream physics, no process squeezes charge to make electrons. It’s not like EM 101. – Ghoster Dec 11 '22 at 05:46

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