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Elementary particles such as the electron are quantum mechanical fuzzy objects described by quantum states or wavefunctions. They are not classical billiard balls with some fixed radius. Can we assign a notion of a natural "size'' of the electron irrespective of the state it is in? The only length associated with the electron that I can think of is the Compton wavelength, $\frac{\hbar}{m_ec}$. But I am not sure if it will be proper to refer that as the size of the electron. I don't have a definite answer. Thanks.

Solidification
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    The only length associated with the electron that I can think of is the Compton wavelength. There is also the classical electron radius, which is about two orders of magnitude smaller. – G. Smith Sep 13 '20 at 05:26
  • Thank you. I forgot that. – Solidification Sep 13 '20 at 05:27
  • Prerequisite question: How should we define the "size" of a quantum particle? Different definitions might lead to different values. One example of a definition: when people say the electron is pointlike, they're really making a statement about the electron's interactions -- namely that all of its interactions are captured by a lagrangian density that is strictly local in spacetime, where one of the fields corresponds directly to electrons. (Protons in QCD don't have this property, so we don't say they're pointlike.) – Chiral Anomaly Sep 13 '20 at 14:59
  • Related: What is the mass density distribution of an electron? and Experimental boundaries for size of electron?. – Chiral Anomaly Sep 13 '20 at 15:06
  • @ChiralAnomaly I had the impression that unlike neutron and proton, the electron and all other elementary particles are pointlike in the sense that there is no substructure (as far as we know now). Is that a false impression? – Solidification Sep 13 '20 at 15:09
  • @mithusengupta123 Your impression is correct. It's another way of saying the same thing. My example was an attempt to define what "no substructure" means in QFT. – Chiral Anomaly Sep 13 '20 at 15:13
  • Would you say that neither the Compton wavelength nor the classical electron radius has anything to do with the actual size of the electron? In that case, what do they refer to? They ought to have some significance because those are two lengths that can be constructed from the properties of the electron. – Solidification Sep 13 '20 at 15:23

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Elementary particles in the standard model of particle physics are axiomatically posited to be point particles, see table. The standard model successfully describes most of existing data and is successful in predictions for new studies, so all the beyond the standard model theories trying to fit the few unexplained data up to now, necessarily embed the standard model . At themoment all measurements are consistent within errors with the hypothesis in the model that electrons, neutrinos, etc are point particles.

Because they are quantum mechanical entities, they are fuzzy because their location follows their wavefunction description whose complex conjugate squared gives the probability of finding the point particle at (x,y,z,t). This probability locus is used to describe charge distributions, but the particle itself is a point, as far as accuracy of measurement presently goes.

For example, experiments that are trying to measure the size of the electron, with the hope of finding discrepancies with the standard model, are at the moment giving limits.

anna v
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