# Can we meaningfully talk about the size of an elementary particle irrespective of its quantum state? [duplicate]

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.

• 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 at 5:26
• Thank you. I forgot that. – mithusengupta123 Sep 13 at 5:27
• 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 at 14:59
• – Chiral Anomaly Sep 13 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? – mithusengupta123 Sep 13 at 15:09