Do we have a well defined mathematical expression denoting the size of a fundamental particle with no internal structure (electron for example) ? If we do, how does it fit in with the uncertainty principle ? And if we don't then what exactly do the experiments reveal claiming radius of electron is of the order $10^{-18} m$ or something like that ? Also in this particular case, does this mean that the probability of the electron being within that radius is 1 and zero outside ? A proper clarification would be very helpful.

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    $\begingroup$ possible duplicate of What is the mass density distribution of an electron? $\endgroup$ – John Rennie Aug 6 '14 at 9:55
  • $\begingroup$ The difference I see is the question about the uncertainty principle. And the answer to that probably is: there is no mass operator. I am not familiar with the Higgs-mechanism, but as I understand it, mass is a parameter (or emerges from one) of the theory. So there is nothing prohibiting you from measuring the mass (indirectly via position or momentum) to arbitrary precision. $\endgroup$ – M.Herzkamp Aug 6 '14 at 10:05
  • $\begingroup$ And about the mass measurement we have: physics.stackexchange.com/q/19424 $\endgroup$ – jinawee Aug 6 '14 at 12:09
  • $\begingroup$ @M.Herzkamp But I am not concerned about mass, I just wanted to ask how exactly the size or radius of these point like particles are defined. $\endgroup$ – smiley06 Aug 6 '14 at 19:39