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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1possible duplicate of What is the mass density distribution of an electron? – John Rennie Aug 06 '14 at 09:55
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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. – M.Herzkamp Aug 06 '14 at 10:05
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And about the mass measurement we have: https://physics.stackexchange.com/q/19424/ – jinawee Aug 06 '14 at 12:09
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@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. – smiley06 Aug 06 '14 at 19:39