As far as I understand, we do not know whether an electron is a point particle or not, but we have a very low upper bound for its potential volume. If it turns out that electrons do have volume, what exactly does that mean? What constitutes this volume and how does it compare with the classical notion of volume?
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This is a very speculative question. I am curious if somebody can elaborate on something else than superstrings... – jaromrax Apr 06 '17 at 16:05
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Ah then maybe I need to open this up to purely mathematical explanations? And I am very interested string theory, so superstrings suit me just fine ;) – Nikolai97 Apr 06 '17 at 16:29
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5Possible duplicate of What is the mass density distribution of an electron? – sammy gerbil Apr 06 '17 at 20:32
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This question has been asked many times before : http://physics.stackexchange.com/search?q=electron+volume – sammy gerbil Apr 06 '17 at 20:34
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As far as I understand, we do not know whether an electron is a point particle or not, but we have a very low upper bound for its potential volume.
It depends what one means by low, physics is not a hand waving discipline. There exist experimental limits as seen in this answer to a related question. It is a low limit with respect to its black hole horizon , but very stringent with respect to laboratory measurements.
In addition, the very successful and predictive standard model of particle physics , depends on the postulate that all elementary particles in the table are point particles.
Postulates are the physics axioms that pick up the subset of mathematical solutions of the equations in the physics models which are relevant to the data and observations. The mathematical successes of the model are quite high as seen in the recent LHC experiment, and thus there is no need to worry about the point nature of the particles.
If it turns out that electrons do have volume, what exactly does that mean?
It means that the postulate of "point particles" has to be changed to accommodate new data and still keep the successes of the previous measurements and observations. Newtonian physics still works fine in its dimensional region of validity, even though we know it emerges from an underlying quantum mechanical frame work and at large dimensions is superseded by General Relativity.
What constitutes this volume and how does it compare with the classical notion of volume?
This is for a hypothetical case, the limits given from experiments are for a classical volume in three dimensional space d(v).
At the moment string theories postulate a one dimension extension, from a point to a line . A line still does not have volume, so it is all a matter of theoretical conjecture for distances smaller than the Planck length .
On the experimental side:in quantum mechanics volume can be gauged by interactions and interactions are bound by the Heisenberg Uncertainty principle and are momentum dependent. That is why the concept of "crossection" exists. It gives the interaction "area" for a given momentum. In this sense the "area" of an electron can be bounded and this is what the experiments utilize in setting the limits.
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The last part of your answer is what I was trying to get at; the quantum mechanical notion of volume. Could you possibly expand on that? Maybe in the context of non-fundamental particles if that's more reasonable. – Nikolai97 Apr 07 '17 at 04:44
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I am an experimentalist. Here are some introductory lectures on strings http://www.physics.ntua.gr/corfu2009/Talks/bachas@lpt_ens_fr_01.pdf also this https://indico.cern.ch/event/431029/ – anna v Apr 07 '17 at 05:59