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  Is it possible to attempt a classical (mathematical) model for a basic particle like electron from the requirements of QM and SR? What are the limitations?

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The following two articles published in the Journal- AIP Advances (March 2011) suggest a classical mathematical model for a basic particle electron, by studying the requirements of Quantum Mechanics and Special Relativity. The model is then expected to give same results in a mathematical analysis as obtained by experiments and suggested by these theories. They are available in the Review Section:

1. Mathematical Model I. Electron and quantum mechanics

https://physicsoverflow.org/45309/mathematical-model-i-electron-and-quantum-mechanics

2. Mathematical model II. Basic particle and special relativity

https://physicsoverflow.org/45308/mathematical-model-basic-particle-and-special-relativity

The main LIMITATIONS of the approach are:

a).  We need a complete and well defined system to generate any classical model of a physical reality.

b).  The model of a basic particle can be relative to another particle, with which it interacts. Say, electron as seen by proton, in a Hydrogen atom. The human observer’s role is limited to observing the effects of interaction within these two particles, such as emission of a photon, using his measuring instruments. The concept of describing a classical model of the basic particle as seen by the human observer needs to be discarded.

asked Aug 18, 2022 in Q&A by anonymous [ no revision ]

"Any classical model" is incompatible with QM postulates/facts (probabilities, interference of probability amplitudes). A classical model is an inclusive QM model, where many different points are averaged into one, "classical". Such a replacement is irreversible (the Moon as a point, for example). See, for explanations, my atomic paper in arXive "Atom as a Dressed Nucleus" and the following papers.

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