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Maybe a silly question but I am looking for an analytic explanation of it.

I think I already have one but I want to see if there is a better one, more fundamental?

What does it mean fundamentally although the proton to have a much larger mass than the electron but to have the same absolute charge value $e$? How is this possible?

Markoul11
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    The basic fundament of physics is observation and measurements. It was found experimentally that the proton and electron have equal and opposite charge, period. All models have to take this into account, and the basic mainstream model does that, – anna v Apr 11 '22 at 13:20
  • This can only happen if the charge is invariant to mass. How the electron with so relative smaller mass can have the same charge with the proton? – Markoul11 Apr 11 '22 at 13:27
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    We observe that the masses are different. Thus, in the models that fit the observations, charge and mass are different things. – John Doty Apr 11 '22 at 13:32
  • To whom it may concern: Here is my answer to the above question: https://physics.stackexchange.com/a/703286/183646 – Markoul11 Apr 11 '22 at 15:51

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Physics is not mathematics. We observe that the proton and electron have opposite charges of equal magnitude. We construct models that reproduce this observation and others. Thus, any "analytical explanation" from one of these models actually traces back to the observations.

You can't have reasoning from unquestionable axioms in physics. The universe gives us phenomena, not axioms.

John Doty
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  • To whom it may concern: Here is my answer to the above question: https://physics.stackexchange.com/a/703286/183646 – Markoul11 Apr 11 '22 at 15:51
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This directly follows from the conservation of charge when considering the $\beta^-$ decay: \begin{equation} n\rightarrow p^++e^-+\overline\nu_\mathrm{e}, \end{equation} where the neutron $n$ and the electron antineutrino $\overline\nu_\mathrm{e}$ don't have charge.

Samuel Adrian Antz
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  • To whom it may concern: Here is my answer to the above question: https://physics.stackexchange.com/a/703286/183646 – Markoul11 Apr 11 '22 at 15:51