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Why is the charge on the electron and proton equal in magnitude?

The charge on electron is $-1.602 \times 10^{-19}$ C and the charge on proton is $1.602 \times 10^{-19}$ C. Their magnitude is the same but why?

The proton gains its charge form two up quarks and one down quark and also the electron itself is an elementary particle. So why do they have same magnitude of charge?

Qmechanic
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Amit Verma
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  • The charge on the electron and proton is $\pm 1.602176634 \times 10^{-19}$ C not $\pm 1.69 \times 10^{-19}$ C. See @ https://en.wikipedia.org/wiki/Electron and @ https://en.wikipedia.org/wiki/Elementary_charge – Brendan Darrer Jul 16 '23 at 12:10
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    Does this answer your question? Why do electron and proton have the same but opposite electric charge? – John Rennie Jul 16 '23 at 12:16
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    @BrendanDarrer my bad but it still doesn't answer my original question – Amit Verma Jul 16 '23 at 12:23
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    The theorists have a story, but that story is motivated by experimental facts, like the observation that the charges cancel in neutral atoms to extremely high precision. That's the true "why": because experiments tell us so. – John Doty Jul 16 '23 at 12:33
  • I asked GPT4 it stated: "The electron is a fermion with a negative charge, while the up quark (two of which are present in the proton) has a charge of $+\frac{2}{3}$ and the down quark (one of which is present in the proton) has a charge of $-\frac{1}{3}$. When these quarks combine to form a proton, their charges add up to $+\frac{2}{3} + \frac{2}{3} - \frac{1}{3} = +1$, resulting in the overall charge of the proton." – Brendan Darrer Jul 16 '23 at 12:35
  • ..."The fact that the charge of the electron is exactly equal in magnitude but opposite in sign to the charge of the proton is a fundamental property of these particles. It is a consequence of the fundamental symmetries of the universe." – Brendan Darrer Jul 16 '23 at 12:36
  • ..."Specifically, the electron and proton have opposite electric charges because they have opposite values of a fundamental property called electric charge. In the Standard Model of particle physics, which describes the fundamental particles and forces of the universe, electric charge is a conserved quantity." – Brendan Darrer Jul 16 '23 at 12:40
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    Brendan I think this is a good example why AI answers are outlawed on StackExchange :-) This answer uses a lot of fancy words to say "it's like that because it is". It doesn't explain why, for example, what might have gone wrong in the theory if there existed a free particle whose charge isn't a multiple of the electron charge? – Nadav Har'El Jul 16 '23 at 12:54
  • Nadav Har'El, good point! Thanks for the advise. I didn't know AI answers were outlawed. However, I thought it gave an impressive answer (I did not include all the answer), or at least a good prompt and starting point for further research. – Brendan Darrer Jul 16 '23 at 13:05
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    @BrendanDarrer The "fundamental symmetry" isn't really fundamental. It is a theorists' summary of a pattern seen in experiments and observations. Physics is an experimental science: it has no fundamental theories, only fundamental experiments and observations. – John Doty Jul 16 '23 at 13:08
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    Grand Unified Theories can explain charge quantization, but unfortunately there is no experimental evidence for a GUT. – Ghoster Jul 16 '23 at 17:09
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    @JohnDoty Physics is an experimental science. Is there any science that isn’t experimental? – Ghoster Jul 16 '23 at 17:55
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    @Ghoster My point is that some physicists seem to forget that the foundations of physics are experiments. They assert that mathematics "explains" the phenomena. But the math is carefully selected to match the phenomena, so that's circular reasoning. – John Doty Jul 16 '23 at 23:16
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    @BrendanDarrer I thought it gave an impressive answer. ChatGPT is often impressive but wrong. In this case, there is no known fundamental symmetry of the universe that requires the proton and electron to have opposite charges, – Ghoster Jul 17 '23 at 02:07

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