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I was curious why protons and electrons have opposite and equal charges which brought me to this post. Essentially, I was told that there wasn’t really an explanation and that the charges are only confirmed experimentally.

However, this answer left me feeling dissatisfied. I can understand why it may seem like an experiment is only enough. We could say two objects have the same mass and there is no other underlying physics principle to why.

But my question is how do we know for sure that opposite charges aren’t a coincidence? Another post in that thread brought up the fact that opposite charges exist because a proton could theoretically decay to a positron (this can be argued through $\beta^{+}$ decay.) Is there some scientific principle for why the things are the way it is?

And if not, does that mean that it is viable for a world to exist with protons and electrons having unequal or different charges and no physics principle would be changed?

Qmechanic
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Ashmit Dutta
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    Charge quantization is a natural consequence of speculative grand unified theories where leptons and quarks are unified as members of the same irreducible representation of some symmetry group. – Ghoster Nov 15 '22 at 01:26
  • I voted to close because this is a science fiction question – anna v Nov 15 '22 at 05:31
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    @anna v, please explain why this question is scientific fiction. I believe that it is one of the fundamental facts of physics that the absolute value of the charge of an electron and the charge of a proton are equal. – HEMMI Nov 15 '22 at 11:59
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    @HEMMI in the post I linked, Anna v made an answer that basically said “ It is amusing that there exist people who think they are interested in physics and cannot accept an experimental fact. They need convoluted theoretical arguments which in the end of course end up on the experimental fact. Data trumps theory every single time. Without data theory is science fiction.” I do agree somewhat with her comments, but I have now edited my post as a type of follow up question. However I will understand if the post remains closed. – Ashmit Dutta Nov 15 '22 at 12:42
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    Meta thread here: https://physics.meta.stackexchange.com/q/14242/ – WillO Nov 15 '22 at 13:18
  • @WillO this statement " does that mean that it is viable for a world to exist with protons and electrons having unequal or different charges and no physics principle would be changed?" – anna v Nov 15 '22 at 14:14
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    @annav : I interpret this to mean "Is the equality of proton and electron charges implied by any known physics principle?". That's a fine question. If somebody asks "Are Kepler's laws implied by any known physics principle?", I am going to answer "Yes, they are implied by Newton's laws". I am not going to answer "Kepler's laws are empirically verified, so your question is science fiction." – WillO Nov 15 '22 at 15:36
  • @WillO a world with unequal / different value charges is obviously a world that does not follow mainstream physics observations but a fantasy. – anna v Nov 15 '22 at 19:17
  • @annav I wrote that question as a thought experiment. I want to know if the nature of the universe will really change if protons/electrons had different charges. It's like if you had two masses that are moving toward each other. Even if you changed the mass of one of the objects, the laws of the universe would stay invariant (momentum, energy, etc). I could remove that question if you want though. – Ashmit Dutta Nov 15 '22 at 19:37
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    Related: https://physics.stackexchange.com/q/55513/226902 https://physics.stackexchange.com/q/146000/226902 https://physics.stackexchange.com/q/514909/226902. Similar but invoking quarks: see this answer https://physics.stackexchange.com/a/435859/226902 – Quillo Nov 15 '22 at 19:39

2 Answers2

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In physics there is nothing that is more fundamental than experiment and observation. That protons and electrons have equal and opposite charge to high precision is known from experiments.

The abstractions of the theory are chosen to match this experimental reality. So, naturally, they appear to "predict" it.

John Doty
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    The obverse of the last paragraph is that the Standard Model abstraction would fail due to anomalies in it: they would fail to cancel if $Q_e+ Q_p\neq 0$. – Cosmas Zachos Nov 15 '22 at 15:37
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A few more points to add to John's answer:

is the fact a proton can decay to a positron a random coincidence or is it due to a more fundamental law of the universe?

The half-life of a (free) proton, by some estimates, is about $10^{34}$ years. That's 10,000,000,000,000,000,000,000,000,000,000,000 years. Some physicists have argued that a proton simply does not decay.

a proton can theoretically decay to a positron.

This idea (free proton decay) was first hypothesized by (I believe) Andrei Sakharov. This has never been observed. In such a mode of decay (or any kind of decay) the product states must be less massive than the initial state(s).

One mode of decay may be $p^+\rightarrow \pi^0 +\beta^+$ but again, this has not been observed even using the most sophisticated experimental techniques and apparatus to date.

it made it seem like opposite charges were more of a coincidence because of one “random” thing protons can do

Whether it's a coincidence or not is irrelevant. The data suggests this is the case, which makes it fundamental in our understanding of particle physics. The way this is worded seems to suggest that free proton decay is something that happens frequently. It never happens at all.

Also, would a world with protons and electrons having different charges be possible? What would it be like?

By different, I assume you mean that electrons and protons would have opposite signed charge? Roughly speaking, the answer would most likely be, no difference, assuming the sign of charge was flipped on every other elementary particle (amongst other things - see CPT invariance which is a fundamental symmetry).

joseph h
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    It's good that you point out that free proton decay is only a hypothesis, but can't you instead appeal to $\beta^{+}$-decay to make the same argument? That's definitely been observed. – Maximal Ideal Nov 15 '22 at 00:08
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    "No it hasn't. To be clear, I was referring to a bound proton, yes. https://en.wikipedia.org/wiki/Positron_emission#Discovery_of_positron_emission – Maximal Ideal Nov 15 '22 at 00:26
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    Okay. Thanks for the clarification. That was the first observation of nuclear beta decay. But can you be a little more clear: What about $\beta^+$ decay can we use to make the same argument? – joseph h Nov 15 '22 at 00:41