# Why do electrons and protons have the same amount of charge?

by Filby
Tags: charge, electrons, protons
 P: 6 to the untrained eye electrons and protons seemed to be very different, different size, mass and composition but they have the same quantity of charge (ignoring the sign). why is this? An even more fundamental question: what is it about an electron or proton which gives it its charge in the first place? Is it the same for electrons and protons or does the property of charge manifest itself in a different way for each particle. Or put another way, what exactly is electric charge wrt electrons and protons? hope u can help, thanks.
 Sci Advisor Thanks PF Gold P: 1,908 Nobody knows why or how, though they can make mathematical statements based on the results. However, if electrons and protons had different charges, then every atom would have a net charge ... and the large scale universe would be dominated by that net charge instead of gravity.
 P: 109 Why do electrons and protons have the same amount of charge? Spin naturally arises from the relativistic schrodinger equation, but that equation already assumes known charge values. Maybe there's some Hamiltonian whose ground state is the minimum charge we see in electrons and protons? Though the fractional quantum hall effect does allow for smaller units of charge...... Ok, I'm confused too.
P: 6
 Quote by rigetFrog Spin naturally arises from the relativistic schrodinger equation, but that equation already assumes known charge values. Maybe there's some Hamiltonian whose ground state is the minimum charge we see in electrons and protons? Though the fractional quantum hall effect does allow for smaller units of charge...... Ok, I'm confused too.
thanks for responding but perhaps i should have mentioned I am not a physics graduate
so i need an explanation in layman's terms although i appreciate that translating concepts
in particle physics into everyday language is often difficult/impossible .
 P: 109 quantization of energy levels, stuff that's learned in physics undergrad, arises from boundary conditions on the schrodinger equation. This equation is a second order partial differential equation that, in some cases, has nice closed form solutions. I was thinking that perhaps charge quantization (area of my ignorance) may have a similar origin to energy level quantization (well known behavior).
 P: 436 In Kaluza-Klein theory (and in string theories) there is a compact fifth dimension. Electric charge is just the fifth component of the momentum vector. Compactness of the fifth dimension automatically gives us charge quantization. So we might easily conclude that the electron charge is just the smallest possible nonzero charge and the proton also must have that charge (or its multiple) despite its mass is different. However things get complicated when we consider the fractional charges of quarks. One may restate the above claim but with the down quark as the particle with the smallest charge. It would mean that the size of the fifth dimension naturally yields the charge of 1/3 e and electron has triple that charge by accident. Situation gets worse when we make the following observation: 1. All chromodynamically color-neutral (white) particles have integer electric charge (i.e. multiple of electron charge). 2. All chromodynamically colorful particles have fractional electric charge. This may hint that electric and color charge are somehow connected and it's an indication of some unified theory of electromagnetism and color. Just as the observation that weak W bosons are electrically charged hinted that electric and weak charge are in fact effects of one interaction. That said I want to stress here that fractional charges of quarks are not really proven! There is an alternative early theory that quarks have integer electric charge. The experiments really don't show which one is better. Staying with fractional quark charges we must also note that the 1/3 factor is connected to the electroweak mixing angle (of measured value very close 30 degrees, that means 1/3 of 90 degrees). If the mixing angle were different, this picture would not be so pretty. So maybe the fractional charges of quarks come from the electroweak mixing angle.
 P: 109 Integer quarks charge would be similar to spin angular momentum coupling I.e. the net spin angular momentum of three electrons can be -3/2,-1/2,+1/2, +3/2. If we measure + or - 1/2, that doesn't mean each electron contributes 1/6 spin.
 P: 6 Can't say I really follow what's been said so far (thanks for trying) but I was just wondering, has anyone ever postulated a charge equivalent of the Higgs particle or are you all satisfied that charge is intimately linked with quarks and electrons without any need for an external field. Also is it theoretically possible to remove the charge on an electron? Ahhh !! this is getting out of hand , i won't understand the answers anyway :-(
 P: 109 @Filby: Start reading up from wherever you need to start and post here when you get stuck. If you send me a personal message, I'll make sure to answer it
P: 6
 Quote by rigetFrog @Filby: Start reading up from wherever you need to start and post here when you get stuck. If you send me a personal message, I'll make sure to answer it
thanks for that. i appreciate that u can only really get to grips with the sub-atomic world by understanding the mathematics which describe particles and forces but it is still interesting to know which phenomena are well understood by science and which are not.

please don't let my ignorance stem the flow of responses, they are still interesting to read.

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