This is something that has long bothered me, and I have asked a few physicists and chemists and never gotten a very satisfying answer. Why are particles charged? And I'm not asking (and this is the answer you often get) why some molecule might be negatively charged because the answer to that is simply is that there was one more negatively charged particle than positively charged particle. That doesn't answer my question, however, of why there are charged particles at all?
So, on a fundamental level, what makes one particle charged and another one neutral.
For instance, protons and neutrons have almost exactly the same mass, which I'm assuming that means they have very similar internal compositions, yet one is positively charged and the other neutral. What is going on that makes these particles different?
On a similar note, and I'd really like to know this, how is it that a proton and an electron have exactly equal and opposite charge, yet an electron is about 1000 times less massive than a proton?
I have particular trouble with this question because if the answer were something along the lines of "particle X which composes protons all have partial positive charges of n amount…" I would just ask why particle X has any charge and we'd be in the same predicament.
I'm sure there is a satisfactory answer to my question, I just can't find it and don't know what resources are reliable or detailed enough to be satisfactory.
Best Answer
This is ultimately a very deep question. We do not have a very easy ability to answer it at this time. Let me give you the pieces that we presently have.
The basic interactions.
The world as we know it today consists of five fundamental things that happen; they are all called "fields" and the first four are called "forces" or "interactions". In rough order from strongest to weakest, these 4 are as follows.
In those four interactions, and mostly in that third one, we think we can find mostly everything that happens in this world. The fifth interaction which is conspicuously absent is the "Higgs field", which we'll talk about in a moment.
We cannot give you a great explanation why Nature hasn't chosen fewer interactions or more interactions; in particular we cannot tell you a deep reason why Nature chose for there to be an electromagnetic interaction at all. We can give you details but you can always persist asking "why" until we find ourselves in ignorance.
And then there was unity.
We can tell you some other things about electric charge though. A full classical theory was available per James Clerk Maxwell, and a full quantum theory became available due to the works of Schwinger, Tomonaga, and Feynman. This became a template for understanding the strong force, with photons replaced by "gluons" and electric charge replaced with three "color charges" (called arbitrarily "red", "green", and "blue") which has to balance out either in the same way that electric charge does (quarks plus antiquarks) or else by having even amounts of the three charges.
In particular, physicists beat their heads against a wall trying to describe the weak interaction in a way that (a) didn't have unphysical consequences and (b) played nice with quantum relativity until 1961, when a young Ph.D. named Sheldon Glashow discovered that you could make relativistic quantum theory and the weak interaction play nice together if you "bundle in" the electromagnetic force and describe them both together, mediated by four types of 'virtual' particles: two of those particles, the Z boson of the weak interaction and the photon of electromagnetism, at very high energies can phase into each other.
Glashow's "electroweak" theory had some unphysical consequences at high energies, which were removed in the mid 60s by postulating this fifth fundamental interaction, which everyone calls the Higgs field. The Higgs field has a weak coupling to all of the "matter" particles but also to some of the "force" particles, giving them mass. In short, the Higgs explains why everything which is not a proton or a neutron doesn't zip off at the speed of light. We believe these days that we've definitively observed some statistical effects of the distinctive particle which quantizes the Higgs field, shedding most of our doubt about this explanation. The interaction-energy that these particles have due to interacting with the Higgs field grants them an effective mass via $E = mc^2$.
Does this habit of Nature unifying these forces go further? Maybe. So-called "grand unified theories" unify the electroweak interaction with the strong interaction, but they often have some strange predictions, like magnetic monopoles or that protons will eventually decay into positrons-plus-photons, which we've never actually seen happen. So it's very hard to endorse these theories at this stage. So-called "theories of everything" incorporate gravity as well.
However, here we're at a significant experimental loss: we simply don't have enough experimental confirmation to decisively say "yes, this grand-unified-theory is good; no, that theory is bad."
What the electroweak theory tells us about charge.
Okay, now that you know that the electromagnetic force is a low-temperature part of this electroweak theory, what does that tell us about electric charge? It says that electric charge comes about as part of two conserved quantities, called "weak isospin" or $T_3$ and "weak hypercharge" or $Y_W.$ The quarks, for some reason, have a weak hypercharge of +1/3. The leptons, for some reason, have weak hypercharge -1. Some things, in addition, have weak isospin +1/2, and some things have weak isospin -1/2, in the same units. What are those reasons? I don't think we really know. (Also don't get too attached to the pluses and minuses; there are 4 "antiparticles" for each of these particles that have the opposite sign for all of them.)
Electric charge in these units is $q(T_3, Y_W) = T_3 + \frac{Y_W}{2}$, leading to four classes of particles: the non-electromagnetic non-strong neutrinos $q(+ \frac 12, -1) = 0$, the electromagnetic non-strong electrons $q(-\frac 12, -1) = -1$, and the electromagnetic strong quarks "up" $q(+\frac 12, +\frac 13) = \frac 23$ and "down" $q(-\frac 12, +\frac 13) = -\frac 13.$
So for example a neutron is made of two downs and an up, total charge $2\cdot\frac{-1}{3} + \frac 23 = 0.$ The weak force will sometimes turn one of those downs into an up plus a $W^-$ boson $q(-1, 0) = -1$ , which then turns into an electron $q(-\frac 12, -1) = -1$ plus an electron antineutrino $q(-\frac 12, +1) = 0.$ The two ups and a down quark will then make up a proton $\frac{-1}{3} + 2\cdot\frac 23 = +1.$
Particles, in short, are charged because they have this intrinsic weak-isospin and this intrinsic weak-hypercharge which they cannot shed. We do not know why they have these exact parameters, except that all of the possibilities are fully represented.
Mass discrepancies.
We've secretly also answered why protons and neutrons have a mass so much higher than the electron: the electron is a single particle which does not feel the strong force; the protons and neutrons are made up of three quarks which are bound together by the strong force. (In general that is a property of the strong force: it is caused by a powerful three-way charge that we call a "color charge"; the color charge has to balance out either by having three particles which each have one the colors, or by having a particle and an antiparticle bound together with the same color charge; if it's not balanced out it will tear particles made with the other weaker forces apart until it is satisfied because it is so strong.) Satisfying the associated strong force comes with a binding energy $E$ which acts like a mass via $E = mc^2.$
Neutrinos and electrons, which don't feel this energy, only get a little bit of mass from their comparatively weak couplings to the Higgs field: up and down quarks also have a little mass from this mechanism. This is much smaller than the binding energy however; it is maybe 1% if the proton/neutron's mass, most of which comes from this strong force.
So that's the tip of the gory details that go into particle-physics. I don't think we can tell you yet why those particular weak hypercharges are associated with having color charge (feeling the strong force) or not; we wouldn't know until we could reliably test the correctness of grand-unified theories and determine which one our electroweak interaction is embedded in, if there even is one. (Nature might just say, "no, that's just the way I roll, no further questions.") In some GUTs, weak hypercharge is totally separate from color charge; in others part of weak hypercharge unifies with color charge at high-enough-energies.