A Particle With A Charge Of 5.5 X 10^-8

[Denisha Simcoe]

Thisis 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?

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?

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.

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.

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.

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.)

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.

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.

The answer to this and the similar questions is : because that is what we have observed and defined by measurements with innumerable data. It is an existential question. Physics is not about existential questions.

Physics is about observations with measurements of the way the natural world behaves and fitting with mathematical models the observed behavior. The models are successful, validated, when they can predict any future behavior accurately.

Starting with the Millikan oil drop experiments the electron was found to have a definite charge and the microcosm of elementary particles made mathematical sense , from nuclear physics to quark physics with assigned charges and masses and a number of quantum numbers. The ingenuity of physicists found that the standard model, a mathematical model , could describe all interactions ( almost) of elementary particles and their composites with great accuracy.

Once a mathematical model is successful many people , mainly theorists, tend to agree with a platonic philosophy ( mathematics creates nature), and that is why your "why" question gets all these explanations from symmetries etc. But the physics truth is that a mathematical model is a tool, not a creator of nature. If we had had different observations we would have had different mathematical models.

The standard model of particle physics is built on gauge theory, which is a theory of local symmetries. This means that the symmetries act differently at different points in space (and time). For example, if you move everything in the universe 1m in one direction, nothing is changed. This is a global symmetry, because everything has been moved by the same amount in the same direction - in other words, it acts the same at every point.

There is a mathematical theorem, Noether's theorem, saying that each continuous symmetry of a physical system leads to a conserved quantity, and the fact that we can choose $\theta(x)$ as we please means that we have come sort of conserved quantity. It turns out that the theory of this rotational symmetry leads to certain particles having an electric charge, which is conserved. So your question ultimately comes down to symmetry.

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The α particle is the nucleus of the helium-4 (4He) atom and it consists of two protons and two neutrons, tightly bound by the strong nuclear force. It is one of the most-studied atomic nuclei and its properties are of great importance for understanding the nuclear forces and the development of modern nuclear physics10,11. Its simplicity makes the α particle a favourable target for a variety of precision studies: its zero nuclear spin (I = 0) means that it can be described by a simple charge distribution, without magnetization distribution, quadrupole or higher moments. In elastic electron scattering, the α particle can thus be described by a single charge-monopole form factor. From the analysis of electron scattering world data, a root-mean-square (r.m.s.) charge radius of the α particle rα = 1.681(4) fm was extracted1, where the value in brackets indicates the 1σ uncertainty in the last digit(s).

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