Inspired by Chad Orzel’s complaint that there was little popularization of solid-state physics, I picked up the only book accessible to laymen I could find which contains any discussion of it: A. J. Leggett’s “The Problems of Physics”. After going through the one chapter (which said it involves complicated emergent macrostate behavior not easily deduced from the fundamentals, along the lines of Robert Laughlin‘s book) on the subject I went back to the beginning to read about stuff I’ve actually heard about elsewhere. I got confused during the discussion of beta decay. It said a decaying neutron gave off an antineutrino, which Murray Gell-Man certainly didn’t mention in his explanation from “The Quark and the Jaguar”. I’m having trouble understanding what makes something an “antineutrino” rather than a regular neutrino since they have no electrical charge or “color”, which is what makes them immune to the electromagnetic and strong forces in the first place. Leggett also said it was a surprise that protons could decay, but when I started looking things up on Wikipedia that decay is apparently how they were first experimentally observed! The Wikipedia page also mentions that the neutrinos involved were later discovered to be antineutrinos, although how they can tell the difference is beyond me. Wikipedia did fortunately explain how they obtained their experimental measurement of the weak coupling constant: through the time it takes a muon to decay. Sure, whatever. And I had assumed it was through actually measuring energies or a balance of forces.

A while back I asked the advanced physics forum why the weak interaction doesn’t decay quadratically like gravity & electromagnetism. They gave me an answer, but checking know the equations used have disappeared. So I am copying their answer in the post below.
Here is a quick rundown on some of the differences between forces. Each force is mediated by an integer spin boson (I know that’s redundant). Essentially the bosons interact with particles by scattering them in some characteristic way and the resulting change of momentum we see, we call a force. Newton referred to such forces as “action at a distance” but that was only because he didn’t know quantum mechanics enough to know that these “forces” were really particles. So we can instead talk about the properties of these particles (bosons) which characterize their scattering properties.

First there’s mass. As you pointed out, massless bosons, such as the photon and graviton, give rise to inverse square laws. This is exactly because the surface area of a sphere goes like the inverse square. Because the particles are massless they must fly away from their source at the speed of light. So if a fixed number leave the source at one instant, the density of these massless particles at a distance r away will reduce by 1/r^{2} (because we divide by the area). So a fraction of the original bosons to leave the source given by 1/r^{2} will interact with a massive particle, and force is proportional to the number of bosons to interact, so force goes like 1/r^{2}. If the bosons are massive, like the W+, W-, and Z bosons that carry the weak charge, then there is no requirement that they leave the source at a constant speed or that they ever even leave the source fully at lal (they could sit still–their mass allows them to move arbitrarily slow) so the number to interact with an object r meters away should go like something less than 1/r^{2}. When you carefully think through this you come to the realization that massive particles will go like e^{-m r}/r^{2} (where I’ve neglected factors of h and c, and m is the boson mass). Notice that this falls off very rapidly with r, much faster than 1/r^{2}. Also, if m=0 it reproduces the inverse square law. So because these bosons are massive they only interact at short ranges.

The next factor that controls the strength of the force is the coupling constant (think electric charge, e, or Newton’s constant, G). If these numbers are large the force can be large as well. For small constants the force is usually weak. The coupling constant for the strong force, g, is quite a bit larger than the others.

Finally we come to the issue of the gauge group, which I won’t go into detail with because it can be involved, but essentially the gauge group tells you how many particles are involved in the interaction, and it gives you some rules that each boson must obey. For the strong force this is a most important consideration. There are essentially 8 gluons (strong bosons) and each one can interact with a quark such that the overall color is neutral (white–quarks come in three colors–color is just another quantum number to label a quark, when all three colors are present you have white). This gives rise to a far more sophisticated scattering process but intelligent people have worked it out (Gross, Wilscheck) and found that these rules imply asymptotic freedom. In simple terms what this means is that the strong force increases like r at sufficiently high energies (that is, up close the force is very weak, but far way it because very strong, so strong the quarks cannot escape, ever). It’s an interesting subject but to fully understand it you will have to wait for a course on QFT (or just start reading early!)

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