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!)
Entitled to an Opinion 
September 10, 2010 at 7:15 am
The weak force is actually the most complicated force if you include all the details. What it does is change the flavors of quarks, and it turns electrons into neutrinos or vice versa (including the second and third generation versions of this – muon / mu neutrino, tauon / tau neutrino). So in this example of beta decay a down quark inside a nucleon (a term which covers both neutron and proton) turns into an up quark by emitting a W-minus, which (because it is massive) decays into an electron and an antineutrino.
You ask what makes an antineutrino different from a neutrino. Pragmatically, antineutrinos have right-handed spin and neutrinos have left-handed spin, so you can tell them apart that way. Also, there is a quantity called “lepton number” which is +1 for electrons and neutrinos and -1 for their antiparticles and which is mostly conserved. So in the decay in that picture, you go from zero lepton number (the W-minus) to net zero lepton number (-1 for the antineutrino, +1 for the electron).
From a more fundamental perspective, the weak force (like electromagnetism and the strong force) is an example of a Yang-Mills field. Gravity is not Yang-Mills, so despite also being an inverse-square force, its nature is different.
Anyway, returning to the question of how to think about these things, electromagnetism is still a reasonable analogy. Classically, the electron is a point particle with an electric potential attached. Quantum mechanically, the electric potential is analysed into a superposition of virtual photon wavefunctions (which ultimately come from the modes of a quantum field). So matter particles have a “weak force” potential too, but it’s more complicated because when a weak boson is emitted, the emitting particle changes flavor, and also the weak boson is massive and will decay into matter particles if it isn’t first absorbed by a nearby, preexisting particle – which would therefore change flavor when it absorbed the weak boson. The four-particle Fermi theory describes this flavor-changing emission-absorption interaction between two particles without mentioning the “intermediate vector boson” which travels between them…
If you’re a string theorist, you suppose that all this has a still deeper explanation, e.g. gravitons are closed strings and Yang-Mills bosons are open strings stretching between parallel branes. (I say “for example” because string theory contains so many possibilities. But that is the standard and simplest way to get standard-model forces from strings.)
September 11, 2010 at 1:53 pm
Yeah, later on in the chapter Leggett mentions neutrino spin. He also uses the term “electron number”, though also saying that electrons are just one instance of the broader lepton category.
In other explanations of beta-decay, there are existing neutrinos (or maybe anti-neutrinos) near the down-quark, and when the boson is emitted it is absorbed by the neutrino to transform into an electron. I think it is explained that way so it seems more similar to quarks swapping colors via the strong interaction.
How does gravity have different “nature”? It has a very weak coupling constant. And it’s analogue of “charge” is a scalar quantity that can only be positive. I don’t know which is due to the Yang-Mills thing.
September 12, 2010 at 2:36 am
The difference is that actual gravity is based on local conservation of energy-momentum, a 4-vector, and not just local conservation of energy, the scalar part of the 4-vector. See 1, 2.
A weak interaction in which a neutrino (lepton number +1) turns into an electron (lepton number +1) also conserves lepton number, only this time the net lepton number is 1 rather than 0. Meanwhile, you can look at quark-gluon interactions the same way, in terms of conservation of baryon number. A Feynman diagram where a quark emits a gluon which then becomes a quark-antiquark pair is OK because the total baryon number of the quark-antiquark pair is zero.
(Though ironically, it violates energy-momentum conservation to just have a quark emit a gluon – there’s no way you can add a light-like vector to the energy-momentum vector of the quark and get a new energy-momentum vector with the same relativistic “space-time length” as the original – so this is a “virtual” or “off-shell” process which only makes sense in the context of a larger sum over histories. Actual, detectable, “on-shell” emission of gluons and subsequent quark-antiquark pair production, where they show up in the final states and not just the intermediate states, requires some further compensating interaction to occur, so that total energy-momentum can be conserved.)
September 12, 2010 at 2:46 pm
Physics sure is complicated.
Another thing I wanted to mention but forgot to include above is the possibility that a weakless universe would be compatible with the anthropic principle. Strange that there are so many interactions for an unnecessary force.
September 14, 2010 at 12:47 am
A randomly chosen physics capable of sustaining life might be expected to have a bit of “unnecessary” extra structure to its interactions, rather than being a minimal implementation.
But I think such reasoning is premature. I think there’s a deep connection between the weak force and the particle masses. Even string theory doesn’t yet have a model which gives us the particle masses – existing stringy realizations of the standard model only reproduce the “multiplet” structure, the qualitative behavior of the particles under the symmetry groups of the interactions. The masses are expected to come from complicated effects due to heavier string modes. There is a very cool derivation of the weak force “mixing matrices” from a model in the “F-theory” sector of string theory, so maybe the particle masses also descend from a related effect. If something like that is true, then right now we’re not in a position to judge how “complicated” the “unnecessary” weak force is, because we’re still ignorant regarding all the connections.
October 29, 2010 at 3:48 am
Intersresting that the intermediate vector “boson” is allowed a rest mass and can go arbritraily slow. Aboson is suuppoesd to have no rest mass and go at the speed of light.
Well perhaps the Higgs does not exist and there is a much more fundamental cause of mass.
See: Harmonic quintessence and the formulation of a fundamental energy equivalence equation. Phyics Essays 23: 311-319
June 5, 2011 at 8:39 pm
[…] referenced Laughlin’s book “A Different Universe” here, and now I’ve finally gotten around checking it out. It’s written to be accessible by […]
June 23, 2012 at 10:42 am
What are the fundamental laws and constants of the strong and the weak forces? It seems that they don’t exist.
June 23, 2012 at 8:44 pm
I think if you go to some of the physics sites mentioned or ask a physicist they will tell you what the laws are, but I can’t explain them off the top of my head. I can tell you that they are transmitted by relatively heavy particles (unlike the at-rest massless photons of electromagnetism) which are prone to decay and hence they operate at very small distances. I would call that a “constraint”.
July 18, 2013 at 1:20 am
No nuclear physicist was able to give me an answer for the strong force. Nobody (except me using electric and magnetic coulomb’s laws) is able to calculate even the simplest bound nuclide, the deuteron.