I am still evaluating WordPress, but I thought it’d be instructive to write something about physics. (For one thing, it’d allow me to check how well I can include HTML equations in a WordPress post.)

Notably, about neutrino masses. The Standard Model (SM) of particle physics says that neutrinos are massless. Fermions in general are organized into left-handed doublets (with neutrinos and leptons forming one pair, while up-type and down-type quarks forming the other) and right-handed singlets, but there is no right-handed neutrino. An important claim of fame of the SM is that it is a theory that is unitary and renormalizable.

Trouble is, there is now plenty of observational evidence telling us that neutrinos are not massless. Why is that a problem? You take a left-handed neutrino that is massless, and it moves at the speed of light. You take a left-handed neutrino that is massive, and it moves slower than the speed of light. So, you move fast enough to catch up with it, pass it, and look back, and what do you see? A right-handed neutrino, that’s what. But in the SM, no right-handed neutrino exists.

So what happens when you add a right-handed neutrino? There are two basic choices: the neutrino may be represented by either a Majorana spinor or a Dirac spinor. Without going into needless detail, the first choice basically means that the neutrino is its own antiparticle, ν = ν. So why is this a problem? Because neutrinos carry lepton numbers (very simplistically, an electron can be thought of as the sum of a W particle that carries its electric charge and an electron neutrino that carries its “electronness”. That “electronness” is the lepton number. Now if a neutrino is its own antiparticle, that means that two neutrinos (each carrying a unit of “electronness”) can annihilate, and the two units of “electronness” disappear: lepton number is not conserved. In addition to aesthetic concerns, there are also stringent experimental limits on the violation of lepton number conservation.

The other possibility is that neutrinos are Dirac neutrinos. Dirac neutrinos have genuine antiparticles, so lepton number violation is not a problem. One big problem, however, is the smallness of the neutrino mass; as I understand it, the main objection is that the dimensionless coupling constant that governs the neutrino mass in the Lagrangian is small (of order 10–12) and this worries a lot of people.

Yet another alternative is to account for the observed neutrino oscillations by putting in new interaction terms. While this can be done without a right-handed neutrino, it breaks the renormalizability of the standard model. Loosely speaking, this means that one can no longer assume that things happening at a low energy scale are not affected by things that only happen at high energy. This is not how we experience nature. On the contrary: we can build mechanical devices (relying on low-energy interactions between surface atoms) without worrying about chemistry; we can perform chemical experiments without worrying about nuclear physics; we can do nuclear physics without having to worry about the internal structure of protons and neutrons; and so on. In other words, most physical phenomena can be “renormalized”, treated as if the upper limit of its applicability was infinite, and still yield meaningful results; you only need to worry about higher energy phenomena once you reach that higher energy scale. Why would neutrino physics be different?