My understanding of current theory is that electrons are excitations in the electron field that, let’s say, “twists it into some kind of knot.”
Are muons and taus, then excitations of their own fields, or might they be a higher energy excitation in the electron field which can then decay back down into the “ground state”?
As an armchair physicist, I think that if the electron (or electromagnetic) field was the only field involved, a muon or tauon could decay to an electron by just emitting a photon (or perhaps multiple photons are necessary because of momentum conservation). But that doesn’t happen: the decay always involves something more: neutrinos. That ‘something more’ can be formulated as a separate field, yes. Another thing is, just emitting photons is easy, it can happen very fast, therefore the decay would happen very fast. In reality the decay is rather slow, and that’s because it involves the weak nuclear force, which is, well, weak.
“Excited electrons” (if they exist) and extra generations of charged leptons are not the same thing. That is, muons are not electrons. There are neutrino oscillations and chiral anomalies, however.
There’s a lot we don’t know about this topic. The conventional (Dirac) view is that there are three different generations of lepton, and the number of particles in each generation is conserved. A muon can and does decay into an electron, but that decay also involves a mu neutrino and an electron antineutrino: Thus, the number of mu-generation-leptons remains 1 (one muon before, one mu neutrino after), and the number of electron-generation-leptons remains zero (zero of anything before, one electron and one electron antineutrino after that cancel out to zero).
However, there’s a competing model for neutrinos called the Majorana model, that states that neutrinos and antineutrinos are actually the same particle, distinguished only by their direction of spin. But in principle, the direction of a neutrino’s spin can be changed, especially at extremely low energies. So this means that there can’t be a conserved “lepton number” at all, certainly not three different lepton numbers, and the fact that there seems to be is just an artifact of the fact that we mostly see neutrinos at high energies where spin-flips are very difficult. If this is the case, then a process should be possible, albeit very rare, where a muon does in fact decay to an electron, releasing nothing else but one or more photons.
Which model is correct? Nobody’s sure. Or rather, some folks are sure, but they’re sure in different directions.
Back when it was believed that neutrinos were massless and traveled at the speed of light, I can see how a direction of spin can be defined – is it left- or right-handed based on the direction of travel. But if they have mass, and therefore can’t travel at the speed of light, one could overtake them and make them appear to be traveling in the opposite direction. As traveling very fast at a constant velocity is a perfectly fine frame of reference, I don’t see how a direction of spin can be defined unambiguously.
Or is that what you meant that the spin direction could be changed at low energies.
One can theoretically do what you suggest (go faster than a neutrino), but that raises a different question: it seems no one has yet been able to observe a neutrino with right-handed chirality.
Yes, that’s it exactly. The spin does matter whenever it’s interacting with anything else, because the Weak Interaction is picky about that sort of thing. But that’s not binding on a free-flying neutrino. There, the only difficulty is that (in the reference frames where they’re created or detected) they’re going very, very fast, so it’s difficult (though as you note, not impossible) to get a faster reference frame.
Under the Dirac model, you would be correct, nor will one ever observe a right-handed neutrino (nor a left-handed antineutrino), because even though they can exist, the weak force wouldn’t allow them to interact with anything, so we if one did exist, we’d have no way of measuring it (aside from rear-ending it with an even faster particle to force an interaction).
Under the Majorana model, though, they do exist and have been detected, and are the things we’ve been calling “antineutrinos” all this time.
The “twists into some kind of knot” metaphor doesn’t do anything for me. It would be less off to just say electrons are particles and leave it at that.
If the electron field is excited to higher energy, that means there are more electrons. Muons and taus are separate particles (or separate fields). They are definitely not electrons with extra sauce on them. That would cause a lot of problems.
A technical note: If we’re talking about right handed in the helicity sense (relative directions of spin and momentum), then right-handed neutrinos can be produced and detected via the weak interaction. It is suppressed greatly in any practical situation, though, given the low mass of the neutrinos.