dm4b said:
Just because something leads to confusion doesn't necessarily mean it is fundamentally incorrect.
Yes, and I wasn't necessarily saying that "photons don't experience the passage of time" is incorrect. Pedagogy always involves judgment calls, which different people can make in different ways; no argument there.
dm4b said:
A more technical and exact discussion can alleviate the chances of that and be more fruitful, but that doesn't mean the same kind of confusion can't happen there too.
No argument here either.
dm4b said:
Exactly, that's the point of a limit. Plot that up and tell me the trend you see.
Exactly, combine that with the trend above and what does that suggest.
That a null interval is exactly zero. Which we already knew since you can plug a null interval directly into the Minkowski interval formula ds^2 = dt^2 - dx^2 - dy^2 - dz^2 and get zero.
dm4b said:
Combine that with the fact that neutrinos would not able to undergo neutrino oscillations if they had zero mass and what does that suggest.
It all suggests that "massless particles do not sense the passage of time"
The general fact that lightlike intervals are zero suggests to me that timelike and lightlike objects are fundamentally different. However, since you mention neutrino oscillations specifically, we can go into more detail for that specific case.
Neutrinos come in three "flavors", electron, muon, and tau, corresponding to the three kinds of "electron-like" leptons. Neutrino oscillation means that a neutrino that starts out as one flavor can change to a different flavor--more precisely, the quantum mechanical mixture of flavors of neutrinos changes over time: the amplitudes for the different flavor eigenstates oscillate.
Oscillating amplitudes in themselves don't require timelike objects: photon amplitudes can oscillate and photons are massless. The point is that the flavor eigenstates of neutrinos--the states in which only one flavor amplitude is nonzero--are *different* than the mass eigenstates--the states in which a neutrino has a definite invariant mass. But for this to lead to neutrino oscillations as defined above, there must be more than one mass eigenstate, so that the amplitudes for different mass eigenstates can oscillate with different frequencies, which in turn means that the amplitudes for each flavor eigenstate (which are just different linear combinations of the mass eigenstates) also oscillate. That means at least one neutrino mass eigenstate must have a nonzero mass. It does *not* require that *all* of the neutrino mass eigenstates have nonzero mass; there could still be one such state with zero mass. AFAIK the current belief is that all of the mass eigenstates have nonzero mass, but that's based on experimental data, not theoretical requirements.
So I would say that the statement "neutrino oscillation requires neutrinos to have non-zero invariant mass" is, while technically correct, a little misleading since it invites the false implication that *any* kind of "oscillation" requires a non-zero invariant mass.