[cschmid]

I don't know what the issue is. Let's assume for simplicity that the sensitivity is exactly 0.2 eV. Then if you measure something slightly above, like 0.201 eV, you can conclude it has a mass. If you measure something slightly below, 0.199 eV, you don't know.

[AmericanChopper]

The way we know for sure that neutrinos have mass is because we know they oscillate between flavours, and in order for them to be capable of undergoing any type of change they must have a mass, because anything without a mass can only travel at the speed of light, and anything travelling at the speed of light has no experience of time and can therefor never undergone any type of change.

[antognini]

This is sort of true. You are correct that we know that at least some neutrinos have mass because they are observed to oscillate between flavors. But the argument is a bit more subtle than it simply being a consequence of the fact that massless particles don't experience proper time.

As a sort of counterexample, photons can have circular polarization. But if you measure the linear polarization of a photon in two locations, you may find that it is polarized up and down at one point, but polarized left and right at the other. Does this imply that the photon has mass because its polarization has changed as it propagated? No. It just means that the axis of polarization you measured doesn't line up with the way that the polarization gets propagated.

There's a very similar thing going on with neutrinos. When we measure a neutrino, it collapses into a particular eigenstate with a specific mass. But when the neutrino propagates, it propagates as a mixture that oscillates between the various eigenstates, a little like how a photon propagates with circular polarization.

It turns out that the frequency of these oscillations depends on two things: a parameter that measures the strength of this mixing, and the difference between the squares of the masses of the eigenstates. Since the frequency of oscillations is nonzero this means that the difference between the masses has to be nonzero, which means that at least one neutrino flavor has to have mass. But even if neutrinos had no oscillations this doesn't mean that they are massless --- they could equally well have a mixing coefficient of zero, or just have equal, but nonzero masses.

[lnauta]

To make it more complicated, they measure mass-squared! The original KATRIN article from 2019 (which I read at the time) measured a mass-squared of m^2 = (-1.0) +0.9 -1.1 eV^2. This is obviously unphysical, as a negative mass, let alone a negative mass-squared does not mean anything. (No they are not tachyons.) To get around this, some statistical tricks like "Feldman-Cousins" and others have to be used to construct a confidence interval that can be physically interpreted. I don't know the details of FC though, but it's widely used in low-statistics experiments.

[MauranKilom]

I would expect that sensitivity to be standard deviations (or some multiple thereof), not hard bounds. If it's actually hard bounds, I'd be curious how they establish those (beyond "it's the 99.9 percentile", which would fall under "a number of standard deviations" for me).

[btilly]

The issue is that your measurement can be below the real value. Therefore you can measure something slightly below even if the real value is somewhat above.

That is 0.199 eV could be measured even if the actual mass was 0.35 eV.

Unless I'm misunderstanding what they mean by sensitivity.