Mass energy equivalence is conditional and situational. Energy and time measurements are subject to uncertainty.
Small electron mass seems to be fairly measured and repeatable. while electron is on the border line between quantum effects and classical events.
For tiny neutrino mass measurement, sometimes we find it and other times we don't. Maybe it is there part time and other times not. Considering that it moves quite close to light speed with tiny mass in one experiment and at light speed with no mass in another experiment.
When feeling the short range weak nuclear force theory is suggesting the neutrino must have mass at least part of the time.
Δm Δt ≥ h /2πc2
Neutrino mass seems to be small enough that uncertainty allows it to be absent part of the time except when the weak force requires the mass to be present.
Present thinking about exchange of kinetic energy with local space and constant h in GR is given a representation for frequency f and relative scale of one in the lower energy range..
dm /df = h / c2
Maybe it represents the rate at which mass can appear and disappear as the neutrino interacts with local space in the normal state. Higher scales at extreme energy would multiply the rate by the scale number, suggesting that the more energetic neutrinos gain and lose mass more quickly.
Does The Uncertainty Principle Apply To Mass?
if the neutrino is your case study and you consider that uncertainty applies to it then yes uncertainty applies to mass since neutrinos must have mass. The best evidence for this is that neutrinos can change form, in order to do this they must experience time therefore they must travel slower than c which means they have mass. However, my reply may be the result of a certain ambiguity in your question. Rather than asking whether it applies to mass would it not be better to ask at what level of mass it applies, after all if its got mass then its got mass. Another possibility that occurs is to wonder how the detection methods are set in your case study, are you certain that mass isn't being detected not because it is subject to uncertainty but because the neutrino detector is not detecting all kinds of neutrinos? its happened before.
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