Is mass something that is "uncertain"?

fillyt

I do not know much quantum mechanics, so I apologize in advance if this question does not make much sense. Since the values of a particle, such as its position, momentum, polarization, and so on are confined by the uncertainty principle, then is mass also something that is "uncertain"?

PatrickPowers

Yes. The general idea is that there is a relation between the lifetime of a particle and how definite its mass is. The more definite the lifetime, the less definite the mass. The less definite the lifetime, the more definite the mass. It is believed that an electron has a completely indefinite lifetime -- it never decays spontaneously -- so it has a perfectly definite mass. Most "exotic" particles have a very short lifetime, like a trillionth of a second, so the lifetime has a very definite length and they have an indefinite mass.

Then there is the muon, which has a lifetime of 2.2 microseconds with quite a small uncertainty. But the uncertainty is much larger than it is for the trillionth second particles so the mass also falls in a small range. I always wondered what was going on inside this tiny timebomb.

fillyt

Oh ok, thank you. Does this have anything to do with the fact that it takes time to make a measurement of mass, and the less time you have to measure it, the less accurate the measurement?

Bill_K

I disagree with the previous answer. The mass of a particle is a perfectly well-defined quantity, even if the particle has a short lifetime. It's true there will be a spread in energy for a sequence of observations, but the particle's rest mass is defined to be the central value, and may be precisely determined.

W and Z bosons, for example are very short-lived. The lifetime of the Z boson is about 10^-25 sec, making its width or spread in energy about 2.5 GeV. Nevertheless its rest mass is currently quoted as 91.1876 ± 0.002 GeV. In fact it is important to obtain the rest masses of the W and Z quite accurately, since they relate directly to Θ_W, the weak mixing angle.

fillyt

Oh I see. That's what my initial guess was. So does that mean that something like an electron has a very small spread in energy?