Mass Uncertainty: Position, Velocity & Mass

[soothsayer]

Whenever I hear the Uncertainty Principle used, It's always to talk about how a particles' momentum can only be known to a certain range if it's position is known too precisely, and in problems I've encountered, or vice-versa. In problems I've encountered, often times I'll be asked to find the range of velocities a particle can have given the particle's know range of positions, implying that the momentum uncertainty is really caused by a velocity uncertainty. My question is, can you know position and velocity extremely well and create an uncertainty in the particle's mass? I've never heard anything deal with this idea but it seems like it would be possible and that the implications of it could get interesting. Is there anything that anyone can tell me about this subject?

 

[tiny-tim]

hi soothsayer!

My question is, can you know position and velocity extremely well and create an uncertainty in the particle's mass?

mass is quantised …

just as you can't have an electron with a charge of nearly one unit, you can't have an electron with a mass of nearly the mass of an electron

(and the whole of quantum field theory relies on there being certain standard masses)

 

[tom.stoer]

mass is quantised …

This is true in nature but nobody knows why.

If you look at the operator algebra for E (energy) and p (momentum) one can derive E²-p² = m² (using on Lorentz covariance i.e. SO(3,1)) with m being a c-number commuting with all other operators. That means that all physical states in a relativistic quantum field theory labelled with E and p must obey (E²-p²)|E,p> = m²|E,p> where m is a Lorentz scalar.

But nobody is able to tell you why there are certain values for m. It could be any value you like. There is no rule, law, alebra or something else from which quantization of mass could be derived.

 

[soothsayer]

So then, shouldn't the uncertainty principle more accurately be written as

?