I posted this question in a subpost before, but got no answers, so here it is again :
Rest Mass of a particle is the mass of the particle at rest. No if the particle is at rest then the momentum is zero (exactly) and hence by Heisenbergs uncertainty principle, the position of the particle has infinite uncertainty. If you don’t even know where the particle is how can you measure the mass ? Does that mean rest mass can never be accurately measured ?
I am obviously missing something here. Any help is appreciated.
Well just to add to the confusion. Velocity is relative. A partical having a certain mass moving at 0 velocity to you will have a greater mass to someone going by at 1/2 the SOL.
fortunatly things don’t vary much from rest mass until you get to a good fraction of the SOL (maybe 1/10th). Perhaps a good definition would be the lowest mass an object can have perhaps that’s a bad one, perhaps someone like Opal can help out (or someone else but since that was the 3rd perhaps it seemed appropiate).
Rest mass can never be perfectly measured. Neither can anything else. However, that does not mean it’s an ill defined quantity. Rest mass is really what’s known as “invariant mass” these days; what that means is that if you know a particle’s momentum and energy, you can always calculate its rest mass. The fact that quantum mechanically, you can’t know both position and momentum is irrelevant; neither determines rest mass. But you’ll have a devil of a time trying to actually measure it, and of course, any measurement one does is inherently limited by the sensitivity of your measuring device anyway.
If it helps, think of rest mass as being the mass needed to make the equation E[sup]2[/sup] = m[sup]2[/sup]c[sup]4[/sup] + p[sup]2[/sup]c[sup]2[/sup] true.
Okay, first of all, why do you say Energy is quantized?
Second of all, even if it were (and I think you may be right, although I’m not sure) how does that mean that mass is quantized? Wouldn’t it mean instead that momentum is quantized?
Thridly, yeah, everything has to be made up of an integer number of certain particles, so you could say rest mass is sort of quantized.
Fourth, you are not missing anything fundamental. I think that maybe you don’t realize how small these quantizations are, though. They’re small.
I was merely quoting Planck when I said Energy is quantized.
If E is quantized and changes with p when the reference frame changes then it follows that p is quantized (following your equation E2 = m2c4 + p2c2). Space and time are continous (?) hence velocity cannot be quantized hence it follows that mass is quantized.
**Thridly, yeah, everything has to be made up of an integer number of certain particles, so you could say rest mass is sort of quantized. **
So what are the particles made of ? How about using that equation of a single particle ?
** Thridly, yeah, everything has to be made up of an integer number of certain particles, so you could say rest mass is sort of quantized **
What has small got to do with it ? Plancks number is small but not insignificant.
Energy is only quantized for bound states. A free electron can have any energy it wants. And the equation I quoted is really true for free particles; it doesn’t include any interaction energy term, which would cause energy quantization. You also have to remember that the equation as given is a relativistic equation which was first derived when there was no quantum mechanics. Nevertheless, it’s also true for real particles (NOT for virtual particles) in quantum mechanics.