Mass Uncertainty: Position, Velocity & Mass

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    Mass Uncertainty
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Discussion Overview

The discussion revolves around the implications of the Uncertainty Principle in quantum mechanics, specifically exploring whether knowing a particle's position and velocity with high precision could lead to uncertainty in the particle's mass. Participants examine the quantization of mass and its relation to the principles of quantum field theory.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions if it is possible to know both position and velocity of a particle very precisely while creating uncertainty in its mass, suggesting that this idea has not been widely discussed.
  • Another participant asserts that mass is quantized, indicating that particles cannot have arbitrary mass values, similar to how they cannot have arbitrary charge values.
  • A further contribution notes that while mass quantization is a feature of nature, the underlying reasons for specific mass values remain unknown, highlighting a gap in understanding within quantum field theory.
  • There is a suggestion to reconsider the formulation of the uncertainty principle in light of these discussions, although no specific alternative is provided.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the Uncertainty Principle and the nature of mass quantization, indicating that multiple competing perspectives remain unresolved.

Contextual Notes

The discussion touches on complex topics such as the operator algebra of energy and momentum, and the relationship between mass and quantum field theory, but does not resolve the underlying assumptions or mathematical steps involved.

soothsayer
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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?
 
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hi soothsayer! :smile:
soothsayer said:
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 :wink:

(and the whole of quantum field theory relies on there being certain standard masses)
 
tiny-tim said:
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.
 
So then, shouldn't the uncertainty principle more accurately be written as
latex2png.2.php?z=100&eq=\Delta%20x%20\Delta%20v%20\ge%20\frac{\hbar}{2}.jpg
?
 

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