5 ms·

Action quantization (colloquially "planck scale") suggests limits on how small these things can get (very small size = very high momentum, which is not observed

Action quantization (colloquially "planck scale") suggests limits on how small these things can get (very small size = very high momentum, which is not observed).

brianberns 6y ago
But electrons are considered to be point particles, so they would have infinite momentum in this case?
- ben_w 6y ago
  σ_x * σ_p ⩾ ħ/2 The product of the uncertainty in each is always at least some constant. They can still be point-like without you knowing where they are; and also knowing exactly where they are regardless of if they are point-like or extended means there is no defined momentum rather than it is defined as infinite. That said: (a) you can’t pick a number from the set of Reals with a continuous uniform distribution, so I guess you can’t ever have perfect knowledge of the location ever even in principle, and (b) I’m self taught so likely only have a half-understanding.
- fungiblecog 6y ago
  No. They are vibrations of the electron field. There are no point particles in the standard model.
- centimeter 6y ago
  “Point particle” is an approximation that doesn’t accurately predict reality. It only works at large actions. Classical is R^3, quantum is R^3 -> C. (Sort of; this glosses over a lot.) Objects don’t really have a concrete location; they have complex-valued distributions.
- 6nf 6y ago
  I'm pretty sure electrons are not considered point particles?
  - qubex 6y ago
    Pretty sure they are. They’re leptons, and elemental (within the confines of the Standard Model, at least).
    - centimeter 6y ago
      Something being a lepton has nothing to do with whether it's a point particle. Pontryagin duality of position/momentum (which comes from both QM and Relativity, depending on your perspective) rules out the physical existence of point particles. It would require infinite momentum to have zero extent.
gizmo686 6y ago
Assuming are understanding of physics is correct at the plank scale. We already have 2 different theories of physics that are not completely consistent with each other, and we have no empirical evidence of anything near the planck scale.

Action quantization (colloquially "planck scale") suggests limits on how small these things can get (very small size = very high momentum, which is not observed).

brianberns 6y ago

But electrons are considered to be point particles, so they would have infinite momentum in this case?

ben_w 6y ago
σ_x * σ_p ⩾ ħ/2 The product of the uncertainty in each is always at least some constant. They can still be point-like without you knowing where they are; and also knowing exactly where they are regardless of if they are point-like or extended means there is no defined momentum rather than it is defined as infinite. That said: (a) you can’t pick a number from the set of Reals with a continuous uniform distribution, so I guess you can’t ever have perfect knowledge of the location ever even in principle, and (b) I’m self taught so likely only have a half-understanding.
fungiblecog 6y ago
No. They are vibrations of the electron field. There are no point particles in the standard model.
centimeter 6y ago
“Point particle” is an approximation that doesn’t accurately predict reality. It only works at large actions. Classical is R^3, quantum is R^3 -> C. (Sort of; this glosses over a lot.) Objects don’t really have a concrete location; they have complex-valued distributions.
6nf 6y ago
I'm pretty sure electrons are not considered point particles?
- qubex 6y ago
  Pretty sure they are. They’re leptons, and elemental (within the confines of the Standard Model, at least).
  - centimeter 6y ago
    Something being a lepton has nothing to do with whether it's a point particle. Pontryagin duality of position/momentum (which comes from both QM and Relativity, depending on your perspective) rules out the physical existence of point particles. It would require infinite momentum to have zero extent.

gizmo686 6y ago

Assuming are understanding of physics is correct at the plank scale. We already have 2 different theories of physics that are not completely consistent with each other, and we have no empirical evidence of anything near the planck scale.