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Yes, I apparently used the wrong word for this. Not a physicist. My point is that it’s not something special about quantum mechanics or particles or even posit

Yes, I apparently used the wrong word for this. Not a physicist. My point is that it’s not something special about quantum mechanics or particles or even positions and momentum. It’s inherent in Fourier transform, conjugate variables and covariance matrices. It happens outside QM, and even outside physics. It’s not a physical attribute, it’s statistical.

tsimionescu 2y ago
> It happens outside QM, and even outside physics. It’s not a physical attribute, it’s statistical. This is not true at all. In classical mechanics, particles have fully definite properties. In the theory, if two particles collide, the position and momentum they'll have after the collision depend on their exact position and exact momentum before the collision, with no bound on precision. Of course, classical mechanics admits that we can't measure things to any level of precision, there is some practical bound below which noise in the measurement will drown out the signal. But the interaction itself has no such bound, it happens with infinite precision. If the speed of one of our particles were higher by just 10^-100 m/s, its trajectory might be completely different. This is not possible in QM. In QM, if the particles collide (they meet at an exact point in space-time), then their trajectories afterwards wouldn't change even if one of their speeds were 10 times higher: if they have definite position, their speed is extremely fuzzy, and it can't significantly affect their trajectories after the event. And QM turns out to be right abput this, when you measure things precisely enough.
- moi2388 2y ago
  I was making the point that the uncertainty principle is not about QM. And it is not. It occurs in a wide range of even classical systems. As for your comment about them not having defined proporties; this is also just one interpretation. You argue for violation of realism. That’s fine, but unnecessary. Violation of locality or realism is only needed in the context of Bell inequalities, and this assumes there is no superdeterminism and you are “free” to choose your experiment, which is of course a rather strange argument to have to begin with.
  - GoblinSlayer 2y ago
    To spare your struggle with language: commutator of hermitian operators is a physical property of mathematical origin, inherited from linear algebra, because QM is described by linear algebra, so physics inherits all aspects of linear algebra as physical properties.

tsimionescu 2y ago

> It happens outside QM, and even outside physics. It’s not a physical attribute, it’s statistical. This is not true at all. In classical mechanics, particles have fully definite properties. In the theory, if two particles collide, the position and momentum they'll have after the collision depend on their exact position and exact momentum before the collision, with no bound on precision. Of course, classical mechanics admits that we can't measure things to any level of precision, there is some practical bound below which noise in the measurement will drown out the signal. But the interaction itself has no such bound, it happens with infinite precision. If the speed of one of our particles were higher by just 10^-100 m/s, its trajectory might be completely different. This is not possible in QM. In QM, if the particles collide (they meet at an exact point in space-time), then their trajectories afterwards wouldn't change even if one of their speeds were 10 times higher: if they have definite position, their speed is extremely fuzzy, and it can't significantly affect their trajectories after the event. And QM turns out to be right abput this, when you measure things precisely enough.

moi2388 2y ago
I was making the point that the uncertainty principle is not about QM. And it is not. It occurs in a wide range of even classical systems. As for your comment about them not having defined proporties; this is also just one interpretation. You argue for violation of realism. That’s fine, but unnecessary. Violation of locality or realism is only needed in the context of Bell inequalities, and this assumes there is no superdeterminism and you are “free” to choose your experiment, which is of course a rather strange argument to have to begin with.
- GoblinSlayer 2y ago
  To spare your struggle with language: commutator of hermitian operators is a physical property of mathematical origin, inherited from linear algebra, because QM is described by linear algebra, so physics inherits all aspects of linear algebra as physical properties.