Timeline for How do we formally define "indeterminism" of physical expressions?
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10 events
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| Jan 4, 2021 at 17:53 | comment | added | TBissinger | We were specifically talking about the "Heisenberg uncertainty principle", not the phrase or usage of "uncertainty principle" in general. The question of the OP is about the former, the paper you supplied talks about the latter (digressing to the former). There is a difference, which is often overlooked. The nature paper I posted talks about this difference and its origin (and even how the HUP can be generalized). You may read it. I will not bother you further with this. | |
| Jan 4, 2021 at 15:41 | comment | added | WillO | @TBissinger: I think we can agree to disagree about the most natural interpretation of the phrase "uncertainty principle", but with regard to your statement about how mathematicians use the phrase, here is a randomly chosen counterexample: projecteuclid.org/euclid.bams/1183551116 | |
| Jan 4, 2021 at 15:24 | comment | added | TBissinger | From this standpoint at least, a theory without measurement can't say much about the Heisenberg uncertainty principle, which is a statement about measurement. The presence of Fourier transforms in the position/momentum representation of the Schrödinger picture of quantum theory is a justification of why the HUP may apply. But Fourier transform alone doesn't give HUP. Think about linear hydrodynamics, which is often treated in Fourier space. Consequently, there are some uncertainty relations in hydrodynamics, but not the HUP. There's a recent paper by Matos et al., but I didn't read that yet. | |
| Jan 4, 2021 at 15:15 | comment | added | TBissinger | I think that is a common confusion. Yes, there is a mathematical inequality concerning the variances of two functions related by Fourier transform, but I have never heard a mathematician call it the HUP. The HUP of physics, at least Heisenberg's original idea, is a relation explaining how a measurement of a partile's position with a certain error causes a disturbance in the momentum of the particle. Heisenberg uses certain assumptions about what states result after measurement to proof his principle by relating it to the mathematical inequality. nature.com/articles/srep02221 | |
| Jan 4, 2021 at 13:55 | comment | added | WillO | @TBissinger: Mathematically, the HUP is an inequality relating a function (or an equivalence class of functions) to its Fourier transform. Physically, I would say that a theory satisfies the HUP if it postulates a state space whose elements satisfy the HUP. | |
| Jan 4, 2021 at 13:43 | comment | added | TBissinger | What do you consider to be the meaning of the Heisenberg uncertainty principle? We agree that it is a statement about measurement, right? | |
| Jan 4, 2021 at 12:35 | comment | added | WillO | @TBissinger: But it doesn't matter whether the resulting theory is not QM. As long as the resulting theory is deterministic and satisfies the HUP, it serves as a counterexample to the claim that the HUP is incompatible with determinism. | |
| Jan 4, 2021 at 8:21 | comment | added | TBissinger | I don't agree. Quantum mechanics without measurement is not a predictive theory. It doesn't link the mathematical objects to reality. There are two types of time evolution in QM, one is unitary evolution between measurements (Schrödinger eq.), the other is projective evolution (part of which is Born's rule and other measurement postulates). One can do better than the naive projective ebolution by going to POVM theories and the like. But one cannot say that, once one ignores measurement, QM is deterministic. The resulting theory is, but this theory is no longer QM. | |
| Nov 12, 2019 at 20:52 | comment | added | user4552 | I don't see anything to disagree with here, but this doesn't seem like an answer that will help the OP, nor is it a very complete answer even for someone who is at a higher level of knowledge. | |
| Nov 12, 2019 at 16:08 | history | answered | WillO | CC BY-SA 4.0 |