Page 1 of 1
Dr H has a paper on quantum measurement
Posted: Wed Jun 22, 2022 7:00 pm
by notFritzArgelander
I may come back to this later.
https://arxiv.org/abs/2206.10445?fbclid ... uRPlCIP_UU
We summarise different aspects of the measurement problem in quantum mechanics. We argue that it is a real problem which requires a solution, and identify the properties a theory needs to solve the problem. We show that no current interpretation of quantum mechanics solves the problem, and that, being interpretations rather than extensions of quantum mechanics, they cannot solve it. Finally, we speculate what a solution of the measurement problem might be good for.
The full text looks interesting but conceptually gnarly.
Re: Dr H has a paper on quantum measurement
Posted: Wed Jun 22, 2022 10:26 pm
by SkyHiker
What strikes me as odd is that they put a strong focus on axioms while it is not clear that all of these axioms are needed. It has been shown for instance that Born's rule (Axiom 5) follows from other fundamental quantum "axioms" namely if the result of a measurement can be assumed to be unique (
https://www.quantamagazine.org/the-born ... 0mechanics.). That same paper says that the axiom that measurements are unique, also leads to Axiom 2 namely that observables correspond to eigenvalues of Hermitian operators (see the bottom of the linked article). Axiom 4 seems to imply that measurements unique, so does this not mean that Axioms 2 and 5 can be omitted, according to the linked article?
Re: Dr H has a paper on quantum measurement
Posted: Wed Jun 22, 2022 11:02 pm
by SkyHiker
They also state that the entries of the stress energy tensor are complex-valued. Looking at Weinberg who calls it the energy-momentum tensor, they are definitely real-valued. Did I miss something? The article is an interesting read, but they end up with more questions than answers. Six axioms, two more equations and big jumps with mostly philosophical arguments it seems.
Re: Dr H has a paper on quantum measurement
Posted: Thu Jun 23, 2022 1:09 am
by notFritzArgelander
SkyHiker wrote: ↑Wed Jun 22, 2022 10:26 pm
What strikes me as odd is that they put a strong focus on axioms while it is not clear that all of these axioms are needed. It has been shown for instance that Born's rule (Axiom 5) follows from other fundamental quantum "axioms" namely if the result of a measurement can be assumed to be unique (
https://www.quantamagazine.org/the-born ... 0mechanics.). That same paper says that the axiom that measurements are unique, also leads to Axiom 2 namely that observables correspond to eigenvalues of Hermitian operators (see the bottom of the linked article). Axiom 4 seems to imply that measurements unique, so does this not mean that Axioms 2 and 5 can be omitted, according to the linked article?
You've put your finger on some of the gnarliness of this paper. Some of the axioms are redundant to be sure. Six of them? Wightman axiomatized QFT with 4 though the first is a doozy in its complexity and may well be sufficient modulo technical details of interest to mathematicians mostly.
So you're right, Dr H's paper does not present a minimal axiomatization.
https://en.wikipedia.org/wiki/Wightman_axioms
https://en.wikipedia.org/wiki/Axiomatic ... eld_theory
Re: Dr H has a paper on quantum measurement
Posted: Thu Jun 23, 2022 1:28 am
by notFritzArgelander
There are many choices for axiomatizing QM and QFT. The fact that Dr H's choice might be redundant could be a matter of strategy for the paper. :shrug:
Anyway Dirac and von Neumann thought 3 would do and they are nowhere near as complex as Wightman.
https://en.wikipedia.org/wiki/Dirac–von_Neumann_axioms
Re: Dr H has a paper on quantum measurement
Posted: Thu Jun 23, 2022 5:41 am
by notFritzArgelander
The "grand conclusion" of this paper is
From the previous section, we see that a satisfactory solution of the measurement problem must achieve the following:
Requirement 1 Agree with all existing data.
Requirement 2 Reproduce quantum mechanics, including the Collapse Postulate (Axiom 4) and Born’s Rule (Axiom 5), in a well-defined limit.
Requirement 3 Give an unambiguous answer to the question what a measurement device is, at least in principle.
Requirement 4 Reproduce classical physics in a well-defined limit.
Requirement 5 Resolve the inconsistency between the nonlocal measurement collapse and local stress-energy conservation.
The paper is useful as a general summary of the state of the quantum measurement as viewed by physicists committed to Realism, i.e. physics is a faithful model of Reality with a capital "R". I think that that is a mistake. Physics merely models phenomena and from that POV there is no measurement problem despite claims in the paper to the contrary. :Think: