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  1. adding 2019 textbook on quantum mechanics by Arnold Neumaier

    Anonymous

    diff, v4, current

    • CommentRowNumber2.
    • CommentAuthorGuest
    • CommentTimeJul 22nd 2022

    Arnold Neumaier uses classical logic throughout his textbook on quantum mechanics. How much of Arnold Neumaier’s textbook remains true if one were using constructive logic?

    Seamus O’Toole

    • CommentRowNumber3.
    • CommentAuthorNikolajK
    • CommentTimeJul 23rd 2022
    • (edited Jul 23rd 2022)

    @Seamus I don’t think that the answer to the question is very particular to his books. If I recall correctly, those are written down in basic Lie group theory and some functional analysis. I think some more recent discussion for practical math could be Commutative algebra (which iirc exists in a more recent version online) and Constructive Analysis (which has Hilbert space discussion). As far as computing quantitative predictions, I’m hopeful that for every practical theorem in mathematical physics, there’s a constructive core that made it useful in the first place. I’m unsure if you’d get far if you want to have verbatim theorems about generic topologies of generic Lie groups. But of course you can at any time impose the classical constraints to get some classical intuition about your objects of study.

    What I can tell you is that Neumaier himself appears to be rather dismissive of intuitionistic logic in relation to physics, see post #88, #102 and #105 here on physicsforums. He seemingly frames it as just a weak version of logic here - a tool for analysis of math and unnecessarily restrictive for physics contemplation. So I get the impression he isn’t aware or at least not interested that you could also use the freedom to get rich consistent, classical-mathematics-contradicting frameworks from it, if you adopt different axioms over the shared computable core. We might get to ask his views here, but then again he hasn’t altered his nLab page in 13 years.