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While physicists have tried multiple times and failed to derive the Born Rule (for example: https://arxiv.org/pdf/quant-ph/0409144.pdf). I was wondering what axiomatic Quantum Mechanics had to say about this? Is it fundamentally impossible to derive the Born Rule or is there hope?

Here's a link of great discussion in the same spirit: https://www.math.columbia.edu/~woit/wordpress/?p=10533&cpage=1

In fact here we have someone summarising good reasons/books to believe that it indeed may be possible: http://www.johnboccio.com/research/quantum/notes/bell.pdf

I suspect Lubos Motl was something of the opinion the measurement that should be a separate fundamental axiom. If so, I suspect it becomes a problem of showing: there is no non-redundant axiom when the Born Rule is included? https://motls.blogspot.com/2018/09/woit-and-probability-in-quantum.html

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    $\begingroup$ Is there axiomatic quantum mechanics? $\endgroup$
    – Sergei Akbarov
    Commented Sep 15, 2019 at 13:09
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    $\begingroup$ @SergeiAkbarov there is Dirac–von Neumann axioms but I suspect there would be other reformulations too by now ... $\endgroup$
    – More Anonymous
    Commented Sep 15, 2019 at 13:11
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    $\begingroup$ here is one recent attempt to derive the Born rule axiomatically: The measurement postulates of quantum mechanics are operationally redundant $\endgroup$
    – Carlo Beenakker
    Commented Sep 15, 2019 at 13:54
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    $\begingroup$ More Anonymous, it's an exaggeration to say that the Dirac–von Neumann "axioms" give an axiomatization of quantum mechanics: mathoverflow.net/questions/80146/… $\endgroup$
    – Sergei Akbarov
    Commented Sep 15, 2019 at 14:58
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    $\begingroup$ Anonymous, this "play book" too much resembles cheating. So that it's impossible to find differences. $\endgroup$
    – Sergei Akbarov
    Commented Sep 15, 2019 at 15:11

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