Maybe she should have been a reviewer. ("I thank Scott Aaronson, Sandro
Donadi, and Tim Palmer for helpful feedback.") As she tweets, this will be
published in Annals of Physics.
This seems to be a fundamental result of what any probability distribution
(under minimal assumptions) on a quantum-theoretic model must satisfy.
@philipthrift
On Sunday, December 27, 2020 at 10:12:56 AM UTC-6 Lawrence Crowell wrote:
> I read this and I have no quarrels with it. The only issue I might have is
> that it is more limited than a full Born rule. The only observable she
> works with is probability. This is then just a variant of Gleason's
> theorem. Sabine does not work with a general Hermitian operator or
> observable. However, the way she does this is similar to the
> Hilbert-Schmidt form and projective bundle. This might be worked into
> greater generality.
>
> LC
>
> On Saturday, December 26, 2020 at 7:48:07 AM UTC-6 cloud...@gmail.com
> wrote:
>
>> Saw this via https://twitter.com/skdh/status/1342435394038726660
>>
>> Sabine Hossenfelder @skdh
>> *Got an email tonight that my paper was accepted for publication. ...*
>>
>>
>> *Born's rule from almost nothing*
>> Sabine Hossenfelder
>> https://arxiv.org/abs/2006.14175
>>
>> Quantum mechanics does not make definite predictions but only predicts
>> probabilities for measurement outcomes. One calculates these probabilities
>> from the wave-function using Born’s rule. In axiomatic formulations of
>> quantum mechanics, Born’s rule is usually added as an axiom on its own
>> right. However, it seems the kind of assumption that should not require a
>> postulate, but that should instead follow from the physical properties of
>> the theory.
>>
>> The argument discussed here is most similar to the ones for many worlds
>> and the one using environment-assisted invariance. However, as will become
>> clear shortly, the ontological baggage of these arguments is unnecessary.
>>
>> Claim: The only well-defined and consistent distribution for transition
>> probabilities on the complex sphere of dimension N which is continuous,
>> independent of N, and invariant under unitary operations is [Born's rule].
>> The continuity assumption is unnecessary if one restricts the original
>> space to states of norm K/N or, correspondingly, to rational-valued
>> probabilities as a frequentist interpretation would suggest.
>>
>>
>> @philipthrift
>>
>
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