On Sunday, December 27, 2020 at 12:42:20 PM UTC-6 [email protected] wrote:
>
> 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
>
That is a fair assessment, which makes this a step in the direction towards
the Born rule.
LC
>
> 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 [email protected]
>> 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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