This sounds almost tautological. I have not read Masanes' paper, but he
seems to be saying the Born rule is a matter of pure logic. In some ways
that is what Born said.
The Born rule is not hard to understand. If you have a state space with
vectors |u_i> then a quantum state can be written as sum_ic_i|u_i>. For an
observable O with eigenvectors o_i the expectation values for that
observable is
sum_{ij}<u_j|O|u_i> = sum_{ij}<u_j|o_i|u_i> = sum_ip_io_i.
So the expectations of each eigenvalue is multiple of the probability for
the system to be found in that state. It is not hard to understand, but the
problem is there is no general theorem and proof that the eigenvalues of an
operator or observable are diagonal in the probabilities. In fact this has
some subtle issues with degeneracies.
LC
On Wednesday, February 13, 2019 at 10:40:32 PM UTC-6, cdemorsella wrote:
>
> Two fascinating (and very different) approaches are presented to derive
> Quantim Mechanics main practical tool (e.g. Born's rule). Wonder what some
> of the physicists on here think about this research?
>
> I find the argument that no laws is the fundamental law... and that the
> universe and its laws are emergent guided by subtle mathematical
> statistical phenomena, at the same time both alluring and annoying.... it
> is somehow unsatisfactory.... like being served a quite empty plate with
> nice garnish for dinner.
>
> One example of emergence from chaotic conditions is how traffic jams (aka
> density waves) can emerge from chaotic initial conditions, becoming self
> re-enforcing within local domains of influence... for those unlucky to be
> stuck in them. Density wave emergence is seen across scale, for example the
> spiral arms of galaxies can be explained as giant gravitational pile ups
> with some fundamentally similar parallels to say a rush hour traffic jam,
> except on vastly different scales of course and due to other different
> factors, in the galactic case the emergent effects of a vast number of
> gravitational inter-actions as stars migrate through these arms on their
> grand voyages around the galactic core.
>
> This paired with the corollary argument that any attempt to discover a
> fundamental law seems doomed to the infinite regression of then needing to
> explain what this foundation itself rests upon.... leading to the "it's
> turtles all the way down" hall of mirrors carnival house... head-banger.
>
> Perhaps, as Wheeler argued, the world is a self-synthesizing system, and
> the seeming order we observe, is emergent... a law without law.
>
> Here is the link to the article:
>
>
>
> The Born Rule Has Been Derived From Simple Physical Principles | Quanta
> Magazine
> <https://www.quantamagazine.org/the-born-rule-has-been-derived-from-simple-physical-principles-20190213/>
> The Born Rule Has Been Derived From Simple Physical Principles | Quanta
> Magazine
>
> The new work promises to give researchers a better grip on the core
> mystery of quantum mechanics.
>
> <https://www.quantamagazine.org/the-born-rule-has-been-derived-from-simple-physical-principles-20190213/>
>
>
>
>
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