On 19-06-2018 23:22, Brent Meeker wrote:
On 6/18/2018 6:03 PM, smitra wrote:
On 17-06-2018 22:42, Jason Resch wrote:
Hi Lawrence,
Is the evolution of states of the wave function computable? If so
then
the result of MRDP implies it is Diophantine.
Jason
Or you could try to see if QM could be a meta-theory that arises when
you try to give a statistical description of the set of all these
Diophantine sets. I tried to do something similar with the set of
algorithms a few years ago, getting a half-baked result, some hints at
how quantum field theory could arise from this.
You want to compute the probability that an observer that's encoded by
some mathematical structure has some given information content. So, if
you observe the outcome of an experiment, that's information in your
brain.
Which is the QBism interpretation of QM. If you take the view that QM
is about predicting and explaining what one will see, there's no point
in going further...the rest is metaphysics.
Brent
QM should then emerge as an effective theory and the correct
interpretation should also follow.
But your brain is supposed to be some mathematical structure and that
then contains also that specific information about the outcome of the
experiment. Probabilities should presumably be obtained by counting
the number of states compatible with some observation, but we must
then impose the restriction that we're only going to count states that
correspond to some given observer making that observation. If
observers are specified algorithms that are specified by a set of
input and corresponding output states, then we must sum over all input
and output states, that fit each other. This is mathematically
inconvenient, one can replace such a summation by an unrestricted
summation by including Kronecker delta factors:
delta_{r,s} = 0 if r is not equal to s, otherwise it is 1.
One can then write:
delta_{r,s} = Integral from 0 to 1 of Exp[2 pi i (r-s) theta] dtheta
One can then sum over the variables freely, but one is then left with
integrations over many different theta variables. The idea is then
that in the limit of a large number of variables you can work with
coarse grained averages over the theta variables, you end up with
something similar to the path integral formulation of QFT.
Saibal
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