On 6/20/2018 6:30 PM, smitra wrote:
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.
?? QBism is an interpretation.
Brent
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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