From: scerir (scerir@libero.it)
Date: Sun Jun 01 2003 - 16:59:51 MDT
Alfio:
> I have to rectract my statement. Some interesting comments are being
> written, and someone is speculating that Quantum effects (and the whole
> QM) is an artifact of experiments reaching the maximum "resolution" of the
> simulation.
Whether or not quantum randomness corresponds to an essential
uncomputability (Chaitin non compressibility) and, thus,
forbids any usual simulation, is still an open question.
Anyway 'physical' properties corresponding to 'experimental' propositions
are identified, in the quantum domain, with 'projection operators'
on the Hilbert space. Thus the Hilbert lattice corresponds to a lattice
of experimental propositions. The algebraic relations and
operations between these experimental propositions are called
'calculus of propositions'. Hilbert lattice and calculus of propositions
should be equivalent. Note, btw, that there is no recursive enumeration
of the axioms of Hilbert lattices.
Now, it is not unreasonable asking something like: do we live in a
quantum universe created by some universal computation?
To test such speculation, it seems that we must look for phenomena
which correspond to a 'calculus of propositions' *not* contained
in a Hilbert lattice. Are there these phenomena? Miracles? :-)
Another interesting way to look at those questions is this.
Determinism is 'defined' as a property of certain theories
according to which the initial conditions of a system
determine, completely, its future evolution and observations.
The probabilistic character of some predictions is entirely
due to some uncertainty we have about initial conditions.
Now the point is that given *any* probability distribution
of some (say n) measurements results it is possible to
construct a *deterministic* theory with hidden variables
that predicts that probability distribution. As far as I know
if we allow 'non-locality'(velocity > c) this is true also
in the case of quantum theory. (I think that John Bell performed
many Montecarlo simulation of quantum events.)
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