Dear Bruno,
You mind want to read and consider the implications of this paper and
related ones:
http://tph.tuwien.ac.at/~svozil/publ/embed.htm
The key passage in it is:
***
4 Summary
We have reviewed several options for a classical ``understanding'' of
quantum mechanics. Particular emphasis has been given to techniques for
embedding quantum universes into classical ones. The term ``embedding'' is
formalized here as usual. That is, an embedding is a mapping of the entire
set of quantum observables into a (bigger) set of classical observables such
that different quantum observables correspond to different classical ones
(injectivity).
The term ``observables'' here is used for quantum propositions, some of
which (the complementary ones) might not be co-measurable, see Gudder [14].
It might therefore be more appropriate to conceive these ``observables'' as
``potential observables.'' After a particular measurement has been chosen,
some of these observables are actually determined and others (the
complementary ones) become ``counterfactuals'' by quantum mechanical means;
cf. Schrödinger's catalogue of expectation values [42]. For classical
observables, there is no distinction between ``observables'' and
``counterfactuals,'' because everything can be measured precisely, at least
in principle.
We should mention also a caveat. The relationship between the states of a
quantum universe and the states of a classical universe into which the
former one is embedded is beyond the scope of this paper.
As might have been suspected, it turns out that, in order to be able to
perform the mapping from the quantum universe into the classical one
consistently, important structural elements of the quantum universe have to
be sacrificed:
·
Since per definition, the quantum propositional calculus is
nondistributive (nonboolean), a straightforward embedding which preserves
all the logical operations among observables, irrespective of whether or not
they are co-measurable, is impossible. This is due to the quantum mechanical
feature of complementarity.
·
One may restrict the preservation of the logical operations to be valid
only among mutually orthogonal propositions. In this case it turns out that
again a consistent embedding is impossible, since no consistent meaning can
be given to the classical existence of ``counterfactuals.'' This is due to
the quantum mechanical feature of contextuality. That is, quantum
observables may appear different, depending on the way by which they were
measured (and inferred).
·
In a further step, one may abandon preservation of lattice operations such
as not and the binary and and or operations altogether. One may merely
require the preservation of the implicational structure (order relation). It
turns out that, with these provisos, it is indeed possible to map quantum
universes into classical ones. Stated differently, definite values can be
associated with elements of physical reality, irrespective of whether they
have been measured or not. In this sense, that is, in terms of more
``comprehensive'' classical universes (the hidden parameter models), quantum
mechanics can be ``understood.''
***
Am I mistaken in my understanding that this implies BIT /subset QuBIT
and NOT QUBIT /subset BIT?
Kindest regards,
Stephen
----- Original Message -----
From: "Bruno Marchal" <marchal.domain.name.hidden>
To: <everything-list.domain.name.hidden>
Sent: Wednesday, August 21, 2002 12:46 PM
Subject: Yetter's "Functorial Knot Theory" and the Mind/Body Problem
snip
> A simplified translation of the mind-body problem can be
> made with those conservative views. The MP problem can be seen
> as a search of a justification of the BIT-QUBIT relation.
>
> It is not a too big exaggeration to say that the work by Everett,
> Graham, Hartle, Zeh Joos, Kiefer (and others) gives an explanation
> of BITS from QUBITS. That is, how classical observers/worlds emerge
> from a quantum reality.
>
> And it is not at all an exaggeration to say my work is an attempt
> to explain QUBITS from BITS. Actually I show more and less:
>
> -More: because my work provides a proof that, IF we take the
> comp hyp seriously enough, THEN qubits *must* follow from bits.
> This is basically done by the Universal Dovetailer Argument UDA (+
> the Movie Graph Argument if you don't like explicit reference to
> OCCAM razor).
snip
Received on Thu Aug 22 2002 - 06:28:41 PDT