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From: Stephen Paul King <stephenk1.domain.name.hidden>

Date: Thu, 22 Aug 2002 09:22:23 -0400

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

Date: Thu, 22 Aug 2002 09:22:23 -0400

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

snip

Received on Thu Aug 22 2002 - 06:28:41 PDT

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