Re: Rovelli on EPR

rof@xxxxxxxxxxxx wrote:

Unfortunately I have not been able to find a copy of Piron's book,
either for sale on the web or at the libraries of two major
American universities.

You can ask your library to get this book through interlibrary loan.
This is a small book with powerful ideas. Definitely worth the effort.
Otherwise, you can look for Piron's journal articles in 1960's and
1970's, e.g.,

C. Piron, Helv. Phys. Acta 37 (1964), 439.

From what you say above, though, it sounds
like Piron does more or less what the others do, namely introduce
a set of reasonable axioms, and then say that quantum mechanics is
one of a set of systems which satisfy those axioms.

He says that QM is, basically, a unique system that satisfies those
axioms.

In my opinion, classical logic developed by Aristotle
and Boole refers only to propositions about classical objects.
For quantum objects we need to take into account the statistical nature
of measurements and indeterminism. This requires a change in the rules
of logic.


When we find that we need to use probability, then we have found
that we need to use probability. It doesn't mean that logic
needs to be revised. The statisticians would be surprised to
hear that one has to discard logic itself in order to do
statistics.

Note that quantum probabilities are quite different from classical
probabilities. Classical probabilities arise in a classical mixed
state. Quantum probabilities are present in both pure quantum state
(a ray in the Hilbert space) and in the mixed quantum state
(the density operator).

Doesn't Feynman's two-slit experiment defies the rules of classical
logic? According to these rules we should admit that the electron
passes through both slits, which is nonsense. Of course, this experiment
can be described by invoking the formalism of quantum mechanics, i.e.,
wave functions and the Hilbert space and al that.
The contribution of Birkhoff,
von Neumann and others was to recognize that at a deeper level this
formalism amounts to the change of the rules of logic.

Quantum logic says that all classical axioms are still OK,
except the axiom of distributivity. This axiom wasn't very intuitive
in the classical system anyway. Quantum logic uses the "orthomodular
law" instead. The distributivity axiom is a particular case of the
"orthomodular law".


Well, the axiom which you claim isn't intuitive is the one which
says that if two statements are not both true, then at least one
of them is false.

Are we talking about the same distributive law? The law I know about
involves three propositions A, B, and C, and it says:

A or (B and C) = (A or B) and (B or C)

I suppose one could be sceptical enough to doubt
that axiom, but I do not think that "if proposition x implies
proposition y, then x and y are compatible" is more intuitive.

I may agree that this axiom is not very intuitive, but it
ought to be true, because it leads directly to the formalism of
quantum mechanics which has been verified by experiment an uncountable
number of times.

So what has happened is that the term "weakest experimentally
verifiable proposition implying two given propositions" was renamed
"meet", and something similar happened with "join". Then it was
observed that "meet" and "join" have algebraic properties similar
in some respects to the logical AND and OR. From this observation
the whimsical and metaphorical name "quantum logic" was chosen.
This name was heard by the masses, who interpreted it as a failure
of "classical" logic. Now we have a population who think that logic
itself is wrong and needs to be modified.

You seem to suggest that logic is independent on physical experience.
I don't think so. I think that Aristotle's and Boole's postulates
look so obvious to us simply because we never meet quantum objects in
our everyday life. For quantum objects, two properties may not be
measurable simultaneously and measurements performed in an ensemble
of identically prepared systems may not be reproducible. From classical
standpoint these are pretty unusual features. So, I wouldn't be
surprised to discover that the rules of logic itself should be changed
in order to accomodate these features.

Eugene.

.

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