Joao:
> I don't believe that there is ANY question that QM is non-local! This is
> the outcome of 30 years of experiments with entangled multiparticle
> states.  I also think that non-locality is pretty well defined in this
> context (the way Bell put it) and we know what implications it has
> in the laboratory and elsewhere.

I'm sure there is 'non-separability' in QM (we do not need experiments,
see below, if I did not make too many errors!).

I'm also sure that QM is not a "closed" (I do not say "complete"
because is too dangerous!) theory.

I'm also sure there are Goedelian issues involved (quantum clocks,
observers, quantum automata which cannot be described by QM, etc.)

But QM is based on "states" and nobody knows what these "states" are.
Informations? Properties of a single, individual physical system?
Properties of an ensemble of physical systems? Representations of
procedures for preparing/measuring physical systems? Potentialities?
Math artifacts? Propensities? States of our imagination as Asher
Peres (!) now writes http://arxiv.org/abs/quant-ph/0310010
"It or Bit?" in Wheeler's and Zeh's terms. Why a superposition of
states is 'physical' (Leggett exps.) and an individual state maybe not?

----------

Let us start from the most general question, which says:
is it possible to assign *definite* values of observables
to individual events?

Our usual *assumption* is that the result of the measurement
of a certain operator A depends only on the state ("psi")
of the quantum system we are measuring, and nothing else.

Let us consider (for simplicity, but the conceptual argument
does not need entanglements, necessarily) two spin 1/2 particles,
particle a and particle b, entangled in a singlet state.

We can measure   s(a,x)       = +/- 1
we can measure   s(a,x)s(b,x) = -1
we can measure   s(a,y)s(b,y) = -1
we can measure   s(a,z)s(b,z) = -1

For a singlet state [s(a,x)s(b,y) , s(a,y)s(b,x)] = 0
thus it is possible to measure s(a,x)s(b,y) and s(a,y)s(b,x)
with no reciprocal disturbance.

We can then write
s(a,x)s(b,y)s(a,y)s(b,x) =
= s(a,x)s(a,y)s(b,y)s(b,x) =
= s(a,z)s(b,z) = -1

Thus s(a,x)s(b,y)s(a,y)s(b,x) = -1

Now let us *assume* that in s(a,x)s(b,y)
s(a,x) does not depend on s(b,y) and viceversa,
and let us assume that in s(a,y)s(b,x)
s(a,y) does not depend on s(b,x) and viceversa.

("Does not depend" just means that we can measure
s(a,x) and s(b,y) *separately*, and also
we can measure s(a,y) and s(b,x) *separately*).

With the above *assumption* we get that
s(a,x)s(b,y)s(a,y)s(b,x) = -1
which is in strong contradiction with
s(a,x)s(b,x) = -1
s(a,y)s(b,y) = -1

The above *assumption* must be wrong.

It is wrong (in general, not when the "psi" of the quantum
system is an eigenstate of the operator A) our usual assumption
that the result of the measurement of a certain operator A
depends only on the state ("psi") of the quantum system
we are measuring, and nothing else.

--------------------

"That which is physically unique cannot be separated from the observer
anymore - and therefore falls through the net of physics. The individual
case is occasion and not causa. I am inclined to see in this "occasio" -
which includes the observer and his choice of the experimental setup and
procedure - "revenue" of the "anima mundi" (of course in "changed shape")
that was pushed aside in the 17th century. La donna  mobile - also the
anima mundi and the occasio."
- W. Pauli
Pauli Letter Collection, CERN, Geneva  9992.063, published in K. V.
Laurikainen: Wolfgang Pauli and Philosophy. Gesnerus 41, (1984) 225-227


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