Dear Lev,
Many thanks for holding up your paper destined for the Greenberger
Festschrift 'till I could take a look at it.
Your argument in section 5, as it is currently formulated, does indeed seem
to be, as others have remarked, amazingly transparently false. It boils down
to the obviously false argument:
Strong assumption LOC-HV leads to contradiction C.
Therefore Weak Assumption LOC cannot lead to C.
You say that you got some positive feed back about your argument, and so
decided to include it. But maybe you should check with the sources of that
positive feed-back, and show them the arguments raised against the rationality
of your argument.
I note that a philosophy student, R.E. Kastner, has sent me two papers of hers
in which she notes that you have been accused of illogical argumentation
in connection with your use of counterfactual reasoning in connection with the
ABL rule, and that she, in her thesis, under Bub at Maryland, has shown that
your argument there is incorrect.
I wonder whether you really want to publish an argument that is so
clearly incorrect? I can see why others who have challenged
my argument have taken pains to point out the irrational character
of your argument: your argument tends, unfairly, to weaken their cases by
association.
The characterization of your argumentation given above is based on your
own identification of your assumption (ii), LOC-HV, as a key element.
But there is a specific identifiable place where your argument departs from
relevance to mine.
I specifically formulated my LOC1 in terms of the nonexistence of
a *backward-in-time* affect of a free choice to be made in the future
upon an outcome that has already appeared to observers of the outcome of
a certain measurement that is actually performed. I have formulated my
assumption in this specific way precisely to avoid possible challenges
of the kind you want to raise. Mermin has noted the power of my way of
formulating my assumption, as a way of avoiding challenges of the kind
you raise. I avoid a hidden-variable assumption precisely by formulating
my assumption in concrete terms based on what has already appeared to
observers of an experiment that has actually been concluded. For you to
slur over this essential point in my formulation, directed specifically at
your kind of challenge by a loose reformulation of my assumption that
is incorrect at precisely the key point is certainly an improper move.
You will be aware that in these discussions I have always taken pains to
assert my assumption in full in terms of ``backward-in-time affects upon
outcomes that have already appeared to real observers of the actually
performed experiment'', instead of permitting any briefer reformulation
in terms of action over space-like intervals. My reasons for always
insisting on my precise wording was to ward off your kind of challenge.
It is trivial make a model in which no outcome is fixed prior to
the actual performance of the local measurement that produces that
outcome (really, the appearing of that outcome to the observers of
the outcome) of that measurement, and which obeys all the predictions
of QM (say for this Hardy set up). This is a non hidden-variable theory
that satisfies all of the predictions of QM: each outcome is fixed at the
time that the measurement is performed by consulting a new random variable
that is not defined until the moment that the measurement is performed.
There is no prior determination of the outcome of any experiment except
as fixed by the quantum laws themselves, and no outcome is defined
for any experiment that is not actually performed, except insofar
as this outcome is fixed by the demands that: (1) an outcome that has already
been performed cannot depend on free choices made later and (2) the
predictions of QM are valid in all ``possible'' worlds allowed in the analysis.
All these conditions can be satisfied in this non-hidden-variable theory.
But ``later'' is defined in one preferred frame, say the rest frame of the
universe, as defined by the black-body radiation. The theory will be
compatible with the theory of relativity in the sense that the LAW of
deterministic evolution (the Schroedinger or Heisenberg equation of
motion) will have a relativistically invariant form, and no ``signal''
will act outside the forward light-cone of its origin. But this
``relativistically invariant non-hidden-variable theory'' will
not be compatible with LOC2 and LOC3: that is what I claim to prove.
Your argument does not come up against my claim in any way that I can
see.
I hope this explanation will bring us back to the agreement that you
at one time said we had achieved.
Best regards,
Henry