From: *Jason Resch* <jasonre...@gmail.com <mailto:jasonre...@gmail.com>>
On Mon, Jul 30, 2018 at 11:04 PM Bruce Kellett
<bhkell...@optusnet.com.au <mailto:bhkell...@optusnet.com.au>> wrote:
From: *Jason Resch* <jasonre...@gmail.com
<mailto:jasonre...@gmail.com>>
Do Kochen and Specker assume counterfactual definiteness? Bell
did, which is why his theorem does not apply to many-worlds.
No, completely wrong. Bell does not assume counterfactual
definiteness. See Maudlin: "What Bell proved: A Reply to Baylock",
Am. J. Phys. 78, 121 (2010).
There is another reply by Robert B. Griffiths "EPR, Bell, and quantum
locality" ( https://arxiv.org/pdf/1007.4281.pdf
<https://arxiv.org/pdf/1007.4281.pdf> ) which says that Mauldin was
wrong in his reply to Baylock. Who to believe?
Oh dear! Oh dear! Oh! the irony of it!
When I first read through Griffiths supposed rebuttal of Maudlin , I
almost fell off my chair laughing. He has made exactly the same mistake
that von Neumann made in his supposed proof of the impossibility of
hidden variables. Bell, in his 1966 RMP paper "On the problem of hidden
variables in quantum mechanics" gives the following account of von
Neumann's proof. "His essential assumption is: Any real linear
combination of any two Hermitian operators represents an observable, and
the same linear combination of expectation values is the expectation
value of the combination. This is true for quantum mechanical states; it
is required by von Neumann of the hypothetical dispersion free states
also." Bell points out that this requirement is quite unreasonable,
because "the latter is a quite peculiar property of quantum mechanical
states, not to be expected /a priori/. There is no reason to demand it
individually of the hypothetical dispersion free states, whose function
it is to reproduce the /measurable/ peculiarities of quantum mechanics
/when averaged over/."
Griffiths does exactly the same thing in his analysis of Maudlin's
argument in Section VI of the above paper. Maudlin provisionally assumes
locality, then looks to see what properties the singlet state must have
to satisfy the quantum predictions. In other words, he looks for a local
hidden variable account -- what is the "common cause" that gives rise to
the observed correlations? So his point M5 is: "Therefore the complete
physical description of particle b must determine how it is disposed to
yield a particular outcome for each possible spin measurement, because
M1 [opposite spin projections for parallel magnets for particles a and
b] holds for any spin component."
This is exactly what one would require the hypothetical hidden variable
account to do -- the hidden variables, in the terminology used above by
Bell, are the supposed dispersion-free states. Griffiths criticizes this
in the following way: "However, at M5 we arrive at a significant
divergence from the principle of Hilbert space quantum mechanics that
states that any physical description of a particle at a single time must
correspond to some subspace of its Hilbert space. Neither |psi_0> nor
any subspace of H_b for particle b can be interpreted as indicating how
particle b is disposed to yield a /particular/ outcome for /each/
possible spin measurement." Exactly, this is what QM says, but that
cannot be demanded of the supposed dispersion-free hidden variable
states , because they are not part of the standard quantum framework.
This is the von Neumann mistake all over again, and Bell's rejoinder is
apposite also to Griffith's so-called "rebuttal" of Maudlin. Hidden
variable states do not obey the same rules as quantum states, and it is
unreasonable to demand that they do.
One just has to realize that Maudlin is presenting an analysis of what
would actually be required of a local account of the EPR correlations.
He is aware that any such analysis has to be in terms of local hidden
variables. He then points out that Bell's theorem tells us that no such
local hidden variable theory can reproduce the predicted quantum
correlations -- that are experimentally confirmed.
Griffiths goes on the claim that Bell's result can be derived by
assuming counterfactual definiteness, but he is not as clear that such
an assumption is actually necessary. And of course, as Maudlin points
out, Bell makes no such assumption. There is no need to make
counterfactual claims about measurements that were not made in order to
derive Bell's result. In fact, derivations that do refer to such
counterfactuals are all highly contrived and artificial --
counterfactual arguments are not necessary, so no assumptions need be
made about conterfactual definiteness or the lack of it.
Griffiths claims to have disposed of Maudlin's argument against Baylock.
His own account of EPR-type correlations starts from the strong
assumption that quantum mechanics is necessarily completely local. If
his section V on EPR correlations, he blathers on at considerable length
without actually saying very much, and then pulls the quantum result
out of thin air! As with many such supposed 'local' accounts, he does
not actually derive anything, he simply assumes the result.
So, to answer the question: "Who to believe?", I simply say that you
have to analyse carefully what each side of the argument says, and then
make up your own mind. I have done this here: Maudlin's argument in
terms of the necessary properties of any proposed hidden variable theory
is simple, and straightforwardly understandable. Griffiths' rebuttal
simple makes an elementary blunder -- he insists that the HV states
behave exactly as quantum mechanical states. Which is the same blunder
that von Neumann made in his proof of the impossibility of any
dispersion-free hidden variable states.
The choice of who to believe out of these is clear.
"An important lesson to be drawn from all of this is the need for a
clear presentation of consistent principles of quantum reasoning in
textbooks and courses. When teaching courses on quantum information I
always stress the fact that there are no nonlocal influences in
quantum theory, and point out that this principle is useful to keep in
mind when analyzing quantum circuits. Unfortunately, physics students
trained in traditional quantum courses have difficulty replacing, or
at least augmenting, the calculational rules they learned by rote with
a consistent probabilistic analysis of what is going on. They may
already have learned that the superluminal influences reflected in
violations of Bell’s inequality cannot be used to transmit
information. But they also need to hear a simple explanation for why
this is so: such influences do not exist."
Neither, of course, do Kochen and Specker. Their proof is entirely
logical and depends on the properties of non-commuting operators.
Bell proved something similar in his 1966 paper on the problem of
hidden variables.
Deflecting Bell's theorem does not actually help in giving a local
account of EPR-type correlations. Bell inequalities can be proved
without ever referring to quantum mechanics -- they depend only on
the assumption of locality. Experiment shows that these
inequalities are violated.
Bell's reasoning also makes use of implicit assumptions about definite
results for unmeasured things. This is not valid in QM.
Bell makes no such assumptions about unmeasured things. He makes no
assumption of counterfactual definiteness. He only ever needs to refer
to the results of actual measurements that have been made. How else do
you suppose that experimental tests of the Bell inequalities have been
carried out?
Bruce
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