On 11/05/2016 2:31 am, Bruno Marchal wrote:
The question is: are the probabilities, or the indeterminacies, and
the non locality, phenomenological (1p) or factual (ontological,
real, 3p)?
QM+collapse admit factual indeterminacies (God plays dice, and there
are action at a distance, even if they cannot be used to transmit
signal quicker than light).
QM-without-collapse is purely deterministic at the 3p level, and
admits indeterminacies at the phenomenological level.
I think everyone agree on this.
I think that your confidence here is a bit premature. The Schrödinger
equation was devised for the quantum behaviour of a single
non-relativistic particle. It is local and deterministic in the many
worlds interpretation for that case. However, the Schrödinger equation
does not relate easily to relativity or spin degrees of freedom (spin is
an intrinsically relativistic notion). These can be tacked on, but not
always with great felicity.
The main problem, however, is that once you move beyond a single
particle system, you have to move from physical space into configuration
space, where there are three independent 'spatial' coordinates for each
particle. This caused consternation for the early practitioners of QM,
and still causes problems today for the overly naïve. So while the
Schrödinger equation for a multi-particle system might be local and
deterministic in configuration space, there is no guarantee that this
will remain true when one moves back into physical space to confront
experiment.
This is precisely the problem that one encounters with the current
example of entangled pairs of spinning particles. Single particle
non-relativistic intuitions can mislead, and do so here. Your confidence
in determinism and locality for this system is seriously misplaced.
The debate is on the following question: does QM-without-collapse
admit factual non-locality (real physical action at a distance, like
QM-with-collapse), or do the non-locality becomes, like the
indeterminacy, phenomenological?
(I think yes, as Jesse, Saibal and others, but it seems Bruce and John
C. differ on this).
Given that one cannot simply assume locality or determinism for the
multi-particle system, one is led back to the Bell and CHSH
inequalities. These apply to the two particle case, and the experimental
confirmation of the violation of these inequalities for entangled
particles leads to the conclusion that quantum mechanics is
intrinsically non-local. Since Everettian QM is claimed to reproduce all
the standard quantum results, it must also violate these inequalities.
So either Everettian QM is as non-local as standard QM, or the Bell and
CHSH theorems do not apply to the no-collapse theory.
This latter has been claimed, and people have sought for assumptions
that these theorems make that are not true in MWI. For example, Price
claims: "Bell and Eberhard had implicity assumed that every possible
measurement - even if not performed - would have yielded a /single/
definite result. This assumption is called contra-factual definiteness
or CFD [S]. What Bell and Eberhard really proved was that every quantum
theory must either violate locality /or/ CFD." The trouble here is that
CFD is either trivially violated in ordinary quantum mechanics, or it is
without content. CFD, if it is to mean anything at all, would be the
claim that an unperformed experiment would produce a definite result
*that could be predicted in advance*. That is, of course false in any
version of quantum mechanics. An unperformed experiment would
necessarily produce a result, not necessarily predictable, in a collapse
model; and all possible results in a many worlds model. But in neither
case is there any lack of a result.
So the notion of CFD remains murky, and its relevance to the Bell and
CHSH derivations is even less clear -- in exactly which line of the
proofs is that assumption made? and what happens if that assumption is
not made? I think the claim of counterfactual indefiniteness, if it
means anything, reduces to the claim that Bell assumes a collapse model.
This is the other argument that is raised against the Bell and CHSH
proofs -- they assume that experiments have single outcomes. In other
words, they assume a collapse model. But this is not true either, or, if
it is true, it is not fatal to the applicability of these theorems to
MWI. I will post a full derivation of the CHSH inequality shortly, and I
claim that this does not make any assumption about single results. In
fact, the whole proof is cast in terms of expectation values over
results, so this works for both single and multiple outcomes for any
particular experiment. The proof is not invalidated by moving to a many
worlds scenario because, for any particular set of outcomes from the
measurements on each of the entangled particles, there is only a finite
number of possible joint worlds that can be produced. Each of these is a
possible world, and demonstrating the inequality in any particular world
(a collapse assumption is equivalent to picking just one typical world
from the ensemble) then serves to invalidate the claim the the
inequalities are not applicable in Everettian approaches: if they apply
in a typical world, they apply in all such worlds. And the violation
these inequalities is indicative of non-locality.
Bruce
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