I have recently acquired Wallace's book and read his section on
non-locality, so I am re-opening this thread (under a different header)
to discuss Wallace's views in more detail. More below......
On 7/06/2017 9:24 am, David Nyman wrote:
On 6 June 2017 at 01:46, Bruce Kellett <[email protected]> wrote:
On 6/06/2017 10:21 am, David Nyman wrote:
Bruce, I'm reading The Emergent Multiverse by David Wallace at
the moment. He's well known as a prominent theorist of MWI. I
don't know whether he falls under your definition of competence
in this area, but as far as I've understood him, he fully accepts
that MWI must be consistent with QM in all respects, including of
course nonlocality. The distinction he makes is between
nonlocality and the question of whether this requires us to think
in terms of instantaneous transfer of information at
greater-than-light speed, or "action at a distance". I can't say
I've been able to get my head around his full exposition of this
yet, but I'm pretty sure he doesn't go along with your
exposition of Price's seemingly faulty version of this.
It is interesting that Wallace has come to this view. He, with
Deutsch, was one of those who attempted to argue that MWI restored
full locality. They also tried to derive the Born Rule from within
MWI, and failed in that too.
I do not know the book you refer to, but if Wallace now accepts
that QM and Bell implies non-locality, then I fully agree. I have
always argued, on this list and elsewhere, that non-locality does
not mean the instantaneous transfer of physical information -- if
you think about it, that would, in a sense, be a local, albeit
FTL, effect. The core of the quantum singlet state is that it does
not involve the physical positions of the particles. It is
expressed in configuration space, and the difficulties appear to
arise from interpreting configuration space as though it were the
same as ordinary 3-space. What has been said is that the singlet
state is always local in configuration space, which translates to
non-locality in 3-space. And this without some FTL information
transfer. If there were FTL information transfer, then that could
be manipulated to give FTL signalling, and there are all sorts of
theorems in QM that show that FTL signalling is not possible.
But it seems as though Wallace is coming to see these things as do
the majority of other physicists -- non-locality is intrinsic to
quantum entanglement.
Wallace uses the term non-separability. He makes an analogy, to a
certain extent, with the ontology of field theories such as
electromagnetism, about which he says "The structural complexity of a
given electromagnetic field is represented not in the properties of
very small spacetime regions (indeed in the limit as these regions
become point sized, the field's structure becomes almost trivial) but
in the way in which those properties vary across spacetime.
Furthermore, this general model is characteristic of pretty much any
classical field theory, except that vector fields seem mathematically
tame compared to the sorts of mathematical objects used to represent
the field values of many classical field theories.". He gives a number
of examples of these latter objects including the affine connections
of General Relativity. He then goes on from this analogy to propose an
ontology for quantum field theory which he calls Spacetime State
Realism. I can't really attempt to elaborate on this here.
Moving on this basis to the question "Does Everettian quantum
mechanics display action at a distance?" he answers in the negative.
He justifies this by elaborating on the observation that "In a quantum
field theory, the quantum state of any region depends on the quantum
state of some cross section of the past light cone of that region.
Disturbances cannot propagate into that light cone." To the question
"Does Everettian quantum mechanics display non-separability?" he
answers in the positive. He justifies this by elaborating on the
observation that "Because of entanglement, knowing the density
operators of regions A and B does not suffice to fix the density
operator of (the union of) A and B. Some of the properties of (the
union of) A and B are genuinely non-local: they have local physical
manifestations only if we arrange appropriate dynamics.".
That is a good extract from the heart of his exposition. In a way, it is
more a matter of words than of substance -- his description of
'nonseparability' is essentially what I have been calling
'non-locality', and Wallace himself actually lapses into this usage from
time to time. His summary is:
"The overall story about locality in Everettian quantum physics, then,
is this: the dynamics of the theory are local: there is no action at a
distance, and no clash with relativistic covariance. But quantum
entanglement means that a great deal of the information contained within
the quantum state is non-local, associated with large spatial regions
but not with any given subregion of those regions. As David Deutsch once
put it, quantum theory is a theory of local interactions and non-local
states."
I cannot find anything in that summary to which I could object.
Wallace than goes on to discuss some examples. His first example is of a
single particle system, such as Schrödinger's cat. He describes the
initial local interaction, and the spreading of the branching via
decoherence. If the cat is system A, and the environment with which it
becomes entangled a set of systems B_i, (i = 1,2,...), then the spread
of the branching results in a situation in which the individual states
of the systems A and B_i become mixed, but the combined state of (A ⋃⋃
B) remains pure. "The state A itself does not change at all in the
process; what changes are the non-local states of successively larger
regions including A." The spreading of entanglement by decoherence is
thus a process that introduces a degree of non-locality. Wallace
illustrates this in his Figure 8.1 on page 307.
Then we get to measurements on two independent particles, and, finally,
two entangled particles. Here Wallace really wimps out, and does not
give any systematic analysis. He does not consider the entangled singlet
state explicitly at all. All he says is that the entanglement between
the particle at A and the particle at B is a non-local property of A ⋃⋃
B. "That property propagates outwards, becoming a non-local property of
the forward light cone of A and that of B. Only in their interactions
can it have locally determinable effects--and it does, giving rise to
the branch weights which, in turn, give rise to the sorts of statistical
result recorded in Aspect's experiments and their successors:
statistical results which violate Bell's inequality."
That is just the standard quantum account, since it is always accepted
that the correlations only become apparent when the results of
measurements by A and B are combined at some later time, when their
light cones overlap.
Wallace seems to find this relatively uninteresting. Bell's result
entails non-separability (non-locality), but not action at a distance
-- but then, no one said it did involve action at a distance. He then
claims that Bell's theorem does not apply to the Everett interpretation
anyway, because is assumes that experiments have unique, definite
outcomes. That is the usual MWI claim against Bell, but Bell's results
are not specifically quantum -- the inequalities obtain for any theory
in which the measurements at A and B are independent, so this passing
swipe at Bell is rather unnecessary.
The upshot, it seems to me, is that Wallace acknowledges non-locality as
I have used the term, only he prefers to call it nonseparability. The
change in terminology does not change the physics, so Wallace accepts
that the Everettian interpretation of QM does not eliminate
non-locality, despite the claims of many MWI supporters.
Bruce
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