On 15/07/2017 4:00 am, David Nyman wrote:
On 13 July 2017 at 12:12, Bruce Kellett <[email protected]
<mailto:[email protected]>> wrote:
[Wallace's] 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.
The question then is what are we to make of such non-separability
(I'll stick to this usage, for what it's worth) if it is not to imply
a corresponding action at a distance? How can it be that the Alice
who has observed, say, spin-up doesn't get to encounter the Bob who
has also observed spin-up? In what does this so-called entanglement
consist?
This is where it is a pity that Wallace did not actually work through
the entangled singlet state in detail. He gives a general expression for
a state with two entangled particles in (8.14), but says: "In this case,
the amplitudes of the four sets of branches into which C eventually
branches are not determined simply by the separate weights of the
branches at A and B. Not is this to be expected: as I stressed
previously, in Everettian quantum mechanics interactions are local but
states are non-local."
Without further detail, it is impossible to work out how Wallace thinks
the weights of the four branches into which C eventually branches are to
be determined. I think he is just going to use the standard quantum
calculation of these weights, but, as I have said, this calculation is
explicitly non-local. Since Wallace accepts this non-locality, it would
not be out of the question that he would accept the standard calculation
at face value.
ISTM, on reflection, that my tentative suggestion that the alternative
cases are in some deeper sense 'unphysical' have some sort of
explanatory force. It's circular of course, but not I think in a
vicious way. IOW it would be the case that there just were no
well-formed physical circumstances in which such encounters could occur.
Well yes, that is what the singlet state means -- there are no physical
circumstances in which the branches that form could violate QM. But that
is a statement of the fact, not an explanation of that fact.
ISTM however that any such notion implies a deeper level from which QM
as we observe it gets 'selected' on what is essentially an anthropic
(hate that term) basis.
If you want to go down this route you still have to give an account of
how this selection might come about -- why is it that violations of QM
are fatal to consciousness?
This in turn would imply that an entangled QM-physics is a
prerequisite for (at least our species of) observation itself.Of
course, if we hypothesise, on the basis of a computational theory of
mind, that QM is indeed observationally selected from a deeper
arithmetical level, then a 'canonical' physics of precisely this kind
is indeed implied. In this scenario, computational continuations
implying non-entangled encounters simply don't correspond to any of
the observable 'physical worlds'.
I have raised problems with the idea that consciousness "selects"
specifically quantum behaviour in another thread. The basis of my worry
with this is that there does not seem to be anything to rule out a
purely Newtonian classical world exhibiting consciousness as we know it
-- that is implied by substrate independence, strong AI, and the assumed
ability to replace our consciousness with the equivalent computations
carried out on a classical Turing machine. Hence quantum mechanics is
not entailed by consciousness, so it is difficult to see how
consciousness could select out specific facts about the world that were
inconsistent with QM.
Bruce
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