On 1/06/2017 6:28 am, David Nyman wrote:
On 31 May 2017 at 04:55, Bruce Kellett <bhkell...@optusnet.com.au
<mailto:bhkell...@optusnet.com.au>> wrote:
On 31/05/2017 12:30 pm, Pierz wrote:
Thanks for these clarifications Bruce. I find your explanations
to be very lucid and helpful - they also confirm my own
understanding.
Thank you for the kind comments, I try my best to be clear.
IIRC, you weren't a particular fan of MWI when I last conversed
with you on this list.
That is indeed the case. I have several reasons to be dubious
about MWI. Firstly, it amounts to reifying a complex valued
function that resides in configuration space -- I am not sure that
this is a well-defined procedure. Secondly, MWI doesn't really do
what it claims to do, which is to provide a resolution of the
measurement problem in QM. MWI doesn't provide any explanation of
the transition from a pure state to the mixed state that is
required for experiments to give definite results. At the crucial
point, MWI simply says "then a miracle happens!" To be more
explicit, deterministic evolution of the wave function by the
Schrödinger equation gives a full account of decoherence, and the
dissemination of the coherence phases into the environment. This
reduces the off-diagonal elements of the density matrix so that
the diagonal elements become *almost* orthogonal, but unitary
evolution can't go the whole way. The only way one can reduce the
pure state to a mixture is to trace over the environmental degrees
of freedom, which is to say that the residual phase information is
simply thrown away. This trace operation is non-unitary, and there
is no warrant for it in the SE itself, so it is, in the final
analysis, just an appeal to magic.
Bruce, is it perhaps finally an appeal to observation per se? IOW what
you say is of course objectively the case, but perhaps in some way the
residual phase information isn't relevant (i.e. can be 'traced over')
in the synthesis of the 'observer-observation' relation. If so, this
relation could perhaps resolve the 'eternalist' pure state (which
after all continues simply to be 'there' in the MWI conception)
subjectively into what would give the 'instrumental' appearance, in
effect, of the probability density characteristic of a mixture?
It is often argued that the density matrix is diagonalized FAPP, and
FAPP is all that is required. Unfortunately, I don't think that that
really works. Even though the individual off-diagonal elements might be
arbitrarily small, there are a very large number of them (increasing as
further environmental degrees of freedom are included). The end result
is that the original superposition is still intact and no 'split' has in
fact occurred -- the situation is still completely reversible. The
problem I point to is that there is nothing in the unitary mathematics
corresponding to "ignoring inessential degrees of freedom". That is what
the partial trace does, but that has to be imposed by hand, it is not
automatic, and suffers from all the old difficulties of the Heisenberg
cut -- it is arbitrary.
Then there wouldn't seem to me to be a necessary idea of 'collapse'
involved, except in a purely epistemological sense. The term
'subjective' here is more in the sense of some fundamental
compositional principle of observer-hood than a restriction to
out-and-out 'waking consciousness'. I'm not sure if this has any
necessary connection to Lockwood's idea of a 'consciousness basis'.
Of course quite clearly any of this would be highly speculative, but
I'm wondering if it could make any sense in principle? I'd value your
opinion.
I think that something like this was what Everett had in mind when
called this idea the "relative state model". I think he saw the observer
as complete in every branch, so that
|psi> = (|1> + \2>)|me>|environment> --> (|1>|me_1> +
|2>|me_2>)|environment>
--> |1>|me_1>|environment_1> + |2>|me_2>|environment_2>
and he then considered the two parts of the development to be complete
in themselves, so we found ourselves in one or the other branch. Everett
had no particular commitment to the existence of the other branches --
it was DeWitt who developed the idea of many worlds. The trouble here,
as is well known, is that the above is still a pure state, and we
require a reduction to a mixed state in order to be able to consider one
or other branch on its own. The 'collapse' can be regarded as
epistemological, but we will still need the mixed state.
Thirdly, the non-observed branches in MWI play no essential role
in the theory, so Occam would say that they are inessential
entities that should be discarded. If one is simply going to
discard them, and they play no observable role, why invoke these
other branches in the first place?
I wonder if you'd care to comment on my original argument on this
thread - which has of course now been swamped by the usual
brawls. Does not a single history + the physical insignificance
of the notion of a current moment mean that there is also only a
single possible future?
We will only experience a single future, but what that future is,
is indeterminate at the present instant.
And if the future is predetermined in this way, isn't this a
serious issue for single universe models of QM? How can the
outcome of quantum events be both inevitable and random?
I don't see that there is only a single possible future. The block
universe notion only requires indeterminate time ordering for
spacelike separated events. The future along and inside one's
future light cone is in the future for all observers, so need not
be determined by some other observer having already seen what
happens. The block universe only constrains the future only in
very limited sense -- it is only for spacelike separations that
simultaneity is ambiguous, timelike separations are not so
constrained.
Quantum non-locality is another matter, however, and there are
growing indications that quantum entanglement and the associated
non-locality might prove to be of fundamental significance for
physics -- such as the possibility that space-time itself might
emerge from quantum entanglements.
Yes, I'm reading Wallace's Emergent Multiverse at the moment on this
topic, amongst others. Here's some rank speculation in the MWI vein
from the observational perspective: Let's say that entanglement does
indeed turn out to be very fundamental in the genesis of what we call
'worlds' in the first place. Mightn't it then be the case that
observers - who themselves by assumption supervene on a very
narrowly-constrained physics - thereby can't help but find themselves
observing the equally tightly-constrained consequences of just such
entanglement?
I am not sure I follow where you are going here. Entanglement is
ubiquitous in QM, but not all entanglement is monogamous in the sense
that the EPR singlet particles are maximally entangled. Of course, if
space-time is basically a manifestation of entanglement, then observers
supervening on physical space-time will be part of this entanglement
IOW, trivially, it's a necessary condition of their own existence. So
consequently there could be the appearance of non-locality without
there being the requirement for actual simultaneity of action across
real physical separations (all the more so if this is conceived as
preceding the very emergence of space-time itself).
Showing that space-time is emergent from entanglements of some kind
might very well explain of the origin of non-locality -- basically
because, in the presence of universal conservation laws, this
entanglement is always non-local in character. But this is all still
very much in the speculative phase of development.
Bruce
I know this argument has an unavoidable flavour of circularity, but
again my question is about principle, not proof. I guess it's also an
argument for a species of super-determinism, but with all the
counterfactuals still permanently in play, as it were.
David
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