On 9/21/2018 9:38 PM, Bruce Kellett wrote:
From: *Brent Meeker* <[email protected] <mailto:[email protected]>>
On Friday, September 21, 2018 at 12:11:01 AM UTC-5, Bruce Kellett
wrote:
Adrian Kent (arXiv:1408.1944) makes some interesting comments
about the recent argument by Sebens and Carroll
(arXiv:1405.7577) that probability in MWI can be understood in
terms of self-locating uncertainty -- when all outcomes of a
measurement are realized in unitary quantum mechanics,
probabilities might arise because one is does not know in which
branch of the universal wave function one is located. Kent
points out that this raises questions about how branches are
formed in unitary quantum mechanics.
The usual Everettian argument is that when one measures a state
with two possible outcomes, say a spin-1/2 particle, unitary
evolution takes the states representing the apparatus, observer,
and environment to a FAPP orthogonal set of states branched
according to each of the possible measurement results.
Schematically, one writes the interaction with
|psi> = (|+> + |->)/sqrt(2)
as |psi>|O>, where O is the "ready" state of the observer
(including apparatus and environment). Thus:
(|+> + |->)|O>
At this point there is just one observer who has not become
entangled with the apparatus or the rest of the environment. To
take this to the next stage, Kent points out that we use the
distribution law of algebra to eliminate the above brackets, and
write
It seems that you are treating this mathematical rewriting as a
physical process. Why insert it between
(|+> + |->)|O> and |+>|O+> + |->|O-> and create the appearance of
a problem?
There is a lacuna in the physical narrative at this point. Each
component of the superposition acts on the apparatus/observer in the
same 'ready' state in order to get |O+> as different from |O->. This
differentiation must take place before decoherence acts to diagonalize
the density matrix. Otherwise all terms in the density matrix would be
the same and there would be no distinction between outcomes. You can't
just paper over this explanatory gap by calling it a mathematical
rewriting.
I think the problem arises from the use of the term "observer" which
implies a kind of sharp "now it's observed". The way I look at is it
explained by this diagram for an EPR type experiment. There is a source
of entangled particles, the red blob, they propagate out to detectors,
diamonds, and at the detectors decoherence starts and essentially is
propagated futureward in the blue and yellow light-cones. The
observers, Alice and Bob, enter those forward light cones at the stars.
They are then within the lightcone of one of the detectors and so they
could observe the result, but whether they look or not they are
decohered because they are interacting with the branch of decohered
worlds corresponding to what that detector detected. The split is
illustrated as the cone rising above and below the original spacetime
plane. On the top side the detectors are A-up, B-up and below the plane
A-dwn, B-dwn.
So showing the observer and being duplicated before interaction is
wrong. They are duplicated when the decohere, whether they "observe"
anything or not.
Brent
Bruce
Brent
|+>|O> + |->|O> (O is uncertain which result he will see)
which, by unitary evolution, becomes entangled with the rest of
the wave function:
|+>|O+> + |->|O-> ( O has a definite result>
representing observers who record '+' or '-' results,
respectively. Before the last step, the observer does not know
which branch he is on, hence the self-locating uncertainty that
is presumed to be the origin of quantum probabilities.
But Kent points out that there is a problem with this -- in the
line in which O is uncertain, the observer has already split:
there is a copy on each branch of the wave function, even though
the observer has not yet interacted with the apparatus or the
environment, so what caused the observer to split and appear on
both branches in this way? We have used the distribution law of
algebra to expand the brackets in such as way as to naively
indicate that such a split has taken place. But how does this
actually happen, physically? Above we are just talking about
equations -- these have to be related to the physics in some
unambiguous way.
Kent comments on the problem that this causes for the Sebens and
Carroll idea of probability as self-locating uncertainty. But it
would seem that the problem is deeper than this. We commonly
divide the Hilbert space into the tensor product of subspaces
representing the apparatus and the environment, as well as the
observer. Then unitary evolution is supposed to act on each
component of this product space so that, ultimately, decoherence
renders the branches FAPP orthogonal, and we can then talk of
separate "worlds". But there is no reason to suppose that this
division into convenient classical components corresponds to any
actual factorization of the quantum Hilbert space -- there is no
clear separation into apparatus-observer-environment, so it is
reasonable to call them all the one thing, as I have done above.
Kent comments on this situation as follows:
"...these are just statements about ink on paper. To translate
them into statements about one or more observers, who are
uncertain about some relevant fact about their location on
branches, requires some principled general account of how we
start from the universal wave function and derive an ontology
that includes (at least) observers and branches.....and
observers must be split into copies before they observe the
relevant event." Kent sees several problems with any such
approach to understanding the above, apparently simple,
mathematical relations.
His conclusion is: "Fifty-seven years of sometimes careful work
on trying to make scientific sense of Everettian quantum theory
ought, surely, to have persuaded the theoretical physics
community that one cannot make useful progress this way.
Whatever one thinks of the scientific status of many worlds
quantum theory, one cannot reasonably, at this point, think it
is so obvious how to translate equations into statements about a
many-worlds reality that arguments and explanations are redundant."
And again: "Moreover, it is worth underlining again here that,
if we /were/ able to find reasonably natural postulates that
respected physical symmetries and defined an objective branching
structure for the universal wave function, it would be
superfluous to postulate many independent real worlds. It would
be simpler and more natural to postulate that precisely one of
the branches is randomly chosen (using the Born wright
distribution) and realized in nature."
That idea would certainly overcome the problem of the apparent
need for apparatus, observers, and the environment to split
/before/ there is any interaction -- one potential branch is
randomly chosen, and then that branch develops in the standard
way. In reality there would be no splitting -- just a stochastic
process.
Bruce
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