This paper https://arxiv.org/pdf/quant-ph/0103079.pdf gives an
explicit account of an EPR type experiment which says observers are
"labeled" so that only the compatible observes can communicate.
So, the splitting of each observer into copies at each measurement
interaction is represented by the local dynamics of the operators
describing their states of awareness relative to what they were at the
initial time t0; in particular, the possibilities for interaction of
observers of entangled systems are determined by the labels attached
to the operators. Determination of the number of each type of
observer-copy produced at each splitting, as well as the specific
state of awareness of each type of observer-copy, involves information
14 about the initial conditions of the system, information which in
the Heisenberg picture is contained in the time t0 state vector.
(DeWitt (1998) emphasizes that quantum systems are “described
jointly by the dynamical variables and the state-vector.”) Just as
observers or other entities may be regarded as receiving and carrying
with them, in a local manner, the labels described above, they may
also be envisioned as carrying with them in a similarly local manner
the requisite initial-condition information.
Since one cannot argue for the existence of counterfactual
instruction sets, the conditions of Bell’s theorem do not apply. Had
angles other than those that actually were used been chosen for the
analyzer magnets, copies of each observer carrying labels appropriate
to those angles would have resulted. There are indeed “instruction
sets” present; but they determine, not the results of experiments
which were not performed but, rather, the possibilities for
interaction and information exchange between the Everett copies of the
observers who have performed the experiments.
Bohr’s reply to EPR can also be reinterpreted in the present
context. Regarding correlations at a distance, Bohr (1935) states that
“of course there is in a case like that just considered no question
of a mechanical disturbance of the system under investigation during
the last critical stage of the measuring procedure. But even at this
stage there is essentially the question of an influence on the very
conditions which define the possible types of predictions regarding
the future behavior of the system.” The Everett splitting and
labeling of each observer constitutes just such an influence,
determining the possible types of interactions with physical systems
and observers which the observer can experience in the future without
in any way producing a “mechanical disturbance” of distant
entities.
The Everett interpretation in the Heisenberg picture thus removes
nonlocality from the list of conceptual problems of quantum mechanics.
The idea of viewing the tensor-product factors in the
Heisenberg-picture operators as in some sense “literally real”
introduces, however, a conceptual problem of its own.3 Entanglement
via the introduction of nontrivial “label” factors is not limited
to interactions between two or three particles; each particle of
matter is labeled, for eternity, by all the particles with which it
has ever interacted. What is the physical mechanism by means of which
all of this information is stored? The issue of “where the labels
are stored” may seem less problematic in the context of the Everett
interpretation of Heisenberg-picture quantum field theory. After all,
in quantum field theory, operators corresponding to each species of
particle and evolving according to local differential equations
already reside at each point in spacetime. (In the EPRB and GHZM
experiments the particles in question are considered to be
distinguishable and so may be treated, for purposes of analyzing the
experiments, as quanta of different fields. More complicated objects,
such as observers and magnets, might be approximated as excitations of
effective composite fields, following, e.g., Zhou et al. (2000).)
Even in the event that such a program for a literal, indeed
mechanistic picture of measurement in quantum field theory cannot be
realized, it remains the case that Everett’s model for measurement
in the Heisenberg picture provides a quantum formalism which is
explicitly local and in which the problem of Bell’s theorem does not
arise.
Brent
On 4/4/2022 4:24 PM, Bruce Kellett wrote:
On Tue, Apr 5, 2022 at 7:16 AM smitra <smi...@zonnet.nl> wrote:
On 04-04-2022 01:38, Bruce Kellett wrote:
On Mon, Apr 4, 2022 at 12:52 AM smitra <smi...@zonnet.nl> wrote:
MWI is deterministic, but it's not a hidden variable theory.
Bell's
theorem is proved by assuming you have local hidden variables
that
specify the outcomes of experiments and then deriving
inequalities
that
certain correlations should satisfy.
The central assumption that Bell makes is that of locality, or
separability. He shows that any local (separable) theory must
give
correlations that satisfy the inequalities. Whereas QM, and
experiment, show that these inequalities are violated.
Determinism is also assumed
It is not. Bell made no such assumption. I require textual proof of
such a claim.
QM is not deterministic. And locality is
not the same as separability.
It is. You show me a separable system that is not local, or a local
system that is not separable.
Humean supervenience, which regards all of physics as supervening on
isolated local point-like objects, is local by construction. It has
no non-separable states by definition. The argument is simple:
All local states are separable (By definition of locality and
separability).
Therefore non-separable states are not local. (Modus tollens)
Quantum mechanics embodies non-separable states.
Therefore quantum mechanics contains non-local states.
QM violates the Bell inequalities,
which means that there cannot be an underlying local hidden
variable
model for QM. But QM itself can be local,
That is not a valid conclusion. Any local account of the
correlations
can always be cast as a hidden variable theory -- if for no
other
reason than if there is a local mechanism at play, this
mechanism is
not evident in the standard theory (therefore hidden).
Everettian many
worlds, if they could actually play this role, would be counted
as
hidden variables for Bell's analysis. Bell does not specify what
form
these hidden variables should take.
If all outcomes are realized then there cannot exist hidden
variables.
That is a rather arbitrary assertion. And it is not true. Hidden
variables are variables or things that are not seen.
The outcome of experiments is fundamentally stochastic in the MWI.
The outcome of experiments is stochastic in ordinary QM -- QM is not
deterministic.
Bells's theorem does not
address theories that are not local hidden variable theories.
QM itself provides a local explanations for all experimental
outcomes, including for the Bell correlations.
Then give it!
I'll write up the local account for a Bell-type experiment
performed in
a quantum computer.
I have seen attempts at such accounts. The trouble is that Aspect's
experiments were not performed in a quantum computer! It is Aspect's
experiments that are to be explained.
It would be more interesting if you could give such an account for a
classical computer. What is it that is significant about the QC? It
is generally understood that a quantum computer might give a
speed-up on some tasks, but it cannot actually do anything that a
classical computer could not do, given sufficient time.
The interesting question is why quantum computer accounts do not
correspond to laboratory experience. I think it has something to do
with the formation of permanent records. But you might have a better
account.
Bruce --
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