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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