On 21-11-2024 22:53, Bruce Kellett wrote:
On Fri, Nov 22, 2024 at 12:12 AM smitra <[email protected]> wrote:
On 18-11-2024 07:02, Bruce Kellett wrote:
On Mon, Nov 18, 2024 at 4:17 PM PGC <[email protected]>
wrote:
Your response presents strong points but contains some
redundancies
and overlapping arguments. Here's a revised version with greater
focus, while maintaining the original’s precision and accuracy:
-------------------------
Bruce, let’s directly address the epistemic interpretation of
the
wavefunction. While this view neatly avoids ontological
commitments
and sidesteps issues like FTL action, it doesn’t fully account
for
experimentally observed phenomena such as violations of Bell’s
inequalities.
The violation of Bell inequalities implies non-locality, and the
epistemic interpretation of the wave function is perfectly
compatible
with non-locality.
The violation of Bell's inequalities does not imply non-locality. In
fact, the violation of Bell's inequality is a prediction of QM which
when describing the dynamics with a physical Hamiltonian, is a
manifestly local theory. It's only in certain interpretations that
there
can be non-local aspects, but then these interpretations make
assumptions that require local dynamics to be violated.
And what might these assumptions be?
Bell's theorem says that no local deterministic hidden variable theory
can explain the correlations that QM predicts. So, Bell's theorem
doesn't say anything about QM itself, it says something about hidden
variable theories that seek to explain the correlations observed in QM
experiments. So, you modify QM and assume that QM is explained by a
classical deterministic hidden variable theory and then you obliged to
take non-locality on board, or else your hidden variable theory will
fail to reproduce at least some of the correlations predicted by QM.
Nothing in here implies that QM is non-local.
But there is
nothing whatsoever non-local about the dynamics of how the
wavefunction
evolves over time.
Not for an isolated non-interacting system. But the Bell inequalities
refer to entangled particles, which do not evolve independently. In
that case, non-local effects are required to explain the observed
correlations.
This means that in any interpretation where you stick
to only the wavefunction as describing physical reality, that
nothing
non-local can occur.
These correlations are not just statistical artifacts of
knowledge
updates; they point to an underlying structure that resists
dismissal as mere epistemic bookkeeping. The wavefunction’s
role
in consistently modeling entanglement and its statistical
implications suggests questioning the existence of a deeper
reality,
challenging the sufficiency of an epistemic-only framework.
Unfortunately, Everettian QM, or MWI, cannot even account for the
correlations, much less the violations of the Bell inequalities. I
have made this argument before, but failed to make any impact. Let
me
try again.
The essence of Everett, as I see it, is that every possible
outcome is
realized on every experiment, albeit on separate branches, or in
disjoint worlds. Given this interpretation, when Alice and Bob
each
separately measure their particles, say spin one-half particles,
they
split at random on to two branches, one getting spin-up and the
other
branch seeing spin-down. This happens for both Alice and Bob,
independent of their particular polarization orientations. If this
were not so, the correlations could be used to send messages at
spacelike separations, i.e, FTL.
It doesn't happen independently, because when Alice makes her
measurement, her state becomes entangled with entangled spin pair.
So,
you now have a macroscopic quantum state where Alice plus her
measurement apparatus are entangled with the entangled spin par.
According to Everett, Alice splits into two branches, one for each
possible result of the spin measurement. That is how the entanglement
is manifested. There is nothing particularly classical about this
situation.
Everett introduces the splits as an effective description appropriate
for describing macroscopic observers. He introduces density matrices so
it should be clear that this isnt an exact qjuantum emchancial
description and it will certainly fail to correctly describe subtle
effects due to entanglement.
And when Bob makes his measurement, he gets entangled with the spin
pair and
as a result with Alice's sector.
When Bob is spacelike separated from Alice and her measurement, he
also splits into two independent branches.
There are no independent branches.
So, in the end it's because you choose
not to describe Alice and Bob quantum mechanically and treat them as
classical objects
That is not the case. Everettian quantum mechanics says that they both
split on to two branches, and there is no clear way in the formalism
to see how the branches for the two individuals are related. In any
model, in which both outcomes are necessarily realized for every
measurement, there is no way to relate the outcomes.
Everettian QM says that this is what effectively happens, but it's
obviously not an exact description and will fail to take into account
subtle effects due to entanglement.
that you end up missing an essential element and that
leads to a paradox.
Nothing has been missed in my analysis. As usual, you are unable to
actually spell out how the correlations are preserved in the
many-worlds scenario.
The correlations are preserved because Alice's and Bob's sectors get
entangled. Suppose Alice, Bob, and Charlie measure x or y components of
the spins of the state:
1/sqrt(2) [|up, up, up> - |down, down, down>]
and two of them measure the y-component and 1 measures the x-component
and we multiply together the 3 results (plus or minus 1), then the
product will always be 1. If you then assume local huidden variables,
then you can argue that both the results of x and y had predetermined
results independently of what was actually measured and independently of
what the other observes choose to measure. Therefore, we can multiply
the 3 potential measurement results where the kth observer measures the
x-component with each other for k = 1, 2, 3. Each experiment would yield
1, and in the product over the 3 spin measurements there are then for
each observer 2 factors for the y-component and 1 or the x-component,
and with the square of a spin being 1, this leads to the conclusion that
the product of the 3 x-components for the 3 observers should equal 1.
However, from the above state you can see that measuring the x
components of all three spins and multiplying the results will always
yield -1. What is then non-local about this result? it's not in the QM,
it's in the fact that the classical reasoning about the measurement
results existing independent of the actual measurement in a local way,
yields a result that QM is in conflict with. So, the non-locality is
squarely in any classical model that is consistent with what QM
predicts.
It's not a problem that the results are correlated per se. Otherwise,
Bell could have saved all the efforts derving his inequalities and just
say that measuring any entangled spin state leads to correlated results.
In the above example one could simply stop at the measurement results of
2 y-components and 1 x-component and say that the results of the 3
observers are correlated. But that
does not demonstrate the necessity of non-local dynamics in an
underlying deterministic hidden variable theory, let alone that QM
requires non-local dynamics.
Saibal
Bruce
Another example of non-locality arising as an artifact of describing
part of a system classically, is the Aharanmov-Bohm effect:
https://arxiv.org/abs/1906.03440
Here too the fact that within the classical realm, you cannot
describe
entanglement causes local dynamics to manifest itself as a seemingly
non-local effect.
Saibal
If N entangled pairs are exchanged, each of Alice and Bob split
into
2^N branches, covering all possible combinations of UP and DOWN.
When
Alice and Bob meet, there is no control over which Alice-branch
meets
which Bob-branch. If the branch meet-up is random, then in general
there will be zero correlation, since out of the 2^N Bob branches
for
each Alice branch, only one will give the observed correlations --
a
1/2^N chance. In the literature, some attempts have been made to
solve
this problem: for instance, it is sometimes claimed that Alice and
Bob
interact when they meet, and this interaction sorts out the
relevant
branches. But no account of any suitable interaction has ever been
given, and also, one can reduce the possible interaction between
Alice and Bob to as little as desired, say by having them exchange
their data by email, or some such. Another suggestion has been
that
since the original particles are entangled, some magic keeps
everything straight. I do not find either line of attempted
explanation in the least convincing, so I conclude that Everettian
QM
cannot account for any correlations, much less those that are
observed
to violate the Bell inequalities.
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