From: *Bruno Marchal* <marc...@ulb.ac.be <mailto:marc...@ulb.ac.be>>
On 8 Aug 2018, at 13:50, Bruce Kellett <bhkell...@optusnet.com.au
<mailto:bhkell...@optusnet.com.au>> wrote:
The real problem I see with many-minds theory is that it does not
actually explain the observed correlations. The correlations are
presumed not to exist in reality -- all possible combinations of
experimental outcomes happen, but when Alice and Bob meet, their
bodies are still in indefinite states -- no actual results are
recorded by entanglement with their bodies -- but their minds will be
in definite states that agree with the quantum correlations. This
step seems to introduce yet more unreasonable magic into the
'explanation'. Why are the minds like this when they communicate?
Because all Alice and Bob are coupled in that way, by the singlet
state. That works if we keep in mind that the singlet state (when not
already observed by neither Alice nor Bob) describes an infinity of
Alice and Bob, with the spin in all directions, but always correlated.
This is not quantum mechanics. The Hilbert space for the singlet is
two-dimensional. This space is spanned by two (mutually orthogonal)
vector, but these basis vector may be chose in an infinity of different
ways, all describing the same state. There is no way that the singlet is
a superposition of all possible basis vectors: it is 2-dim, not
infinite-dimensional.
I think you are describing a particular hidden variable model, in which
there is actually an infinite dimensional space of the hidden variables,
one dimension for each hidden vector that picks out a particular spin
orientation. If we now place an infinite of Alices in this space (by her
interacting with the singlet, say), the Alice's measurement locates her
in this infinite space according to the direction in which she made her
measurement. The other particle of the singlet in this space has an
"element of reality" corresponding to spin component in the direction
opposite to Alice's result. When Bob measures this second particle, he
gets 100% correlated results *provided he measures along the same axis*
as Alice. Before his measurement, Bob is in the same
infinite-dimensional space as Alice was, so by measuring along the same
axis, he self-locates into the same subspace, when his particle was
already primed to have its spin pointing along that axis in the
direction opposite to Alice's particle. This hidden variable account
will work to give the correct correlation for measurements along the
same axis at both ends. But it immediately fails if Bob makes a random
rotation before he makes his measurement. That will then locate him in a
different subspace to that inhabited by Alice, so the only possible
results he can obtain are up or down with 50% probability for either.
This does not give the correct correlation with Alice for any angles
other that 0 or 180 degrees.
I had thought through this possible explanation for your insistence that
the measurements of both Alice and Bob serve only to locate them in the
relevant subspaces some time ago. But I realized very quickly that this
crudest of hidden variable models could not work for general magnet
orientations. The point about general relative orientations is that the
probabilities for Alice and Bob getting the same or different results
depends on the relative angle of their measurements. In any single trial
on an entangled pair, they can get any one of four combinations of the
possible results. It is the relative probabilities of these results that
are crucial for reproducing the quantum correlations. And these
probabilities depend on the relative magnet orientation, a fact which is
available only non-locally. Besides, the above is a hidden variable
model that has nothing to do with conventional quantum mechanics.
When Alice and Bob make their measurement, if they are space
separated, it makes no sense to ask if they are or not in the same
world or branches. The result they obtained only entangle each of them
with the environment, locally, and that spread on the whole universe
(at subliminal speed) so that both of them will encounter only their
“correlated” counterparts.
This is just nonsense. A world is defined as a branch of the wave
function that is fully decohered and disjoint from all other branches.
Alice and Bob are semi-classical objects, and they do not oscillate
between branches of the wave function according to random quantum
fluctuations of their constituent molecules. Perhaps the best way to
understand the inevitable quantum substructure of and macroscopic object
is in analogy with statistical mechanics. We do not change worlds
according to the thermal fluctuations of the molecules in a gas -- these
fluctuations are averaged over (coarse-grained) in the bulk properties
that characterize the gas, such as volume, temperature and pressure,
etc. The same is the case for people and other macroscopic objects. They
are obtained by averaging over the quantum fluctuations of their
constituents, and it makes no sense to pretend otherwise. We live in a
(semi-)classical world in which quantum effects are averaged out to
insignificance for macroscopic bodies. So, if Alice and Bob are
together, or share a pair of entangled states, they are in the same
world by any reasonable definition of a "world".
Especially since there are pairs of observers who get results that do
not agree with QM (the 'mindless hulks!’).
Alice and Bob always get results which confirms QM. But when they are
space-like separated, their consciousness will only be able to
differentiate into histories which contains the correlation.
They confirm the correlations because they are always in a world in
which the quantum correlations hold. It is not a matter of consciousness
-- the correlations could be calculated mechanically from their lab book
results. Consciousness need never enter into it.
In his 2011 thinking I can only imagine that he would have seen
many-minds in much the same way as he later saw many-worlds -- if
appeal is made to the wave function to make sense of the correlations
in many-worlds, then we have to recognize that this is not a /local/
account since the wave function is not a local object.
I don’t really understand what you mean by that.
That is, in many ways, the crux of the matter. The singlet state of two
entangled spinors is a paradigm non-separable state: it cannot be
written as the product of two components, one referring exclusively to
particle 1, and the other referring exclusively to particle 2. And such
a separable two particle state is required if one is to incorporate
Einstein's concept of local realism. But the singlet cannot be written
in that way. The only state that is symmetric under rotations about the
axis joining the particles is the non-separable state:
|psi> = (|+>|-> - |->|+>)/sqrt(2).
No rotationally symmetric separable state can be constructed. This
non-separable state has no dependence on the separation between the
particles, so the same entangled state persists for arbitrary
separations. But because particle 2 is intrinsically entangled with
particle 1, any interaction with one particle necessarily affects the
other particle. Thus the non-separable state is intrinsically non-local.
If you wanted to make it local, you would have to break the entanglement
and make it into a separable state. And that is not possible in quantum
mechanics. If you have a hidden variable, or any other system, that does
this, then you do not have quantum mechanics but some other theory. You
would then have to re-establish all the well confirmed results of
quantum theory in your new theory. Not impossible, perhaps, but highly
unlikely.
I am reading your paper, which is nice and well written, but too quick
for me on both Tipler and Baylock. It helps me to better see how you
interpret the wave, and where we might differ.
Thank you. I hope that I have managed to express myself more clearly
than is often possible in emails.
It seems to me that when Alice and Bob prepare the singlet state, even
before their long distance separation, there is no sense to say that
they are still in the same world.
Of course they can be in the same world. The singlet is prepared at some
point between them. The entangled particles then separate and reach
Alice and Bob respectively. Since the particles were prepared together,
they separate in the same world in which they were entangled. They
cannot jump between disjoint worlds. So when they meet Alice and Bob (or
copies of these two from multiple possibilities) their meeting and
interacting with the entangled particles ensures that Alice and Bob are
in the same world when they make their respective measurements. If you
try to say anything other than this you are clearly just blowing smoke.
They are only because their interact and entangle and re-entangle very
quickly, but still always at light speed or slower. But even if there
is only one cm between Alice and Bob, it makes no sense to say that
they are in the same world. They might find uncorrelated results, but,
at the speed of alight, each one will only be able to talk to its
correctly correlated counterparts.
This is gibberish.
The same can clearly be said of the many-minds approach.
The wave function is not local because the entangled singlet state is
non-separable.
OK.
Non-separability means that if you interact with one part of the
state, you affect the whole state:
I am not sure you affect any state. You just discover in which branch
you are.
There are not many copies of the individuals involved in this scenario.
You are just obfuscating.
The wave only described a multiplicity of realties(available history),
and in this case, when someone, Alice say, look at something
inseparable, she got information about her branche(s), and of course
she knows that any possible future Bob will have the correlated
result. But Bob, if space-separated, might very well find a non
correlated result, which means that he localised itself in another
branch, where him too will only be able to meet his corresponding
correctly correlated Alice.
As I explained above, this is a hidden variable account that does not
work for general measurement orientations.
That is how I interpret the QM wave, or the Heisenberg matrices. I am
afraid that a “real” treatment would need a quantum theory of space
itself, but this needs a solution to the quantum gravity problem.
Maybe a deeper understanding of the nature of space-time would help us
to understand non-locality. But absent such a deeper understanding, we
are left with the fact of non-local instantaneous influences. Maudlin in
his 2011 book makes sense of this via the relativistic "flash" version
of the GRW collapse theory. That is a possibility, but I reserve
judgement. I see no problem with co-existence of non-locality and
special relativity via the "no signalling" theorems.
the state cannot be split into separate non-interacting parts, one
for each particle in the singlet.
I agree with this. But that can be interpreted by the fact that we are
ignorant in which branch we are.
No, it can't
Being in the same branch is an equivalence relation on the object with
which we can interact with, and space separation entails that the
measurement are truly uncorrelated “in the absolute”, yet all the
Alices and Bobs couples localises themselves in the branches violating
the Bell’s inequality. Alice would need to go quicker than the speed
of light to see some Bob finding an uncorrelated result, like
overpassing the decoherence time.
That is a descent into magical gibberish.
Bruce
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