From: *Bruno Marchal* <marc...@ulb.ac.be <mailto:marc...@ulb.ac.be>>
On 9 Aug 2018, at 06:55, Bruce Kellett <bhkell...@optusnet.com.au
<mailto:bhkell...@optusnet.com.au>> wrote:
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.
Due to the fact that a^2 and b^2 can be irrational number, I interpret
even any a_u_+b_d_ has involving infinities of histories possible. The
singlet is the superposition of two base vectors, I agree, but the
number of worlds is not related to the dimension of the Hilbert space.
But the number of elements in any quantum superposition is related to
the dimension of the associated Hilbert space. If you want to stay
within the bounds of more-or-less conventional quantum mechanics (that
which is taught in text books), the only way you can get your infinite
number of copies of Alice who can self-locate in some branch is to have
the branches form a quantum superposition. If it is just a matter of an
infinite number of worlds in some multiverse, then there is no coherent
superposition, and the concept of self-location in the quantum sense
loses meaning.
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.
OK. (I would not called that a hidden variable theory though, as it is
the description of the multiverse that I associate to the singlet
state). If Bob choses an arbitrary direction, the perfect correlation
is transformed into correlation leading to the violation of Bell’s
inequality.
It has to be interpreted as a hidden variable model if you are to use
the machinery of Hilbert space to form a coherent superposition within
which one can self-locate. Just as working in 2-dim Hilbert space for
the spin projections of a spin-1/2 particle, one is working with a
superposition of up-down in any basis at all. Then one self-locates in
the measurement basis by making a measurement. This is quantum physics,
after all. We are not doing classical duplications as in your H-->W/M
thought experiments.
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.
OK, but same subspace do not entail that the original Alice and Bob
will get the correlated results. It means that they will share the
correlated result only with their respective counterparts.
The original Alice and Bob are those in the same branch of the wave
function all the way along. There are no unmatched Alices or Bobs.
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.
But there is no reason that Bob and Alice will ever be able to share
those incorrect correlation result. They don’t know to which worlds
they belong.
There can be no incorrect correlation results. Did you not understand
the argument backwards from the final meeting of the pair with their lab
books. That proves that they must have been in the same branch of the
superposition all along. All possible branches involve such a meeting.
And all such meetings confirm the correct statistics. There are no loose
ends -- unmatched operators. This is actually an essential feature of
this whole scenario in the many-worlds (no collapse) picture.
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.
I will think about this. My feeling is that you are using the usual
mind/brain identity thesis.
I have no idea why you might think this. As far as I can see I am not
using any thesis at all about either the brain or the mind. All of these
measurement scenarios can be carried out entirely automatically by
appropriately programmed computers. The programs will always halt with
the correct quantum statistics.
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.
Yes.
In any single trial on an entangled pair, they can get any one of
four combinations of the possible results.
OK.
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.
Yes.
That is interesting. So you agree that the relative magnet orientation
information required to get the correct statistics is available only
non-locally? In which case, physics is proven to be non-local, and we
are done.
Besides, the above is a hidden variable model that has nothing to do
with conventional quantum mechanics.
I am not sure what you mean by conventional QM.
Quantum mechanics as taught in text books. That need not be Copenhagen
or a collapse interpretation. It can just as easily be an Everettian
many-worlds interpretation. As you might have seen, I am happy to move
freely between the two models, because I have sufficient familiarity
with quantum mechanics to be able to tell which I am using at any
particular time, or in translating results from one picture to the other.
Without collapse and FTL potential, or FTL (non-local) hidden variable
theory, how do you interpret the singlet state?
That is actually a rather strange question. How do you think I might
interpret the singlet state? I think that I have been talking about it
here for long enough for you to have worked it out. The singlet state is
a non-separable state that is symmetric under rotations about the axis
between the particles. However, that symmetry will generally be broken
by any interaction with one or other of the constituent particles. In
particular, the symmetry is broken by the imposition of a directional
magnetic field, as in a Stern-Gerlach magnet used to measure the spin
component of one of the particles in the direct defined by that external
magnetic field.
The singlet is strongly non-separable, so this external interaction with
one of the constituents is instantaneously felt by the other component
particle. That non-local influence is the essence of the
non-separability of the state -- it is a unit, and any interaction with
a part is an interaction with the whole.
Before any measurement I interpret it as a multiverse where the spin
can be in any direction, for both Alice and Bob, but in all branches
their spin are opposite. Then I use the fact that if their measure in
non “orthogonal direction”, they have only partial knowledge, and it
concerns only what they can share with their respective counterpart.
That account of the result of measurements at arbitrary relative angles
is too vague and hand-waving. If you want to convince me that you can
actually get the right answers, you will have to spell this "only
partial knowledge" out in considerably more detail, with precise
mathematics.
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.
I disagree.
The definition of a "world" that I have given is coherent and
unambiguous. You appear to want to equivocate between several different
meanings of the word.
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.
Even if that is true, it is not relevant. It is not a question of
oscillating between branches, but of ignoring to which branches their
belong before they do a measurement. I suspect again some naive
brain/mind identity link.
Again you raise this. It makes no sense to me because I am not assuming
anything about brains and/or minds. I am doing objective physics.
(Note that even Everett is ambiguous on this, and some of its
motivation consists in assuring that brain-mind identity link. That
cannot work with mechanism, and eventually we need to take mechanism
into account.
Whether or not anything can work with mechanism is entirely irrelevant
to this discussion. We are discussing quantum mechanics, not your
"mechanism".
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”.
I do not think such notion of worlds makes sense, already with just
Mechanism. I suspect we have quite different notion of worlds.
That is possible. I work in quantum theory, whether in Everett's
many-worlds or Copenhagen collapse. Everett, after all, is just
Copenhagen with collapse. Both are based on the Schrödinger equation.
One just retains the non-observed branches that the other disregards.
There is actually very little difference between them, since both give
the same predictions for all observable results. Why get so hung up on
the differences?
I would even prefer to abandon that term, and use the notion of
consistent histories instead, but of course that too should be handle
with caution. I don’t think there is a viable notion of quasi
classical world in any non-collapse theory
I disagree. There has been a lot of work on the transition from the
quantum to the classical worlds. After all, our experience is of the
classical world, and it is that experience that we have to explain via
its quantum substrate. It is not a viable option just to claim that the
classical does not exist.
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.
Right.
And such a separable two particle state is required if one is to
incorporate Einstein's concept of local realism.
I disagree here.
I don't think that this is a debatable point. Einstein's concept of
classical realism is enunciated by people such as Bob Griffiths in
exactly these terms, as well as by almost all other authors I can think of.
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.
I agree.
This non-separable state has no dependence on the separation between
the particles,
I agree. But before any measurement is done, the couple Bob and Alice
belong to each possible situation, including possible non correlated
one, in which case, they will never be able to meet again: only to
meet their counterparts.
That is the point at which your account becomes hopelessly confused.
There are no couples of Alice and Bob that never meet again. You confuse
a pre-existing ensemble of experimenters with the actual case of a
possible superposition in a hidden variable theory. Quantum physics can
cope with superpositions, but it does not have to assume infinite
ensembles of anything. The Schrödinger equation does not require a
pre-existing ensemble in order to get many-worlds (or relative state
branches).
so the same entangled state persists for arbitrary separations.
From the point of view of all observers. OK. That is a relative notion.
But because particle 2 is intrinsically entangled with particle 1,
any interaction with one particle necessarily affects the other
particle.
I don’t see why you say this, except that you talk like if Bob and
Alice where related to the same branch, which makes non sense to me if
they are space separated.
I think you need to think some more about this. Two people can be in the
same branch if they are time-like separated, *and* if they are
space-like separated: Just meet up and walk a few paces away from each
other! Neither party has moved to a different world, but they are now
space-like separated.
Thus the non-separable state is intrinsically non-local.
Yes, but without the need to the FTL if you use the only available
mind-brain identity link possible with Mechanism (in cognitive science).
You are clearly obsessed with FTL and the mind-brain link. Forget these.
They are strictly irrelevant to the discussion.
If you wanted to make it local, you would have to break the
entanglement and make it into a separable state.
That cannot work. That violate QM, but that is not needed, it is
simpler to abandon the brain mind identity link.
No, you cannot make the singlet separable, and separability is the
essence of locality. There is no brain-mind identity link here. Perhaps
only in your mind, but that is not the issue at hand.
Alice and Bob always belong to infinities of histories, and totally or
partially localise themselves in the branch of the universal wave.
Start with one Bob and one Alice. If you say this is impossible, then
you are not doing quantum mechanics, but some weird theory of your own
devising. Ostensive definitions of these two people will do just fine.
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.
You are still quick, but I think we differ, not on QM, but on the
theory of mind used in the non collapse theory. I think we might
progress on where we depart.
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.
Alice ((|+>|-> - |->|+>)/sqrt(2)) = Alice((|+'>|-'> -
|-'>|+'>)/sqrt(2)), so I don’t know which worlds you are talking about.
Your equation is true only if Alice does not interact with the singlet.
Any interaction breaks the symmetry. Or do you still not understand this?
They know only that whatever their measure, will be correlated with
what the other is measuring, but the “other’ refer to infinities of
“Bob” before any measurement is done.
Not necessarily, if you are doing conventional quantum physics. (And
don't raise your usual point that you don't know what conventional
physics is!)
The singlet is prepared at some point between them. The entangled
particles then separate and reach Alice and Bob respectively.
That makes no sense to me. You talk like if the singlet state fixes
the base{ |+>, |->}.
I do no such thing. The two particles of the singlet can separate --
that is the whole point of this set-up. If nothing interacts with the
singlet, it is preserved in its full rotational symmetry up to infinite
separations.
I take into account a possible phase factor, which makes the
multiverse rotationally invariant,
The multiverse is not rotationally invariant because it contain
non-symmetric objects -- such as trees, rocks, and people.
and this remains true forever in the non collapse view. The breaking
of the rotational invariance below only to the relative person views,
like decoherence.
No, the multiverse is not symmetric at the start, nor at any subsequent
time. It is only the isolated singlet state that is symmetric. And that
is an objective fact, not dependent on any relative person view.
Measurement objectively breaks this invariance.
Since the particles were prepared together, they separate in the same
world in which they were entangled.
As long as no-one look at the particles, I don’t see how you select
the worlds.
As I say below, I can talk of the world to which they belong because
they cannot jump to another world.
They cannot jump between disjoint worlds.
They both just belongs to infinity of “worlds".
That is not the concept of "world" that is applicable here. As usual,
you equivocate on the meaning of the term in order to confuse the
argument in your attempt to prove me wrong. You are not going to
succeed, because I am not wrong on this.
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.
Well, I understand this will re-introduce FTL. I see no QM reason to
interpret the singlet state in the way you do.
Then you do not understand quantum mechanics well enough. You are mixing
in too much of your own "mechanism", which is simply confusing you.
[deleting a lot of repetitive stuff...]
So, just tell me how you interpret the singlet state without singling
a base out of all possible base. That should be possible in the
non-collapse case.
I think I have already done this in sufficient detail -- in both
collapse and non-collapse interpretations -- to convince even the most
committed skeptic.
Bruce
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