From: *Bruno Marchal* <marc...@ulb.ac.be <mailto:marc...@ulb.ac.be>>
On 19 Aug 2018, at 09:36, Bruce Kellett <bhkell...@optusnet.com.au
<mailto:bhkell...@optusnet.com.au>> wrote:
From: *Bruno Marchal* <marc...@ulb.ac.be <mailto:marc...@ulb.ac.be>>
You do seem to have got yourself into a bit of a tangle, Bruno.
What I still do not understand in your view is how can you interpret
|psi> = (|u>|d> - |d>|u>)/sqrt(2)
as a unique superposition. It seems to me you can do that because
Alice and Bob have prepared that state, but that state represents
also another superposition, like |psi> = (|u'>|d'> -
|d'>|u'>)/sqrt(2). Why would |psi> denotes a superposition of |u>|d>
and |d>|u> and not |u'>|d'> and |d'>|u’>. It seems to me that you
choose a particular base, when Everett makes clear that this would
lead to nonsense. The physical state represent by |psi> must be the
same whatever base is chosen.
Of course. When Have I ever said otherwise? Let me spell it out for
you. The basis vectors |u> and |d> are just examples -- place holders
if you like -- for whatever basis vectors are most convenient for
your purposes. Given the expression in terms of |u> and |d>, we can
always rotate to another basis by applying the formulae for the
rotation of spinors that I gave in my paper:
|u> = cos(theta/2)|u'> + sin(theta/2)|d'>,
|d> = -sin(theta/2)|u'> + cos(theta/2)|d'>.
Substitute these expressions in the above, and you will get the state
in terms of the rotated spinors:
psi = (|u>|d> - |d>|u>)/sqrt(2) = (|u'>|d'> - |d'>|u'>)/sqrt(2).
That is what is meant by rotational symmetry, and that is all there
is to it. Nothing could be simpler.
No problem with this.
Maybe you just need to apply this insight a little more carefully.
That leads to considering that psi describes not one superposition,
but many superposition. That get worse with GHZ and n-particles
state, and that is why I have often (in this list or on the FOR list
of Deutsch) explained why the multiverse is a multi-multi-multi-…
multi-verse. I don’t insist too much because more careful analysis
would require a quantum theory of space-time, and the Everett theory
will certainly needs some improvement.
|psi> does not describe just one superposition
Good. That is the key point.
You jump in too quickly with your typical misunderstanding. Read the
rest of the sentence/paragraph before you jump to conclusions.
-- by rotation the spinors we can go to any basis whatsoever. You
certainly do not get many superpositions, one for each possible
basis. Let me spell out in detail how superpositions arise in
Everettian quantum mechanics. You start with a state |psi>, which is
just a vector in the appropriate Hilbert space. The Hilbert space is
spanned by a complete set of orthonormal eigenvectors for each
operator in that space. Again, the basis is not unique, so we can
perform an arbitrary rotation in the Hilbert space to any other set
of vectors that span the space. But this is rather beside the point,
because we usually choose a basis because it is useful, not just
because it is possible. (This relates to the preferred basis problem,
which I prefer not to got into at the moment.)
Yes. My feeling is that you do introduce some preferred base.
Yes, your feelings are very much at fault here. If you thought a bit
rather than go with feelings, we might be better off. I do not introduce
a preferred basis. Where do you think I do that? You argue against a
straw man, as usual. A typical base is not a preferred base.
Given a basis, the state |psi> can be expanded in terms of these
basis vectors:
|psi> = Sum_i c_i |a_i>,
where we the basis we have chosen is the set of eigenvectors for some
operator A and labelled them by the corresponding eigenvalues. This
expansion is the basis of the superposition, and of the formation of
relative states (or parallel universes, or the many worlds of
Everett.) We operate on the vector |psi> with the operator A, which gives
A|psi> = A(Sum_i c_i|a_i>) = Sum_i c_i a_i |a_i>
where |c_i|^2 is the probability that we will be in the state
relative to the observed eigenvalue, a_i. We could continue the
operation of the Schrödinger equation to include the apparatus for
operator A, the observer, and the rest of the environment, but you
should be able to do this for yourself.
The point is that this is the only way in which superpositions can be
formed, and from those superpositions, the many worlds or relative
states of Everett develop by normal Schrödinger evolution. But you do
not have such a superposition for the different possible orientations
of eigenvectors for the singlet state.
? (That seems to contradict what you just show above).
You deliberately misunderstand me. There is no grand superposition of
possibles bases. Choose a base, then you can express a superposition.
That is all there is to it. Only one superposition for the chosen
(typical) basis.
Nor do you have an operator in some Hilbert space that picks out the
angle in which a measurement is to be made.
That is correct, but if Alice can choose her spin direction, a choice
is made on the way to partition the multiverse, or better the
multi-multiverse.
But there is no multiverse to partition unless there is a superposition
of these separate universes that make up the multiverse. But there is no
such superposition. You have just made it up.
So the "many superpositions" that you posit are entirely arbitrary,
pulled out of the air without any justification.
If she measure u, Bob get d. But is she measure u’, Bob get d’ (with
certainly, if they have decided to measure in the same base u’d’
before). To account for that, obviously maintaining locality, we must
take into account the initial uncertainty, due to psi = (|u>|d> -
|d>|u>)/sqrt(2) = (|u'>|d'> - |d'>|u'>)/sqrt(2).
You cannot assume locality when locality is the issue in question. If
the measurements are in the same direction, then Bob's direction must
rotate with Alice's. There is no prior partitioning of anything. There
is no uncertainty due to rotational symmetry. That symmetry is broken by
the choice of measurement direction. And that is a choice, not the
result of a measurement that locates the observer in some branch of a
superposition, because there is no relevant superposition.
They clearly do not form any part of standard quantum mechanics,
because the account of superpositions and Schrödinger evolution to
many worlds that I have given above is the only way in which these
can be formed in quantum mechanics.
It is also why I prefer to describe the “many-worlds” as a many
relative states, (or even many histories), and you are right, they
are not all reflecting simply the superpositions, but different
partitions of the multiverse.
You just made this up. It is not part of quantum mechanics.
When Alice choses a direction for measuring her particle’s spin, she
choose the partition, and enforced “her” Bob, that is the Bob she
can meet in the future, to belong to that partition, wth the
corresponding spin. But she could have used another direction, and
they both would be described (before the measurement), by a
different (locally) superposition, despite it describing the same state.
That is nonsense, because it does not correspond to anything that can be
derived from the Schrödinger equation acting on a state vector in
Hilbert space.
That is where you are completely wrong. This is not how the singlet
state is treated in quantum mechanics.
Everett is still ambiguous. I argue this is the way to get the closer
to Everett local relative state theory. Unfortunately Everett is
quick, even in his long text, on the EPR-Bell issue.
So you know better that Everett did, or any other advocates of many
worlds theory do? It seems from what you say that Everett didn't really
get to grips with the entangled state. He eliminated collapse for simple
states, but the entangled state defeated him. That is not surprise -- it
has defeated many. Because you can't eliminate the collapse of a
non-separable state occasioned by interaction with any part of that state.
Alice could measure the same state in a different direction simply by
rotating her basis to the new angle at which her magnet is set.
Nothing mysterious, no waving of your magical Everettian wand to
produce more superpositions from thin air.
Those superpositions exist, as you show it yourself.
They do not pre-exist. There is a difference between the superposition
of the rotated state and rotating into a pre-existing superposition.
Your error is in thinking, without any justification, that these
superpositions all exist before Alice chooses her measurement direction.
That is just nonsense.
(You were right that it is different from the position of the
electron in the orbital).
So if you can clarify your view of the MW-description of the
equality between (|u>|d> - |d>|u>)/sqrt(2) and (|u'>|d'> -
|d'>|u'>)/sqrt(2), it could be helpful.
Done above.
I don’t see it. I see two different superposition, describing the same
unique psi state, but describing different relative state according to
Alice’s choice.
But these do not exist until Alice makes her choice.
The two different superposition are supposed to give exactly the same
prediction, but this entails (by locality, I agree) that Alice and Bob
are indetermined on the many correlated worlds right at the start.
You cannot assume locality as part of your argument when locality is the
issue in question. The rest of your comment here is wrong.
It seems to me that the “many-worlds” are not dependent of the
choice of the base |u>,|d> or |u'>,|d’>. I mean, unlike Deustch
(initially) and some many-worlders, the whole multiverse has to be
the same physical object whatever base we are using.
Sure, physics has to be independent of the base. But that does not
mean that some bases are not more useful that others.
Locally yes, but that should not change the basic ontology which has
to be base independent.
Where has it been claimed otherwise?
Or that one cannot pick out a typical basis vector, or branch of the
wave superposition, to argue that anything proved in that branch, and
does not depend on the particular branch chosen, must apply equally
to every branch, and so to the superposition as a whole. This is the
basis of my proof that quantum mechanics is non-local,
Yes. I begin to see that you do accept in the MWI some FTL influence
(as opposed to FTL information transfer).
Forget FTL. You are obsessed with FTL. The non-local influence
occasioned by interacting with a non-separable state may be
instantaneous, but that means FTL only on some models of space-time. You
might have heard of the EPR = ER conjecture. That is the idea that the
entangled particles are linked by a worm hole (ER = Einstein-Rosen
bridge), so that space is bypassed in the instantaneous interaction.
There might be other models of space in which the instantaneous
connection does not involve any FTL communication. For example, the
Relativistic Flashy GRW model introduced by Tumulka and supported by
Maudlin in the 3rd edition of his book: "The essential new feature is
that if our pair of particles starts off in an entangled state, like the
singlet state, then the collapse of the wave-function associated with a
flash on one particle can change the probability distribution for the
location of flashes of the other particle, even if it happens to be at
space-like separation. So a pair of entangled "particles" in flashy
relativistic GRW can exhibit behaviour that violates Bell's inequality
for experiments at space-like separation, even though the theory only
makes use of the relativistic space-time structure in specifying its
dynamics." (p.246f)
Your horizons are too limited, Bruno.
even in the many-worlds interpretation. Bell's theorem proves
non-locality in a typical branch.
The violation of Bell’s inequality proves this, indeed. But with the
many-world, you need to favour some base to get the FTL influence.
No, you might need some particular model of space-time structure, but
that is a different thing.
That non-locality does not depend on the eigenvalue measured in that
branch (in other words, the proof is branch-independent), so
non-locality is proved for the singlet state as a whole. And since
for the singlet state, for the universal wave function as a whole.
OK. But the FTL influence associated to non-locality is based on the
choice of some base.
No, it is base-independent because it is branch-independent and applies
to the wave function as a whole. It might depend on other things, but it
does not depend on the choice of basis vectors.
Bruce
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