From: *Bruno Marchal* <[email protected] <mailto:[email protected]>>
On 18 Apr 2018, at 15:45, Bruce Kellett <[email protected]
<mailto:[email protected]>> wrote:
From: *Bruno Marchal* <[email protected] <mailto:[email protected]>>
On 17 Apr 2018, at 13:52, Bruce Kellett <[email protected]
<mailto:[email protected]>> wrote
But note particularly that the spin measurement is made in the
basis chosen by the experimenter (by orienting his/her magnet).
OK.
The outcome of the measurement is + or -,
For Alice and Bob, OK.
not one of the possible infinite set of possible basis vector
orientations. The orientation is not measured, it is chose by the
experimenter. So that is one potential source of an infinite set of
worlds eliminated right away. The singlet is a superposition of two
states, + and -: it is not a superposition of possible basis vectors.
? (That is far too ambiguous).
????? It is not in the least ambiguous. The singlet state is not a
superposition of basis vectors.
?
The singlet state is the superposition of Iup>IMinus> and (Minus>Iup>.
Those are not generalized basis vectors: they are eigenfunctions of the
spin projection operator in a particular basis. The singlet state is not
a superposition of vectors from different bases.
If you think about it for a little, the formalism of QM does not
allow the state to be written in any way that could suggest that.
I don't know what Everett says in his long text, but if it is any
different from the above, then it is not standard quantum
mechanics. Deutsch is a different case. He has a very strange
notion about what constitutes different worlds in QM. Standard QM
and Everett's interpretation are very clear: different worlds arise
by the process of decoherence which diagonalizes the density
matrix. The net effect is that worlds are, by definition, non
interacting (contra Deutsch's ideas).
?
This relates to your lack of comprehension above.
Patronising !!!!!!!
Merely pointing out your apparent lack of comprehension when you fail to
appreciate the difference between the eigenvectors of a particular
operator and the free choice of a basis for Hilbert space.
Deutsch has two distinct notions of "world" in his approach. He has
the standard Everettian notion of a "relative state" corresponding to
each term in the superposition of possible measurement outcomes.
These relative states are made definite by decoherence,
Relatively. Decoherence is only entanglement (with NON-collapse).
So what?
and then correspond to different, effectively orthogonal, worlds,
each of which represents the experimenter observing one particular
result. But Deutsch also has the idea that the infinity of possible
bases for an unpolarized qubit also represents an infinity of worlds.
That is necessary, and Everett explains this well when he shows that
the choice of the base to describe the universal wave is irrelevant.
Sure, the choice of basis is irrelevant. It is just that some bases are
more useful than others. And there is no use at all in trying to use all
bases at once!
(A bit like the choice of the universal Turing formalism is irrelevant
to get the theology and the physics).
This is quite a different notion, and does not occur in Everettian
theory.
I disagree with this.
Well, you are wrong.
In this second notion of "world", the worlds remain in superposition
and continue to interfere -- there is no separation into disjoint,
non-interacting worlds. In fact, it is precisely this continued
interference of these supposed "worlds" that is the explanation for
the action of quantum computers -- which Deutsch seems to think
actually *prove* his notion of quantum "many-worlds". He is out on a
limb on this one, and few experts, even in the quantum computing
field, agree with Deutsch on this new notion of "worlds". The
essential continued interference between the different basis states
in fact means that the "worlds" remain inextricable "one world". (See
some of Scott Aaronson's comments on Deutsch and many-worlds in his
lecture notes on quantum computing.)
So when you continue to refer to an "infinity of worlds" for the
measurements on the entangled spin states, you are using a notion of
"world" that does not occur in Everett, and is inherently
controversial, if not entirely meaningless.
I use the “Herbrand” interpretation of quantum mechanics without
collapse. I mean: it is literal QM (in a sense that logicians have
made precise) without collapse up to a choice of any arbitrary base.
I don’t believe in any worlds, to be clear. It always means some
reality satisfying some formal constraints.
I think you believe in a world. How else do you go about your daily
life? Or are you like most mathematicians: believing in platonism at
work, but believing in nominalism the rest of the time?
But even if you can manufacture an infinity of universes, you
still have not shown how this removes the non-locality inherent
in the quantum formalism.
You have not shown non locality.
I have demonstrated non-locality in the Everettian context many
times. The simplest demonstration was in the timelike separation of
Alice and Bob's measurements. It is in the archives if you don't
recall the details. The argument then is that any local influence
that would explain the timelike separated measurements must also
work for spacelike separated measurements, and that is not possible.
At all time there is an infinity of “worlds”. When Alice chose her
direction, that remains true, and her measurement will tell us if
she belongs to a world with “spin” down or up, she will
automatically know that whatever Bob she will meet, will have the
corresponding results, no action at a distance here.
Again, you keep referring to this non-existent infinity of worlds —
“worlds” would be better.
a notion that has nothing to do with Everett or his interpretation of
quantum theory. "... She will automatically know that whatever Bob
she will meet, will have the corresponding results...". This is
precisely the question that you have not answered -- how does this
happen?
Because in ALL “worlds” Alice and Bob have they spin described by the
no-separable singlet state. The statistics seems non-local, due to
their ignorance of which partition of the wave function they belong to.
No, due to the fact that any any "world" in which they find themselves
the correlations indicate non-locality.
What is the particular magic that you put in the mix to ensure that
the correct correlations emerge?
Only QM, without collapse.
That is truly magical, and you have no evidence for this whatsoever.
Bruce
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