On 7/05/2016 2:50 am, Bruno Marchal wrote:
On 06 May 2016, at 01:13, Bruce Kellett wrote:
There is a widely cited paper by Tipler (arxiv:quant-ph/0003146v1)
that claims to show the MWI does away with non-locality.
I read it a long time ago, but I have stopped to believe that MWI can
be non-local before. If you agree that a world is a sect of
object/event close for interaction, then Jesse mazer argument directly
leads to locality.
Jesse's model may be local, but it does not reproduce the observed
correlations.
Where Alice is separated from Bob light cone, she can be in the same
world at all. There will be no action at a distance because there will
no interaction possible.
This is your basic linguistic confusion at work again. It is because the
interaction occurs between spacelike separated objects (where no local
interaction is possible) that it is said to be non-local.
The correlation will not be confirmed by them, but only by their
respective doppelganger which will inhabit their worlds soon or later.
You have yet to make this particular mantra work in the sense of a
physical model. And by a physical model I mean an account that starts
with a well-defined initial state and follows its time evolution in
terms of well-defined dynamical laws (generally expressed in the form of
differential equations).
It is instructive to go through his argument, and to see how he has
managed to deceive himself. We start with the singlet state:
|psi> = (|+>|-> - |->|+>)/sqrt(2)
and then expand the state for the second particle in a different
basis (at relative angle theta):
|+>_2 = cos(theta/2)*|+'> + sin(theta/2)*|-'>,
|->_2 = -sin(theta/2)*|+'> + cos(theta/2)*|-'>.
Substituting this into the singlet state above, we get
|psi> = -[ sin(theta/2)*|+>|+'> - cos(theta/2)*|+>|-'> +
cos(theta/2)*|->|+'> + sin(theta/2)*|->+'>]/sqrt(2),
which exactly represents the requisite four worlds, corresponding to
the (+,+'), (+,-'), (-,+'), and (-,-') possibilities for joint
results, each world weighted by the required probability.
OK, but you cannot look at them like if it was a mixture. No collapse
has ever occurred, nor will ever occur.
I have expressly said that I am working in the MWI paradigm -- I make no
appeal to collapse of any kind.
Tipler claims that this shows how the standard statistics come about
by local measurements splitting the universe into distinct worlds.
He is, of course, deluding himself, because the above calculation is
not local.
That does not make sense to me. The calculation is local. What it
depicts is a coherent whole which behave thorugh local interactions,
with the apparition of phenomenological indeterminacy and non locality
due to the fact that the observers differentiates.
The use of the relative orientation angle theta is intrinsically
non-local. That angle cannot be obtained by local means in the above
derivation. The equation for |psi> derived above shows the full coherent
wave function as evolved from the initial state according Schrödinger's
equation. There is nothing else -- no more worlds or dopplegangers than
the four explicitly shown. The observers can only differentiate into one
of these four worlds. And that is correct -- it is in agreement with
experience. But it is still non-local.
It is, in fact, nothing more that the standard quantum calculations
(with the projection postulate evident)
Yes, but the projection is only a first person (plural intra world) view.
But the above equation does not involve projection! Projection only
comes from the individuals self-locating in one of the four possible worlds.
that I gave above for the possible (+) and (-) results for Alice,
combined in the one equation. It still uses the fact that Alice's
measurement of particle 1 affects the quantum state for particle 2
(which is, by then, a large spacelike distance away).
I don't see that.
You need to do a bit more work.
Tipler utilizes the non-local nature of this change to extract theta,
the relative orientation of magnets -- a relative orientation that
can only be known by comparing orientations at A and B directly. So
Tipler's derivation is every bit as much local or non-local as the
conventional calculation -- he has not eliminated non-locality by his
trivial reworking of the derivation.
But non-locality never entered in the picture. It is only the
abstraction of the parallel states which make us feel something has
acted at the distance, but what the many Alice and Bob are doing is
just localizing themselves in the universes (first person plural view)
that they can share.
That makes no sense in terms of the physics.
Tipler's calculation is exemplary in every way as a standard quantum
calculation on this entangled state. He has merely ignored the
effects of decoherence in order to retain the full superposition.
Decoherence is only superposition contagion. It is done as sublight
speed, and differentiate the stories, providing new bits of
information to the participant. for the outer picture, it is only a
rotation in some complex space, without leading to any new bit of
information.
Quite. So self-location in the multiverse cannot add anything new. The
correlations must be there in all possible worlds because Alice and Bob
could find themselves in any of these worlds. In other words, the
correlations cannot be created by the process of self-location.
There is nothing wrong with this if you want to work in the many
worlds paradigm. His problem, as I have pointed out, is that this
standard quantum calculation is irreducibly non-local:
The problem would be if the physical get non local. "local" does not
apply to the calculation done by the observer.
The physics is non-local -- that is what the calculation above shows.
Any particular observe, of course, sees only the local environment, but
the features of that environment could be non-local: that would be shown
by the fact that no local explanation for the observations was
available, which is the case here.
The question Tipler (and you) must answer is where the angle theta in
the above calculation comes from? Theta is the angle of the relative
orientation of Alice and Bob's polarizers -- an angle chosen only
after the two entangled particles are widely separated. This angle
can only be known by having information about both polarizer angles
to hand, and these polarizers are at spacelike separation when the
angle is needed for the above clculation. The calculation therefore,
involves an essential non-locality. Doing the standard calculation in
the many worlds paradigm has not removed this non-locality.
This is the analysis that you have to rebut,
The angle theta comes from Alice choosing a measurement angle. Bob
might make a measurement, giving him a differet theta', if he is
spacelike separated from Alice. In that case both will localized
themselves in different differentiation of their environment, and they
will never discover the discrepancy between theta and theta', as both
are entangle with the corresponding doppelgangers provided by the
singlet state.
Theta is the relative angle of their separate polarizers -- it is
determined only jointly. The rest of your statement is unintelligible.
To sum up, your mistake, I think, consists in deriving a physical
mixture from the projection postulate. At no points the MWI ever
becomes a mixture. It is one wave all the time. We are just relatively
embed in it. The same with the sigma_1 complete space (computationalism).
The above argument does not depend on deriving a mixture from the
projection postulate -- one can't do that anyway because the projection
postulate is distinct from the effect of the decoherence that leads to a
mixed state. In the argument I have given, I only ever use the
superposed pure state. I have demonstrated that even to calculate that
you have to call on information that is not locally available to any
observer -- hence the necessary non-locality.
To sum up, your inability to come to terms with the clear and
straightforward argument that I have put forward appears to stems from
you have allowing your religious dogmatism, stemming from your
computationalist convictions, to cloud your rational judgement. You are
unable to rebut my argument because you are temperamentally unable to
fully come to grips with it -- you keep creating straw men out of what
I have said. Answer my actual arguments, not your own recreations.
Bruce
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