On 07-05-2016 09:03, Bruce Kellett wrote:
On 7/05/2016 4:28 pm, Brent Meeker wrote:
On 5/6/2016 10:51 PM, smitra wrote:
On 07-05-2016 02:36, Bruce Kellett wrote:
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 wrong to invoke this angle in this way in the MWI. While it
leads to the correct answer, one has to consider that the evolution
of the state vector is still due to local dynamics. It's therefore a
trivial fact that there cannot be any non-local effects here.
The illusion of a non-local effect comes from cutting corners in
the derivation by assuming that there exists a macroscopic Alice
here with some polarizer setting and a macroscopic Bob over there
with some other polarizer setting and then we can can compute the
correlations by just applying the usual formalism. And then we make
hidden assumptions based on the classical behavior of Alice, Bob and
the polarizers as they are macroscopic. That sounds reasonable, it
also yields the correct answer but it's still wrong as a description
of the physical situation according to the MWI.
A correct MWI derivation must involve working with a wavefunction
that evolves under unitary time evolution.
But that wavefunction is a function of different points in space,
some of which are spacelike separate. The wf dynamically evolves the
probabilistic location of the singlet particles to their interaction
with the polarizers and detectors. The interaction at the polarizers
changes the wf at other locations. In the usual formalism this change
is instantaneous, i.e. spacelike. If it's not instantaneous, as Rubin
argued, then it must propagate within the forward lightcone and the
reduced wf only describes the correlation in the part of spacetime in
which the forward lightcones of Alice and Bob's measurments overlap.
Yes, there is nothing in the derivation that violates unitary
evolution. Some details are left out, certainly, but nothing of any
importance. A wave is extended over space and intrinsically non-local.
In momentum space, positions are completely undetermined, so
calculations in momentum space are the epitome of non-locality.
If you do that you're just going to re-derive the same old result,
but using a much more cumbersome formalism. But that cumbersome
formalism then does falsify your claim that the MWI is non-local.
The crucial point where your analysis is faulty is when you
invoke the angle in an ad hoc way. The angle arises from the
setting of the polarizers, we can e.g. assume that the polarizers
were set a priori to some settings and that information was known
globally. But then there is no issue with non-locality. You can
also assume that Alice and Bob decide to choose the polarizer
settings later, but then the evolution of Alice and Bob leading up
to their choices must be included in the dynamics. If we are to
assume that Alice cannot even in principle know what Bob's setting
is, then that means that the physically correct state will be a
superposition of many different polarizer settings for both Alice
and Bob.
There is no such additional superposition in the quantum formalism,
so if you are going to postulate one such, then you are talking about
some different theory, not quantum mechanics.
If you have a problem with the reduction of 4 outcomes to two outcomes,
then you need to trace back where the information implied by this
originated from. Your current argument is hiding this. In the theory
where there is no collapse that has non-local features and where there
are only local interactions, the information about the angles was either
put a priori in the initial state (you can have modeled it in the
effective Hamiltonian that describes how Alice's and Bob's spin will
interact with the polarizers), or it arose out of the dynamics itself.
In neither case does the result point to some strange non-local effect.
That doesn't follow. Suppose the polarizers are set according to
the detection or not of a photon from distant stars who are opposite
on another on the celestial sphere. Alice can see how her polarizer
is set and Bob can see his, so there's no need to postulate a
superposition; but their seeing of the settings are spacelike.
While you can project out the subspace where Alice chooses some
angle and finds some particular result and then claim that if Bob
had chose that same angle two of the four outcomes would
mysteriously have vanished, there isn't anything on Bob's side
that makes him make that same choice. Invoking that he'll do so
amounts to just planting the information that exists on Alice side
to Bob's side, that's then not a non-local effect at all.
But when the results are compared Alice and Bob will be able to
sort out which results went with which polarizer settings. That's
how the correlation is seen. No one claims that this can used to
communicate FTL. Only that the interactions are spacelike and
violate Bell's inequality.
Not only with which polarizer setting, but also from which particular
entangled pair. Alice has to have some way of knowing that a
particular result (and polarizer setting) came from the same entangled
pair as that which gave Bob's particular result with his setting.
Simply generating lots of pairs of results does not change this basic
requirement: _post hoc_ pairing to get the required statistics is
ruled out by the requirement that both measure the same entangled
pair.
Here you use single World reasoning which doesn't apply to the MWI.
Brent
If we are to assume that Bob's and Alice's settings were fixed, so
we eliminate this improper planting of information from Alice's
side to Bob's side, then you have to ask how it's possible that
Bob's polarizer setting would always come out the same way as
Alice's? Clearly you've then build this in in the dynamics so,
you've hidden a non-local correlation in the Hamiltonian that
describes the time evolution.
But Alice and Bob's settings need not be the same. You seem to be
dabbling with superdeterminism here -- claiming that the settings
cannot be freely chosen. Recent experiments that use photons from
opposite sides of the visible universe -- photons that have never
before been in causal connection -- to set polarizer settings clearly
rules out all superdeterministic theories.
No, superdeterminism will only need to be invoked in single World local
deterministic theories.
The bottom line is that a manifestly local theory cannot possibly
yield a non-local results other than via trivial common cause
effects. Fundamentally there is nothing more to this thought
experiment that handing Alice and Bob correlated playing cards.
It's just that quantum mechanics gives you a bit more room to hide
the trick.
You have clearly not understood the basic weirdness of quantum
mechanics.
I have, but it's clear that you refuse the analyze this problem properly
according to the MWI. What you do is you take the l formalism of how we
compute things in practice as "the truth" when it's not the truth
according to the MWI.
The reduction of 4 outcomes to 2 outcomes is not a non-local effect in
the MWI, because the information contained in the absence of ++ and --
outcomes did not arise in a non-local way. If you have a real collapse
then there is problem. But in the MWI all possible outcomes are
realized, and if we are to assume that Alice and Bob's polarizer
settings were predetermined then you have hidden this information in the
initial state or the effective dynamics.
Alternatively, you can let Alice and Bob do additional measurements of
quantum systems and then set the polarizer settings according to what
they find. In that case the information about the settings was not put
in the initial state but it then arises out of the dynamics. However,
you then get a superposition of all possibilities, it's only when you
choose to look at the sector where the settings were the same or
opposite settings were chosen that you get the reduction of the number
of states. But that sector is defined by what happens on both sides, so
there is no strange non-local effect here that is present in collapse
theories.
Saibal
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