On 5/8/2016 10:17 PM, smitra wrote:
On 09-05-2016 03:40, Bruce Kellett wrote:
On 9/05/2016 2:58 am, smitra wrote:
On 08-05-2016 01:52, Bruce Kellett wrote:
The set-up of the experiment belies the second part of your comment.
The information about the angles was not in the initial state. Sure,
the dynamics of the interaction between the particles and the
polarizer is local, and the polarizer angle is also set locally, but
the entangled state that interacts with the polarizer is itself not
local -- it is spread out in space. It is because the original
entangled state is spread out that the polarizers at each end react in
tandem -- giving rise to the non-locality. Interactions in this are
all local, the non-locality arises from the fact that the singlet
state itself is not localized.
Yes, but that's again a trivial non-local effect as the entangled
spins were created locally in the past. In the MWI this only gives
rise to non-local effects that are trivial common cause effects,
unlike in single World interpretations.
It is not a common cause effect. The singlet state is, but the
polarizer setting of A and B are independently and freely chosen after
the particles are widely separated. There is no common cause for this.
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,
Superposition of all which possibilities? I imagine that what you are
saying is that if the setting is chosen according to the outcome of
some other quantum event, then all possible outcomes of that event are
realized in different branches of a superposition, or in different
worlds. This does not actually help you. Remember that each of the
worlds in which these different settings obtain also contains a copy
of the same particle that is part of the entangled pair (Alice
measured the other part). So in each branch of your new superposition,
the same state is measured in some direction. Whichever branch Bob
then finds himself in, he still has eventually to communicate with
Alice. And all the Bob's in this picture have their own particular
theta and |+> or |-> result. The multiplication of possibilities for
Bob has not removed the problem of how this theta is determined for
each copy. The essential non-locality remains.
The relative angle theta is not determined for each copy separately,
each branch of Alice contains all the branches of Bob where Bob
chooses some angle and vice versa. The relative angle is only going
to be determined later when Alice and Bob communicate, it's only
then that Alice and Bob get localized into branches where the
relative angle is determined.
This additional superposition that you are invoking is actually
irrelevant. It is quite common in physics to deal with such
superpositions by considering just one typical member of the
superposition and performing the calculation for that particular case.
The general superposed case can be added back later if required, but
it does not add anything new.
The paradigm illustration of this is in particle physics. Because of
the uncertainty principle, a particle is effectively never in an
eigenstate of either position or momentum -- it is typically a wave
packet, in which the spreads over various position and momentum
eigenstates are related by a Fourier transform. In order to calculate
scattering probability, for example, one works in momentum space by
choice since conservation of energy and momentum give considerable
kinematic simplifications. But one does not have to do the calculation
for every momentum in the superposition constituting the original wave
packet: one chooses a typical momentum and works with that eigenstate
alone. If one wants to recreate the packet effect, a simple
integration over the momentum distribution is all that is required.
So introducing a multiplicity of copies of Bob, each with its own
measurement angle, is a red herring. One need consider only one
typical orientation, because in the final analysis, there is only one
polarizer setting for Bob that has to be compared with Alice's
polarizer setting. The important point remains the same -- the
settings for both Alice and Bob are chose and set classically by
decoherence long before they ever meet up again. So the relative angle
is not determined only when their future light cones overlap -- that
relative angle was set when they were at a spacelike separation.
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.
The reduction from four to two states has never been the problem --
it is the origin of the probabilities for any particular combination
of results that has to be explained. And you have not come near to
achieving a local explanation for this.
Probabilities are assumed to be given by the Born rule, whether it
can be derived is a controversial issue. I think the source of the
problem is that you don't consider the step where Alice communicates
with Bob as a measurement of Bob's setting. In the MWI this is an
essential step that effectively splits up Alice further into
different branches and this has a non-trivial probability
distribution. And there is nothing non-local about this step.
I dispute the idea that this exchange of information when Alice and
Bob meet is the same as a further quantum measurement -- it is simply
a mutual confirmation of settings and results that have already been
rendered effectively classical by decoherence. In fact, this claim
here contradicts your earlier statement that "each branch of Alice
contains all the branches of Bob where Bob chooses some angle and vice
versa".
There is no specific quantum operator that leads to a new result in
operation when Alice and Bob meet -- there is simply an exchange of
information that confirms results that have already been obtained.
Schrödinger's cat does not die when we open the box to obtain
information -- it was dead (or still alive) long before the opening
since, as a hot macroscopic object, decoherence had set the outcome
firmly in place long before. It is exactly the same here -- when Alice
and Bob compare results, nothing new is created. The relative
orientation angle was set long before.
The idea that Alice splits further into different branches according
to Bob's results only after their respective light cones overlap is an
interpretive gloss on the theory (which, as already pointed out, you
do not apply consistently) -- it is not there in the mathematics.
Alice and Bob are in the same world even at spacelike separations.
This must be the case, or else my feet would be in a different world
from my head at every single instant of time. So Bob and Alice
separate in the same world. When they perform their measurements there
is a Bob in each world created by Alice's results, and an Alice in
every world created by Bob's results. The fact that neither Alice nor
Bob do not know the other's result does not mean that there are no
such results. Are there separate worlds in which these results are
combined? It doesn't really matter, because anything that can be seen
when information is exchanged is already set: the exchange of
information is like opening the box -- the cat is already either alive
or dead, opening the box does not change that. So Alice and Bob
talking to each other does not change anything either. The results are
already present in the universal wave function -- talk of splitting
into worlds is irrelevant to the universal wave function and the
unitary dynamics. So the fact that A does not know B's results at some
time is irrelevant -- the results are already there. The question of
who knows what is not a relevant question for the universal wave
function. And the universal wave function takes account of the unity
of the singlet state and the reality of non-local effects.
And this is the core of the disagreement, you say that the results are
already there, but in the MWI this is false. In the MWI the cat is not
either dead or alive before you open the box, the superposition has
become entangled with the environment, but both branches are relevant
until you get to know the result.
And ONLY you? What about Wigner's friend looking in first? And what
makes the interference pattern disappear in a Young's slit experiment
with hot Buckyballs; even though no one (except the walls) detects the
IR photons? I think at some point you must either accept that the
environment can complete a measurement and create a classical world, OR
take a QBist approach that the wf is epistemic and specific to individuals.
Brent
If you find a dead cat then that does not mean that this outcome was
predetermined.
See also this article:
http://arxiv.org/abs/1212.0953
where it is claimed that all real world probabilities arise from
quantum mechanics, e.g. a coin throw experiment amounts to a quantum
measurement.
Saibal
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