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.
Bruce
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