On 08-05-2016 01:52, Bruce Kellett wrote:
On 8/05/2016 3:11 am, smitra wrote:
On 07-05-2016 09:03, Bruce Kellett wrote:
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.
I don't understand where you got this from. I do not have a problem
with the reduction from 4 outcomes to 2 outcomes in the case of
parallel polarizers -- it is there in the formalism: two of the terms
vanish when theta=0º. You seem to be implying that there cannot be
any non-local effects in QM because it is, by definition, a local
theory. The apparent locality of the theory is why some people have so
much trouble understanding the non-local effects that can arise in QM.
I quote the following from a recent post on another list by an
experienced physicist:
"An entangled pair of states just share the same wave function, and
the uncertainty principle is ultimately what is behind the nonlocality
of the wave function. A wave function with a spread means there is no
localization of the wave. This is even for a classical wave, which
prior to the quantum physics was not seen as a problem. Yet when that
wave was found to describe the motion of a material particle then
suddenly all types of strange issues came forth. This extended in some
ways to the quantum theory of light for entangled states of
polarization and so forth.
"The spread of a wave, which for a spherical wave front can be
considerable, and the uncertainty principle are the primary reasons
for all of these nonlocal physics."
What is being said here is related to what I said recently about
working in momentum space: in momentum space particles are completely
non-localized. Non-locality is now widely accepted as a fact of
quantum theory. It cannot be removed by definition!
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.
.........
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.
So what is the MWI "truth"? How is the standard quantum calculation
modified? Remember, that the quantum formalism is taken to be the
most complete possible formulation of the state -- if you go beyond
this formulation, by calling on additional non-visible information,
for instance, you are no longer talking about quantum mechanics but
some other theory.
There is no modification, MWI demands that all physical degrees of
freedom are included in the Schrödinger equation, if you want to
describe the physical situation in terms of macroscopic observers, you
are necessarily going to have to resort to an effective treatment of the
problem.In MWI language one introduces "branches" that describe the
sectors where the observers find different outcomes. Here one makes
hidden assumptions whose validity in theoretical arguments must always
be checked.
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.
There is no assumption that Alice and Bob's settings were
predetermined -- that is explicitly ruled out in the formulation of
the problem.
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.
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.
Saibal
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