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=0ยบ. 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.
.........
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.
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.
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.
Bruce
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