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. 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.
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.
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.
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.
Saibal
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