On 5/6/2016 10:51 PM, smitra wrote:
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.
But that wavefunction is a function of different points in space, some
of which are spacelike separate. The wf dynamically evolves the
probabilistic location of the singlet particles to their interaction
with the polarizers and detectors. The interaction at the polarizers
changes the wf at other locations. In the usual formalism this change
is instantaneous, i.e. spacelike. If it's not instantaneous, as Rubin
argued, then it must propagate within the forward lightcone and the
reduced wf only describes the correlation in the part of spacetime in
which the forward lightcones of Alice and Bob's measurments overlap.
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.
That doesn't follow. Suppose the polarizers are set according to the
detection or not of a photon from distant stars who are opposite on
another on the celestial sphere. Alice can see how her polarizer is set
and Bob can see his, so there's no need to postulate a superposition;
but their seeing of the settings are spacelike.
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.
But when the results are compared Alice and Bob will be able to sort out
which results went with which polarizer settings. That's how the
correlation is seen. No one claims that this can used to communicate
FTL. Only that the interactions are spacelike and violate Bell's
inequality.
Brent
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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