From: *smitra* <[email protected] <mailto:[email protected]>>
I guess I need to explain my point a bit better, so I'm starting from
the beginning and will then address your points. We know that QM is
non-deterministic as far as measurements results are concerned, one
can ask if there exist hidden variables that would fix that problem in
a local way using local hidden variables. Bell's theorem combined with
the QM prediction (or you could invoke Aspect's experimental results
confirming the predictions of QM) rules out any such fix.
So, all that Bell's theorem implies is that QM is incompatible with
local hidden variables. This then means that measurements generate new
information. If you measure the z-component of a spin polarized in the
x-direction then after the measurement, one bit of information appears
locally at your place (Bell's theorem rules out that this bit of
information was not somehow already present locally at your place).
It is at this point where MWI differs from single World collapse
theories. In the MWI, the state evolves into a superposition where
both outcomes are realized, that superposition doesn't contain more
information than the initial state. But each member of the
superposition where there are definite measurement outcomes contain
one bit of information more than the entire superposition. So, in the
MWI, information appears due to copies of observers, analogous to what
happens in Bruno's thought experiment, instead of really new
information popping into existence physically as would be the case in
a collapse interpretation.
New information 'pops into existence' for every observer in MWI, exactly
as in a collapse model. So I don't see much significance in your point.
In case of entangled spins being measured at two space-like separated
places with identical polarizer setting, only one bit of information
will appear, but this will happen at two space-like separated places.
In collapse interpretations this is a benign but strange non-local
effect. Bertlmann's sock-type explanations don't work here because
that would require the existence of information about the measurement
results prior to the measurements already being present locally.
Bells' theorem rules that out.
Actually, Bell's theorem does not rule out a local hidden variable
account of the case for aligned polarizers. But this is not relevant for
the general case of non-aligned polarizers. In that case Alice's
measurement does not make one bit of information appear at Bob's
location -- he can still get either up or down, and there is no way to
tell which. What does change are the probabilities for these results.
And those probabilities depend on the relative orientation of the
polarizers, and that can only be known non-locally.
In the MWI things are different, because there is no new information
that appears in the global final state. What happens is that the
initial state evolves into a superposition that can be split into two
components where the observers find their measurement results. These
results are then correlated as a result of the evolution of the
wavefunction.
As I keep saying. The wave function for the non-separable state is
itself non-local. You cannot avoid non-locality by appealing to the
evolution of the wave function.
You can then say that the wavefunction has non-local properties,
therefore there is no difference between the MWI and collapse
interpretations in this respect. However, in collapse interpretation
the collapse is just an ad-hoc postulate without further explanation,
while in the MWI it happens as a result of local dynamics, the
non-local wavefunction involved here itself evolved allowing one to
trace back the source of the non-locality right to the point where the
entangled spins were created.
How does one do this trace-back? The reason that the EPR correlations
cannot be explained locally is that the relative angle of the separated
measurements cannot be accommodated in local hidden variables. Maudlin
spends quite a lot of time exploring this in his book 'Quantum
Non-Locality and Relativity'. Unless you have some means of determining
the relative orientation of the polarizers in MWI that is not present in
the single-world model, then you have not explained the correlations
locally.
While one can then still argue that MWI does have non-local aspects to
it because the branches do not split in a local way, for me what
matters is that all such issues are explained by local dynamics,
Everett thought he had abolished all forms on non-locality when he
discarded the collapse postulate. Schrödinger's concern about the
non-locality of his wave theory was about precisely this -- pass a
particle through a hole; the wave front expands spherically. But when it
meets a screen, only one point is seen -- the rest of the wave appears
to have mysteriously collapsed. Everett explains this by saying that
things split into an (infinite) number of worlds, in each of which the
spot on the screen appears in a different place. Overall there is no
collapse -- it is just that for any particular observer it appears as
though there has been because he sees only one of the infinity of spots.
This works fine for this sort of collapse. But it does not work for
entangled particles -- the collapse in that case is independent of the
separation, and depends on non-local details at both ends of the
entanglement.
while in collapse interpretations you have more problems precisely due
to the unexplained collapse. In collapse interpretations, new
information appears right at the moment of collapse and does so
non-locally in case of entangled spins. In the MWI, the branching is
only an effective picture, the exact picture does not contain any
branching. No new information appears in the global state. The
self-localization of observers within this global state has non-local
aspects to it, but there is an explanation for that that invokes only
local dynamics.
But you still have not given a local account of how this happens. Spell
out for me the local dynamics that lets the state that Bob measures
reflect the relative angle between his and Alice's polarizers. It is all
very well to appeal to the dynamics of the wave function. But those
dynamics are non-local. You really do have to to better than this. Try
writing out some equations rather that blanketing everything with
imprecise words.
Bruce
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
