On 22-04-2018 04:51, Bruce Kellett wrote:
From: SMITRA <[email protected]>
On 22-04-2018 01:27, Bruce Kellett wrote:
From: SMITRA <[email protected]>
On 20-04-2018 04:54, Brent Meeker wrote:
So a measurement on one can, assuming some conserved quantity
entangling them, will have an effect on the other, even if the
all the
details of measurement and decoherence are included and the
measurement is treated as Everett does. It still zeroes out
cross
terms in the density matrix that correspond ot violation of the
conservation law and that entails changing the wave function at
remote
places.
Brent
That's then an artifact of invoking an effective collapse of the
wavefunction due to introducing the observer. The correlated two
particle state is either put in by hand or one has shown how it was
created. In the former case one is introducing non-local effects in
an ad-hoc way in a theory that only has local interactions, so
there
is then nothing to explain in that case. In the latter case, the
entangled state itself results from the local dynamics, one can put
ALice and Bob at far away locations there and wait until the two
particles arrive at their locations. The way the state vectors of
the entire system that now also includes the state vectors of Alice
and Bob themselves evolve, has no nontrivial non-local effects in
them at all.
Saibal
I think the confusion arises from a failure to distinguish between
'local interactions' and 'non-local quantum states'. In the entangled
singlet case we have a non-local state since it involves two
particles
that are correlated by angular momentum conservation no matter how
far
apart they are, or whether measurements on the separate particles are
made at time-like of space-like separations. No one has ever denied
that the interactions involved in the separate measurements on the
two
particles are all local, or that decoherence effects that entangle
the
particles with environmental degrees of freedom are all local,
unitary
interactions. Decoherence leads to the effective diagonalization of
the density matrix, and the effective separation of copies of the
experimenters that obtained different results, but this effective
collapse of the wave-function is brought about by purely local
interactions.
The usual many-worlds argument for the absence of non-local effects
points to the fact that all the interactions involved in measurement
and decoherence are purely local to argue that there is no
non-locality. But this entirely misses the fact that the original
singlet state:
|psi> = (|+>|-> - |->|+>)/sqrt(2)
is intrinsically non-local. It refers to correlations due to angular
momentum conservation that persist over arbitrary separations, and
these correlations are neither enhanced nor destroyed by any number
of
purely local interactions.
So many-worlds or many-minds interpretations of quantum theory do
not
obviate the need for non-locality: they cannot, because the basic
state that is talked about in all interpretations is non-local. The
point to be made is that in no theory, either a collapse or a
non-collapse theory, are there any non-local interactions: all
interactions in measurement and decoherence are local. But that does
not mean that what one does to one particle of the singlet does not
affect the other particle -- directly and instantaneously. It is just
that this effect is not instantiated by a local (or non-local) hidden
variable. There are no faster-than-light physical transfers of
information. That would involve a local hidden variable, and there
are
none such.
The point is that quantum mechanics is weirder that you think in
that
it is intrinsically non-local, even though all physical interactions
are necessarily local. Thinking of the 6 spatial dimensions of the
separated singlet particles as forming a single point in
configuration
space may help one to visualize this. Alternatively, one can note
that
the tensor product Hilbert space of the two spin states is
independent
of spatial separation.
Bruce
Quantum mechanics is a lot weirder w.r.t. to its non-locality aspects
in single world theories. It is there that Alice, after she makes her
measurement, has to wonder how the implied information about Bob's
measurement result popped up at his place. This is not an issue in the
MWI.
Saibal
There is no difference between collapse and no-collapse theories in
this regard. MWI does not eliminate the non-locality in the
wave-function for the singlet state. This can easily be seen by
following the unitary development of my state |psi> above through its
interactions with the measuring device, observer, and the environment.
The extra worlds in MWI just come along for the ride -- they do not
add anything of substance to the argument. All the discussion about
whether Bell's theorem is invalid for MWI because he assumed collapse,
or he assumed counterfactual definiteness, or he assumed that
measurements had only one outcome, etc, is totally irrelevant to the
issue of non-locality. It is in the original quantum state, so it is
not eliminated by simply retaining all possible measurement results.
Bruce
In the MWI the non-locality becomes a common cause effect that can be
traced back to the creation of the entangled spins. As pointed out by
Vaidman here:
https://youtu.be/jKGuGptafvo?t=1876
it's in the ordinary collapse models where there is real problem.
Saibal
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