From: *smitra* <[email protected] <mailto:[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
--
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.
