On 03-06-2017 02:10, Bruce Kellett wrote:
On 3/06/2017 9:16 am, smitra wrote:
In a single universe theory, this implies non-locality, because of the
absence of local hidden variables. If local hidden variable were to
exist then you could say that Alice and Bob where to find whatever
they found anyway only due to their local interactions with the spins
and polarizers. But with that ruled out, whatever Alice will find is
information that just popped into existence when Bob made his
measurement.
What is ruled out by Bell's theorem is that local hidden variables can
account for all possible correlations between the observations, Bell's
theorem does not rule out the possibility of a local hidden variable
explanation in special cases, like that of polarizers set at the same
angle.
Either there exists a local hidden variable theory from which QM can be
derived or such a theory doesn't exist. If we assume that a local hidden
variable theory underlies QM, then we find that regardless of the
details, it cannot reproduce QM in certain cases. Bell inequalities can
be derived for such theories that QM violates. Then, with QM confirmed
and in particular the violations of the Bell inequalities conformed, we
can then discard any local hidden variables theory.
This means that even in cases that do not involve violations of Bell
inequalities, we can still say that there are no local hidden variables
that can explain the results in those experiments, because we've
verified that there is no hidden variable theory that can reproduce QM.
Then it suffices to consider a simple case of entanglement between two
spins where in a single universe interpretation there is non-local
behavior, e.g. Alice and Bob measuring the z-components of a system of
two spin 1/2 particles in the singlet state. You may consider more
complex cases where Alice randomly chooses another direction, but I
remember from a previous discussion that this led to a disagreement
about how to treat the source of this randomness.
Ultimately all randomness has a quantum mechanical origin as pointed out
in this article:
https://arxiv.org/abs/1212.0953
There simply exists no known way to get to purely classical randomness.
In the case where both polarizers have the same setting, the fact that
Bob knows what Alice will find poses a problem for locality because
local hidden variables have been ruled out. So, what Alice will find
is random, new information will appear at her place after she measures
the spin that didn't previously exist locally. But the fact that Bob
could predict her result means that this information did exist at Bob's
place. This demonstrates the non-locality aspect of single universe
theories.
Then in the MWI, Alice is identical in the two branches, so her
measurement result is not predetermined as she is not yet located in
either of Bob's branches. Her measurement result will do that.
If we change the set-up by letting Alice choose different setting of her
polarizer to bring in the additional baggage of having to rule out
hidden variables within the same experiment so that non-locality
arguments have to be re-argued based on that, then that's not going to
add anything but confusion.
Saibal
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