On 21-12-2021 07:12, Bruce Kellett wrote:
On Tue, Dec 21, 2021 at 4:40 PM Jesse Mazer <[email protected]>
wrote:
I wasn't linking to the paper for the argument about semantics
(there
doesn't seem to be any agreed-upon definition of 'realism'
distinct
from local realism in physics, from what I've seen) but rather for
the
toy model they provide in section 5 with the experimenters being
duplicated when they try to measure the entangled particle. The
point
is that Alice is locally duplicated when she measures her
particle,
and Bob is locally duplicated when he measures his, but there is
no
need for the universe to decide which copy of Bob inhabits the
same
"world" as a given copy of Alice, or vice versa, until there's
been
time for signals limited by the speed of light to pass between
them
(or to a third observer). This is not the sort of "local realist"
theory that Bell was trying to refute (one of the implicit
assumptions
in his derivation was that each spin measurement produces exactly
one
of two possible outcomes), but the dynamics of such splitting can
be
perfectly local, and it can still be true that if you randomly
select
one of the copies of an observer in a Bell type experiment, the
probabilities that your randomly selected copy will see various
outcomes can be made to match the QM predictions that violate Bell
inequalities.
This seems to be the hand-waving way in which this is usually
argued.
I was asking for something a little more concrete.
There is a fairly simple argument that shows that many worlds
ideas
can have no role to play in the violation of the Bell
inequalities. In
other words, there is an indirect no-go theorem for the idea that
MWI
makes these experiments completely local.
The argument goes like this. Take Alice and Bob measuring spin
states
on members of entangled pairs of particles -- they are presumed to
be
distant from each other, and independent. Alice, say, measures a
sequence of particles at random polarizer orientations,
randomizing
the polarizer angle between measurements. She records her results
(up
or down) in a lab book. After N such pairs have been measured, her
lab
book contains a sequence of N 0s or 1s (for up/down), with a
record of
the relevant polarizer angle for each measurement. If MWI is
correct,
there are 2^N copies of Alice, each with a lab book containing a
similar binary sequence. Over the 2^N copies of Alice, all
possible
binary sequences are covered. Bob does the same, so he has a lab
book
with some binary sequence of 0s and 1s (and 2^N copies with
different
lab books). For each copy of Bob, and each lab book, all N
measurements were necessarily made in the same world (because
individuals cannot move between worlds).
After all measurements are complete, Alice and Bob meet and
compare
their lab books in order to calculate the correlations between
results
for different relative measurement angles. Once Alice and Bob
meet,
they are necessarily in the same world. And since they carry their
lab
books with them, the measurements made in each lab book must all
have
been made in that same, single, world. The correlations that Alice
and
Bob calculate are shown to violate the Bell inequality. (That is
experimentally verified). But this violation of the inequality
takes
place in just one world, as has been seen by the above
construction.
The alternative copies of Alice and Bob also meet to compare
results.
As before, all these meetings take place in the same worlds as all
the
relevant measurements were made. Consequently, the many-worlds
analysis for each Alice-Bob pair is exactly the same as the single
world analysis obtained if collapse is assumed. Many-worlds adds
nothing to the analysis, so MWI cannot give any alternative
explanation of the correlations. In particular, MWI cannot give a
local account.
Bruce
It is the violation of the Bell inequality in each world that is the
evidence of the existence of the other worlds.
