On Tue, Dec 21, 2021 at 4:40 PM Jesse Mazer <[email protected]>
wrote:
On Mon, Dec 20, 2021 at 8:10 PM Bruce Kellett
<[email protected]> wrote:
On Tue, Dec 21, 2021 at 11:53 AM Jesse Mazer <[email protected]>
wrote:
But one of the big selling points of the MWI is to give some sort of
objective picture of reality in which "measurements" have no
distinguished role, but are simply treated using the usual rules of
quantum interactions.
At one time, that might have been a point on which to prefer MWI
over Bohr's version of the CI, but that is no longer true. Modern
collapse theories do not have to distinguish particular
"measurement" events, and do not have to assume a classical
superstructure . In modern fGRW, for example, everything can be
treated as quantum, and the theory is completely objective.
fGRW has the added advantage that it is an inherently stochastic
theory. Probability is treated as a primitive notion that is not
based on anything else. MWI struggles with the concept of
probability, and while it has to reject a frequentist basis for
probability, it cannot really supply anything else. Self-locating
uncertainty does not, in itself, serve to define probability. You
have to have some notion of a random selection from a set, and that
is not available in either the Schrodinger equation or in
self-locating uncertainty.
What does fGRW stand for?
It is short for Flash-GRW, in which the random collapse interactions
of GRW are replaced by "flashes". The point here is that this
formulation is Lorentz invariant and completely relativistic.
If it's stochastic, do you mean it's one of those theories that
involves stochastic spontaneous collapse? Such theories are usually
in principle experimentally distinguishable from QM, would that be
true of this theory as well?
In principle this collapse model is distinguishable from no-collapse
models. The experiments to detect this might be outside current
capabilities.
If you have to say "OK, I believe in the MWI plus Born rule for
measurements" with there being no dynamical definition of what
qualifies as a measurement, where the moments we call 'measurements'
are just something we feed into the theory on a
know-it-when-I-see-it basis, then this claim to objectivity is lost
and it's not clear what theoretical appeal it has over the
Copenhagen interpretation.
Personally I still lean towards some version of the MWI being true
mainly because you can come up with a toy model with MWI-style
splitting that deals with Bell style experiments in a way that
preserves locality
No you can't.
but doesn't require hidden variables (see
https://www.mdpi.com/1099-4300/21/1/87/htm ) but I see it as a sort
of work in progress rather than a complete interpretation.
They set up a contrast between realism and locality.
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
