On 2/28/2022 7:14 PM, Jesse Mazer wrote:
On Mon, Feb 28, 2022 at 7:39 PM Brent Meeker <meekerbr...@gmail.com>
wrote:
On 2/28/2022 3:39 PM, Jesse Mazer wrote:
On Mon, Feb 28, 2022 at 6:12 PM Brent Meeker
<meekerbr...@gmail.com> wrote:
On 2/28/2022 1:12 PM, Jesse Mazer wrote:
Superdeterminism goes well beyond Laplacean determinism.
Determinism is just about the dynamical laws--if you know
some "initial" state of the universe at time T1, it says you
can perfectly predict the state at a later time T2 (or an
earlier time, in a time-symmetric theory). Superdeterminism
is a constraint on the initial conditions which is meant to
rule out some broad class of possible worlds that are *not*
ruled out by the dynamical laws.
In a deterministic system any given initial condition rules
out infinitely many futures.
Yes, the conditional probability P(later conditions B | initial
conditions A) is 1 for a unique value of B, 0 for every other
possible value of B. But the dynamical laws themselves don't tell
you anything about the non-conditional probability P(initial
conditions A) for different possible choices of A.
Superdeterminism adds an extra constraint which says P(initial
conditions A) is 0 for the vast majority of possible initial
conditions in the phase space, and only nonzero for a tiny
fraction with some very special characteristics.
But if the universe is deterministic it had only /*one*/ initial
condition...so of course it had special characteristics. Just as
the winning lottery ticket had a special number on it.
But if you don't know that initial condition, then absent knowledge of
some lawlike constraint on initial conditions, I think it makes sense
to treat all initial microstates consistent with the historical data
you've seen so far as equally likely in terms of the subjective
probability you assign to them (this sort of assumption is needed in
classical statistical mechanics, where to make probabilistic
predictions about an isolated system, you generally start with the
assumption that all microstates consistent with your knowledge of the
macrostate are equally likely). So even if Bell inequalities have been
consistently violated in the past, if you believe that's just a
consequence of a particular "lucky" set of initial conditions and not
the dynamical laws or a lawlike constraint on initial conditions, then
if you believe the dynamical laws are local ones you should expect the
pattern to break down in the future, since there are many more
possible initial microstates consistent with the experimental results
you've seen so far in which the pattern of Bell inequality violations
would break down and the inequalities would subsequently be respected.
I agree. And if that happens I guess it will be (weak) support for
superdeterminism.
In quantum theory, superdeterminism is invoked to allow for
the possibility that the dynamical laws are local realist
ones (of a single-world kind), so that under "generic"
initial conditions one would expect statistically to see
Bell inequalities respected (in contradiction to quantum
predictions), but superdeterminism constrains the initial
conditions to a special set
Then postulating that the initial conditions were in this set
seems like just another dynamical law; like Born's rule.
Can you elaborate on the analogy to Born's rule? Born's rule is
not a constraint on initial states.
Born's rule for measurement results is not a dynamical law either.
I would say that in the Copenhagen interpretation the experimenter's
choice about what to measure is not determined by dynamical laws, but
once the state of the detector is set, the interaction between the
detector and the quantum system being measured does obey a dynamical
law, one that says the system's wavefunction will collapse onto one of
the eigenstates of whatever variable the detector is set to measure
(the projection postulate) with probability determined by the square
of the prior amplitude on that eigenstate (Born's rule).
In any case, if you don't consider Born's rule to be any sort of true
dynamical law, were you saying it "seems like" a dynamical law in some
sense, and that the constraint on initial conditions "seems like" a
dynamical law in the same sense?
I'm pointing out it could be imitated by superdeterminism even though
it's used as a law in QM. It's analogous to computer programs; there's
really no sharp distinction between program and data.
Even if we accept in principle the idea of laws that consist of
constraints on allowable initial conditions, there is also the
argument that the mathematical formulation of such a constraint
would have to be incredibly complex in an algorithmic sense,
Why? "No hidden variable" isn't very complex.
Are you interpreting superdeterminist theories as ones where there are
no hidden variables?
No, I'm saying no hidden variables rules out superdeterminism. Since
either their are hidden variables that are sensitive to the polarization
settings, or the polarization settings are influenced by the hidden
variables. But if there are no hidden variables...no superdeterminism.
Unless superdeterminism is assumed to measurably depart from the
predictions of QM, it does require hidden variables--the idea in a
Bell test measurement involving spin measurements, for example, is
that the particle pair have hidden variables which predetermine what
spins they will have along the axes the experimenters will later
choose to measure.
that it would have to have some built-in "concept" of high-level
observers and measuring instruments so that the hidden variables
could be assigned to particle pairs in a way that anticipated the
fact that the two particles would later be measured by
instruments in a certain configuration (the orientation of
stern-gerlach devices used to measure each particle's spins, for
example).
But in a deterministic system all those things have a common
cause; their past light cones overlap.
The event of the particle pair being emitted from the source is in the
past light cone of each of the measurements, but each experimenter
could for example base their decision about what axis to measure on a
pseudorandom algorithm that took as its seed some astronomical data
from a region that's outside the past light cone of the pair emission,
That's three past light cones that must not overlap to rule out a common
cause violation of statistical independence. That means they need to be
more that 14 billion light years apart.
Brent
and also outside the past light cone of the other experimenter making
their own decision. And the hidden variables assigned to the particles
when they're emitted have to act as though they "anticipate" what
measurements will be performed on them, even if the choice of
measurements depended on information outside the past light cone of
the emission event.
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