On 7/2/2021 2:43 PM, Tomas Pales wrote:
On Friday, July 2, 2021 at 2:54:19 PM UTC+2 Lawrence Crowell wrote:
The GRW interpretation states there is with any quantum wave a
fundamental phenomenon of collapse. The collapse occurs
fundamentally by a stochastic rule.
Fundamental, irreducible probability seems like an incompletely baked
concept. Mathematically/structurally, probability can be defined in
terms of pure sets, like any other mathematical/structural concept.
Pure sets (combinations of combinations of combinations etc. founded
on the empty combination) are the fundamental concept from which it is
possible, in principle, to build up any structure. MWI attempts to
define the quantum probability in terms of sets, whose most
straightforward interpretation seems to be worlds. But the problem is
that there seem to be infinitely many worlds in MWI and a system of
infinitely many objects may have different probability measures that
give different results, so it seems that the Schrodinger equation is
not sufficient to calculate probabilities even in MWI and MWI also
needs a probability measure as an additional property of the quantum
multiverse, namely such that it results in the Born rule. There have
been some claims that such a measure is the only possible one
There's only one consistent measure on a Hilbert space and that's the
Born rule, as proven by Gleason's theorem.
and as a layman I can't comment on that but as far as I know there is
no consensus among physicists on how to derive the Born rule and so it
may be a property of the quantum multiverse in which we happen to live
and other quantum multiverses may have different probability measures.
Or the Born rule might be derived with the help of another property
that emerges from a deeper theory such as quantum gravity (which
perhaps restricts the number of worlds to a finite number).
The problem is not the Born rule. The problem is to say what this
probability means in the physical interpretation. In Copenhagen it's
just that repeating the same experiment gives different results and so
the theory predicts probabilities by the Born rule. But Everett noted
that every observer gets entangled with the result and then exists in a
superposition of different observed values. He claimed this meant that
any observer would observe the Born rule probablity. But this depended
on considering the observer in one special basis of the Hilbert space
(the pointer states) and then zeroing out cross terms in the density
matrix. By what mechanism the observer or instrument gets into this
state is unclear. In Copenhagen it's just modeled by application of a
projection operator. Everett writes down the same mathematics but then
says there's a physical process described by the Schroedinger equation
that reaches this result. Critics point out that isn't any better than
Copenhagen because the crucial process of interaction is just asserted
because... well that's the way it has to work in order that the Born
rule hold and we know it must hold because it's in Hilbert space.
Brent
--
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 view this discussion on the web visit
https://groups.google.com/d/msgid/everything-list/ff23168a-cc43-6d09-a830-4fd4b90e6a4d%40verizon.net.
