On 07-09-2019 13:04, Philip Thrift wrote:
On Saturday, September 7, 2019 at 4:09:27 AM UTC-5, John Clark wrote:
On Sat, Sep 7, 2019 'Brent Meeker' via Everything List
<[email protected]> wrote:
_>> Sean Carroll is on a nationwide speaking tour now evangelizing
Many Worlds. What is the predictive power of Many Worlds?_
None, unless someone can figure out how to derive Born's rule
from it...which I think is impossible.
Many Worlds predicts that the best any observer will be able to do
is make probabilistic predictions, and Gleason's theorem says that
in 3 spatial dimensions only the square of Schrodinger's wave (the
Born rule), and not the cube or anything else, can yield a
probability without inconsistencies.
John K Clark
MANY WORLDS, THE BORN RULE, AND SELF-LOCATING UNCERTAINTY
Sean M. Carroll, Charles T. Sebens
(Submitted on 30 May 2014 (v1), last revised 25 Mar 2015 (this
version, v3))
We provide a derivation of the Born Rule in the context of the Everett
(Many-Worlds) approach to quantum mechanics. Our argument is based on
the idea of self-locating uncertainty: in the period between the wave
function branching via decoherence and an observer registering the
outcome of the measurement, that observer can know the state of the
universe precisely without knowing which branch they are on. We show
that there is a uniquely rational way to apportion credence in such
cases, which leads directly to the Born Rule. Our analysis generalizes
straightforwardly to cases of combined classical and quantum
self-locating uncertainty, as in the cosmological multiverse.
This argument (the mathematical part is based on Zurek's derivation) can
be made even stronger by invoking the fact that even in principle an
observer cannot locate herself precisely in one effectively classical
World. Everything you can in principle be aware of only fixes a finite
number of physical degrees of freedom of your brain, so you're always
going to be in a superposition of not just the entire observable
universe, even your own brain state is never going to (effectively)
collapse into a definite state.
So, if you're simulated by a classical computer, the macroscopic
registers of your classical brain will be in a superposition
corresponding to slightly different data processing being carried out. A
more powerful conscious agent implemented by a much larger computer can
observe the exact state of all your registers, but he can never
communicate this to you as the computer rendering you cannot store all
that information. So, you will always be located in a superposition of
states where this information is different. And that more powerful
conscious agent will itself be in a superposition of states where its
registers are in different states.
These superpositions are entangled superpositions with the environment
that specify that if the input information from the environment where
slightly different than that the output bran state would have to be
correspondingly different. So, such a superposition then defines the
algorithm that is running. The conscious agent is then aware of the
processed data, but only to some finite resolution, he's then in a
superposition of everything that happens below that resolution and that
then Defines the algorithm that renders the consciousness.
If a conscious agent could be located in a precisely defined single
World then that leads to the problem that the state doesn't define the
algorithm that is actually running. In a purely classical picture
counterfactuals cannot be relevant, whatever the physics is makes you
conscious all that happens is that you pass from one state to another
state at some arbitrary moment that you have some conscious thought. So,
any trivial device that doesn't so any nontrivial computations that is
set up such that it will always pass through these states, such as a
recording of these states, will also be conscious.
We can avoid this paradox by taking serious that at each moment we're
algorithms that are defined by the counterfactual data processing that
fall within the region of uncertainty defined by the finite precision of
our awareness.
Saibal
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