On 11 Oct 2013, at 13:09, Pierz wrote:
On Friday, October 11, 2013 12:25:45 PM UTC+11, Brent wrote:
So there are infinitely many identical universes preceding a
measurement. How are these universes distinct from one another?
They aren't 'distinct'. The hypothesis is that every universe branch
contains an *uncountable* infinity of fungible (identical and
interchangeable) universes. While this seems extravagant, it
actually kind of makes more sense than the idea of a universe
"splitting" into two (where did the second universe come from?).
Instead, uncountable infinities of universes are differentiated from
one another. Quantum interference patterns arise because of the
possibility of universes merging back into one another again.
With comp too, it is best to see one consciousness differentiating
than actual splitting of "universes".
Do they divide into two infinite subsets on a binary measurement, or
do infinitely many come into existence in order that some branch-
counting measure produces the right proportion? Do you not see any
problems with assigning a measure to infinite countable subsets (are
there more even numbers that square numbers?).
The former. Deutsch goes into the problem of infinite countable sets
in great detail and shows how this is *not* a problem for these
uncountable infinities (as Russell points out)), whereas it may be a
problem for Bruno's computations - a point I've tried to argue with
Bruno, but he bamboozles my sophomoric maths with his replies. To me
it seems you can't count computations that go through a state,
because for every function f that computes a certain function, there
is also some function f1 that also computes f such that f1 = f + 1 -
1. But maybe that can be solved by counting only the functions with
the least number of steps (?).
You have to take all the programs, and all computations. Your relative
1-indeterminacy bears on all computations going through your state.
Using little programs would beg the 1-p/3-p problem.
There is an uncountable set of such computations, as they dovetail on
the reals. Just keep in mind that the UD is enough dumb to implement
the infinite iterated self-duplication, which leads to uncountably
many histories.
(Having said that, there are many ways to put probability and measure
on any set, finite, enumerable, non enumerable, etc. Sometimes people
just relinquish the "sigma-additivity" condition, and still get
something very close to a measure).
And why should we prefer this model to simply saying the Born rule
derives from a Bayesian epistemic view of QM as argued by, for
example, Chris Fuchs?
I don't know about Chris Fuchs, although isn't that just Copenhagen?
It's clear that one would need strong reasons to favour MWI with its
crazy proliferation of entities, which at first blush seems to run
against Occam's razor. However Deutsch makes a damn good fist of
explaining why we in fact have those reasons. For instance, when a
quantum computer calculates a function based on a superposition of
states, MWI can explain where these calculations are occurring - in
other universes. The computer is exploiting the possibility of
massive parallelism inherent in that infinity of universes. It is
entirely unclear how these calculations occur in the standard
interpretation. MWI also solves the problem of what happens to non-
realized measurement states once a system decoheres. And of course
it gets around the intractable difficulties of non-computable wave
"collapse". So it's a case of choose your poison: infinite universes
or conceptual incoherence. I'll take the former, even though in some
ways I'd "like" the universe (or the multiverse) better if it wasn't
that way.
Max Born was my great grandfather. I wonder what he would have made
of Everett if he'd been a bit younger. When he died in 1970, it was
still probably too out there for him to have seriously considered.
That would have been nice to know. I really love the correspondence
between Max Born and Albert Einstein. I think both would have accepted
Everett, even if with some grimaces, like François Englert and many
quantum cosmologists.
I disagree with the idea that Everett propose a new interpretation of
QM. Everett proposes a new theory, which is just Copenhagen without
the collapse. Everett himself talk about a new formulation of QM, not
a new interpretation. that is not so important, except when we begin
to use logic, which forces to be precise on what is a theory, and what
is an interpretation of a theory.
And Everett QM obeys Occam in the sense that he used less hypotheses.
Bruno
Brent
On 10/10/2013 6:11 PM, Pierz wrote:
I'm puzzled by the controversy over this issue - although given
that I'm not a physicist and my understanding comes from popular
renditions of MWI by Deutsch and others, it may be me who's missing
the point. But in my understanding of Deutsch's version of MWI,
the reason for Born probabilities lies in the fact that there is no
such thing as a "single branch". Every branch of the multiverse
contains an infinity of identical, fungible universes. When a
quantum event occurs, that set of infinite universes divides
proportionally according to Schroedinger's equation. The appearance
of probability arises, as in Bruno's comp, from multiplication of
the observer in those infinite branches. Why is this problematic?
On Saturday, October 5, 2013 2:27:18 AM UTC+10, yanniru wrote:
Foad Dizadji-Bahmani, 2013. The probability problem in Everettian
quantum mechanics persists. British Jour. Philosophy of Science
IN PRESS.
ABSTRACT. Everettian quantum mechanics (EQM) results in ‘multiple,
emergent, branching quasi-classical realities’ (Wallace [2012]).
The possible outcomes of measurement as per ‘orthodox’ quantum
mechanics are, in EQM, all instantiated. Given this metaphysics,
Everettians face the ‘probability problem’—how to make sense
of probabilities, and recover the Born Rule. To solve the
probability problem, Wallace, following Deutsch ([1999]), has
derived a quantum representation theorem. I argue that Wallace’s
solution to the probability problem is unsuccessful, as follows.
First, I examine one of the axioms of rationality used to derive
the theorem, Branching Indifference (BI). I argue that Wallace is
not successful in showing that BI is rational. While I think it is
correct to put the burden of proof on Wallace to motivate BI as an
axiom of rationality, it does not follow from his failing to do so
that BI is not rational. Thus, second, I show that there is an
alternative strategy for setting one’s credences in the face of
branching which is rational, and which violates BI. This is Branch
Counting (BC). Wallace is aware of BC, and has proffered various
arguments against it. However, third, I argue that Wallace’s
arguments against BC are unpersuasive. I conclude that the
probability problem in EQM persists.
http://www.foaddb.com/FDBCV.pdf
Publications (a Ph.D. in Philosophy, London School of Economics,
May 2012)
‘The Probability Problem in Everettian Quantum Mechanics
Persists’, British Journal for Philosophy of Science, forthcoming
‘The Aharanov Approach to Equilibrium’, Philosophy of Science,
2011 78(5): 976-988
‘Who is Afraid of Nagelian Reduction?’, Erkenntnis, 2010 73:
393-412, (with R. Frigg and S. Hartmann)
‘Confirmation and Reduction: A Bayesian Account’, Synthese,
2011 179(2): 321-338, (with R. Frigg and S. Hartmann)
His paper may be an interesting read once it comes out. Also
available in:
‘Why I am not an Everettian’, in D. Dieks and V. Karakostas
(eds): Recent Progress in Philosophy of Science: Perspectives and
Foundational Problems, 2013, (The Third European Philosophy of
Science Association Proceedings), Dordrecht: Springer
I think this list needs another discussion of the possible MWI
probability problem although it has been covered here and elsewhere
by members of this list. Previous discussions have not been
personally convincing.
Richard
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