On 22 Feb 2013, at 11:55, Richard Ruquist wrote:
On Fri, Feb 22, 2013 at 4:57 AM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
On 22 Feb 2013, at 04:10, Joseph Knight wrote:
Question: Why is the "derivation"* of the Born Rule in (Everett,
1957) not
considered satisfactory**?
Good question. I asked it myself very often.
*Everett shows that the amplitude-squared rule for subjective
probability
is the only measure consistent with an agreeable additivity
condition.
And that was shown by Paulette Destouches-Février some decade
before. My
study of Gleason's theorem (in Richard Hugues's book, Harvard press)
convinced me, at that time, that the Born rule follows indeed from
the
formalism + a version of comp first person indeterminacy (implicit in
Everett, I think).
Given the time made by some people to grasp that first person
indeterminacy,
or even just the notion of first person in the comp setting, maybe
the
problem relies there. Wallace is close to this, though.
**It is apparently not satisfactory because there have been
multiple later
attempts to derive the Born Rule from certain other (e.g.,
decision-theoretic) assumptions in an Everett framework (Deutsch,
Wallace).
I have not yet studied these later works so cannot yet comment on
them (but
would appreciate any remarks/opinions that Everything-listers have
to
offer).
I did study them, but I think I miss something as I think that
Everett, in
his long paper (thesis) is more convincing, especially in quantum
computing
where high dimensional Hilbert Space is required. Gleason theorem
requires
three dimension at least.
Now comp requires an arithmetical quantum logic on which "a Gleason
theorem"
should be working, and up to now, it looks like this is quite
plausible, and
then we got both the wave and the Born rule from arithmetic alone.
Bruno
http://iridia.ulb.ac.be/~marchal/
Do you get separate universes from comp alone?
We get many separate dreams. It is an open question if some
collections of sharable dreams define an unique complete physical
reality.
The laws of physics are the same for all Turing machines, as they
emerge from all computations, but they still can have non isomorphic
solutions.
My feeling is that an unique complete physical reality is not quite
plausible. I don't think this is compatible with the SWE+comp. If the
SWE is correct, then the SWE is an epistemological consequence of
comp, including the MWI; and if QM is not correct, with comp, this
could lead to multiverses but also to multi-multiverses, or multi-
multiverses, etc. Even them might be only local, without any definite
global physical reality.
If the zero of the Riemann function corresponds to the eigenvalue of
some hermitian operator, like some hope to show for solving Riemann
conjecture, reality could emerge from a quantum chaos, which would
implement a quantum universal dovetailing. To solve the mind body
problem with this would still need to extract this from the
(quantified) arithmetical hypostases. I mean this quantum chaos should
be prove the "win" the "measure competition" among all universal
systems.
Let us be clear. If computationalism is correct, we are really only at
the very start of getting the comp physics. We have only the logic of
the observable, and a tuns of open mathematical problems, which does
not interest anyone, by lack of motivation on the mind-body problem.
To use the comp-physics to do cosmology or particle physics is like
using superstring theory to do a coffee. It is the "weakness" of comp,
it leads to complex mathematics, very quickly, and cannot have direct
applications (unlike most of physics).
The main non direct but important, in my sight, application is in the
understanding that machine's theology is a science, indeed a branch of
computer science, and so with comp (usually believed even if
unconsciously) theology can be approached with the modest attitude of
science. That can help the understanding that science has not decided
between the two quite opposite conceptions of reality developed by
Plato and Aristotle.
Comp provides a lot of jobs for the futures. Even without comp,
biotechnologies will develop into theotechnologies, we might get
artificial brains because some doctor might not ask you, and just
consider it is the best treatment for you. We, here and now, might get
consistent extensions in computers build by our descendents, etc.
It is not a luxe to dig on what that could mean.
To sum up, computationalism leads to the many separate physical
universes, in any large sense of physical universes.
With a too much strict definition of physical universe, it is possible
that comp leads to just 0 universes. Just a web of dreams, defining no
global sharable physical realities.
A problem: physicists don't try to define what is a (primary or not)
physical universe.
Bruno
Richard
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