Title: Re: MWI of relativistic QM
At 10:03 -0700 20/09/2002, Wei Dai wrote:

On Thu, Sep 05, 2002 at 12:08:39PM +0200, Bruno Marchal wrote:
> This comes from the fact that MWI is explained most of the time
> in the context of non relativistic QM (which assumes time and space).
> But this problem disappear once you take into account the
> space time structure of relativistic QM, where roughly speaking
> moment of time are handled by "parallel" universes (see Deutsch FOR).

Wei: I got Deutsch's book, but it doesn't mention relativistic QM at all. Can
you elaborate on what the MWI of relativistic QM is, or point me to
another paper or book, or give me a page number in FOR that deals with
this?


Bruno:
I mentioned Deutsch for his account of time in term of parallel universes.
I don't remember if Deutsch deduced this explicitly from relativity.
(I lend his book so I cannot verify now).
I was just doing the following caricatural reasoning:
General Relativity (GR): gravitation = space-time curvature
Quantum mechanics (QM): forces should be quantized (and unified through
symmetry/broken-symmetry)
Now GR + QM gives: space-time itself should be quantized. A MWI view of this
doesn't give many minkowski worlds, but something more like a discrete minkowski
multiverse. This should not be a problem for those who accept some
many (relative) observer-moment view. It just asks for less intuitive relations
between those observer-moments.


Bruno:
> With quantum *general* relativity, where the universe differentiate
> at the level of the space-time structure aswell, we get the
> all topological approach transforming the search of natural law
> into the search of knot invariant. I urge everyone interested
> in TOES to read the pedagogical chef d'oeuvre "KNOTS and PHYSICS"
> by Louis H Kaufmann. It is a shortcut to "standard TOES" (like
> quantum gravity approach) and the link with the self-reference
> logic approach is just a matter of ... time ;)



Wei:
I assume you're still working on the promised English paper/book.

If you call being stuck in front of a white page working y're right. Sorry.

Wei:
 Can you
give us a complete list of prerequisites now for understanding it, so we
can get started on them now? :) I.e., what books must a person read before
reading your upcoming paper/book?

This is a not so easy question due to the ambiguity of the word
"understanding". Especially for the AUDA(*) part.

  [(*) For new-comers I have made a thesis which can succinctly be described
as UDA + AUDA, where UDA is for "Universal Dovetailer Argument"---an
argument showing that the computationalist hypothesis (comp) makes physics a
branch of machine psychology---and AUDA, which is an Arithmetical translation
of the UDA, which provides the skeleton of an actual derivation of physics,
including geometry, from comp. (See my url below).]



           I--- for the UDA ---


For the UDA, no more is needed but a passive knowledge of:
1) Church thesis (to understand in what sense the universal dovetailer UD
is universal).
It is enough to read the beginning of any good computer science textbook
like Cutland 's "Computability". Cutland helps also for the
AUDA, but any good intro to universal turing machines is enough for UDA.
2) Philosophy of math. For the arithmetical realism postulate.
Mmh... Perhaps the better one is the book by Hao Wang "From Mathematics to
Philosophy", Routledge & Kegan Paul, 1974. (A little old but the best in its
genre). The book by Judson Web (ref in my thesis or paper) is still more
genuine but harder to read, especially if you don't know the German (due to many
untranslated quotes).
Rudy Rucker's "Mind Tools" and "Infinity and the Mind" are quite
profitable.
3) For the thought experiment any good science fiction book can help. See the
very nice selection by Dennett and Hofstadter "Mind's I". I guess you know it.
You must do the thought experiment by yourself and learn to distinguish
degrees of rigor in thought experiments. (Not so simple!).



           II--- for the AUDA ---


For the AUDA. I insist that the fundamental prerequisite is ... the UDA.
(Unless you are only interested in (pure) mathematics).

Jeffrey's book or any good intro to logic. Perhaps the book by Van Dalen, for
having an idea of intuitionist logic.
And of course the classical Boolos and Jeffrey (or Cutland):

- Formal Logic its scope and limits, by Richard Jeffrey (McGraw-Hill, Second
      Ed.1981).    A good elementary introduction to formal logic.
- Computability and Logic, by George Boolos and Richard Jeffrey (Cambridge
      University Press (third ed. 1989).

You know the main books: Boolos 1993 (or Smorynski 1985).
and Goldblatt 1993: Mathematics of Modality. (for two papers inside).
(Ref in my thesis).



           III--- for the comparison with physics ---

For quantum logic here is a nice site:
http://lagrange.uni-paderborn.de/~ziegler/qlogic.html

A nice book is:
"Quantum Logic in Algebraic Approach" by Miklos Redei (Kluwer Academic Press)
1998, is an excellent book on quantum logic, but you need to read no more
than 20 pages of that book to follow formally the AUDA. Perhaps just reading
the birkhoff von neumann basic 1936 paper is enough.

For the "B Modal Logic of Quantum Logic" look at:

Maria Luisa Dalla Chiaria, "Quantum Logic" 1986 (ref in my thesis). This gives
the link between the B modal logic and quantum logic. Or read the original
papers by Goldblatt (semantic anlysis of orthologic) in his "mathematics of
modality" refered above.

+ Everett papers, and good book on QM (with emphasis on conceptual problems
like d'Espagnat 1971).



           IV--- for beyond the thesis ---

Here comes the Kauffman books, which is probably at the intersection of the
road "mind--->body" and the road "body--->mind". Category theory and knot
theory should help to provide models for the weak Z and X logics. Traditional
TOES should clear the way. Thanks for Saibal pointing on a good free treatise
on fields theories.
(http://xxx.lanl.gov/abs/hep-th/9912205)


SUMMING UP:
For the UDA: Mind's I, + elementary computer science.
For the AUDA: Boolos 1993, Goldblatt 1993, Ziegler's site, and some
knowledge of the conceptual problem of QM.
For beyond: Category, Algebra, Logic, topology, etc. It looks like
knot theory collected the needed math, and perhaps knot theory by itself
is a shortcut.
The "for beyond"'s book can help for other TOE approaches including
traditional (physicalist) toe like (super)string theory, quantum gravity, ...

Bruno

-- 
http://iridia.ulb.ac.be/~marchal/



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