Re: MWI of relativistic QM
Title: Re: MWI of relativistic QM At 13:09 -0400 25/09/2002, Wei Dai wrote: Is there a paper or book that describes this discrete minkowski multiverse in more detail? Tim gives some interesting references. A formidable paper on discretization is "Foundations of Discrete Physics (Working Document January 1999)", by Kauffman. Click on Discrete at http://www.math.uic.edu/~kauffman/ANPA-98.ps 1Oth line from the bottom. > If you call being stuck in front of a white page working y're right. Sorry. I don't understand your difficulty. Why don't you just take your thesis and all of the posts you've written for this list, put them into some logical order, edit, and publish? Thanks for the suggestion. My "stucking" is more psychological and linked to "things of life sort of things". I don't want bore you with that. I'am just asking some patience and indulgence for my slowness Thanks for the list of prerequisites, BTW. I'm going to read Three Roads to Quantum Gravity, Quantum Logic in Algebraic Approach, and Mathematics of Modality, and get back to you. OK. Nice choice. The last two are rather technical, reading will not be enough! Don't forget to look at Ziegler web page for a nice summary of Quantum Logic. Also Ziegler makes the link with quantum probability. Not all quantum Logician are aware of the importance of linking logic and probability. Ziegler = http://lagrange.uni-paderborn.de/~ziegler/qlogic.html Miklos Redei makes the link with probability also. And also with Stalnaker Lewis approach to counterfactuals (like Joyce). Bruno
Re: MWI of relativistic QM
On Wednesday, September 25, 2002, at 10:09 AM, Wei Dai wrote: > On Tue, Sep 24, 2002 at 03:20:54PM +0200, Bruno Marchal wrote: >> 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. > > Is there a paper or book that describes this discrete minkowski > multiverse > in more detail? Several of the papers by Rafael Sorkin, Carlo Rovelli, Chris Isham, Fotini Markopoulou, John Baez, and others discuss "causal sets" as a model of spacetime. For example, picking just one of them, arXiv:gr-qc/9910005 v 1 2 October 1999 C.J. Isham, J. Butterfield, "Some Possible Roles for Topos Theory in Quantum Theory and Quantum Gravity." Here's one small part to provide some of the flavor: "By a causal set we mean a partially-ordered set P whose elements represent spacetime points in a discrete, non-continuum model, in which p <= q, with p, q elements of P, means that q lies in the causal future of p. "The set P is a natural base category for the presheaf of Hilbert spaces in which" (etc.) I talked about these issues in my article several weeks about time as a lattice of partially-ordered events. Now, whether time and space are "really" continuous or discrete (at some very small scale, presumably near the Planck scale) is not terribly important for this analysis. Just as both QM and relativity are usually involved with events (measurements, clocks, light flashes, etc.), and just as much of the traditional "causal analysis" of everyday events (a la Pearl) is of discrete, chunked events, the causal set model is very generally applicable. And again I have no choice but to recommend Lee Smolin's "Three Roads to Quantum Gravity" as a good introduction to the ideas of the authors named above. --Tim May
Re: MWI of relativistic QM
On Tue, Sep 24, 2002 at 03:20:54PM +0200, Bruno Marchal wrote: > 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. Is there a paper or book that describes this discrete minkowski multiverse in more detail? > If you call being stuck in front of a white page working y're right. Sorry. I don't understand your difficulty. Why don't you just take your thesis and all of the posts you've written for this list, put them into some logical order, edit, and publish? Thanks for the list of prerequisites, BTW. I'm going to read Three Roads to Quantum Gravity, Quantum Logic in Algebraic Approach, and Mathematics of Modality, and get back to you.
Re: MWI of relativistic QM
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 t
Re: MWI of relativistic QM
At 10:39 -0700 20/09/2002, Tim May wrote: >* Deutsch's "Fabric of Reality" is a slender book, with only the >first few chapters really making his main point (about how the >single- and double-slit experiments already "proved" the MWI >interpretation a century ago, had we known what to look for, and >that quantum computers make the point as well). You are a little bit unfair with Deutsch imo. His FOR book is only superficially slender, I would say. I think it is a courageous book. It is more philosophically rigorous than most books written by physicists ... It is also very clear, so clear that it is refutable, in particular his use of comp is incompatible with his physicalist revision of Church thesis. My opinion is that Deutsch book is a nice companion of Smolin's three roads, which, as I said once, is ambiguous on its QM interpretation. Like Tegmark, Schmidhuber or me, Deutsch is aware of the power and importance of the "everything" idea, even if its use of it is weakened by its physicalist prejudices. I share also its view on Popper. Bruno
Re: MWI of relativistic QM
Dear Wei, It seems to me that there is no need for a "relativistic" version of QM for the simple reason that the wave function is not taken to be a field over space-time. It exist in Hilbert space not in spacetime. One could even argue somewhat coherently that "spacetime" is derived from the wavefunction, e.g. each "branching path" in MWI is a trajectiory in a spacetime and we might be able to "generate" some approximation of the spacetime of relativity by arranging together those trajectories that have common histories (branch points). Just a crazy thought. ;-) Kindest regards, Stephen - Original Message - From: "Wei Dai" <[EMAIL PROTECTED]> To: "Bruno Marchal" <[EMAIL PROTECTED]> Cc: <[EMAIL PROTECTED]> Sent: Friday, September 20, 2002 1:03 PM Subject: MWI of relativistic QM > 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). > > 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? > > > 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 ;) > > I assume you're still working on the promised English paper/book. 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? > >
Re: MWI of relativistic QM
On Friday, September 20, 2002, at 10:03 AM, 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).
>
> 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?
This topic dovetails (no pun intended) on several points I've made as
well, so I'll add some comments.
* Deutsch's "Fabric of Reality" is a slender book, with only the first
few chapters really making his main point (about how the single- and
double-slit experiments already "proved" the MWI interpretation a
century ago, had we known what to look for, and that quantum computers
make the point as well). I don't recall whether he says much about
relativistic vs. nonrelativistic QM, but I'll take your word that he
says nothing. His focus is on the quantum aspects, not cosmology or
relativity or a unified theory, so this is not too surprising.
* Much more is said in a book I have recommended a couple of times
here: Lee Smolin's "Three Roads to Quantum Gravity." Also, his earlier
book, "The Life of the Cosmos."
* The idea is this:
-- conventional ("classical") QM assumes Newtonian space and time,
i.e., a universal coordinate system
-- conventional ("classical") relativity (SR and GR) assumes a
non-Newtonian, non-constant space and time, via Lorentz transforms on
a Minkowski spacetime, but it has no quantization a la QM
-- in other words, two very different spacetimes. This is sometimes
characterized as the "very small" (quantum effects) vs. the "very
large" (astrophysics), and experiments at most ranges don't produce
contradictions, as gravity effects are miniscule at the usual quantum
levels and quantum effects are miniscule at cosmological or
astrophysical scales. However, understanding black holes will almost
certainly require a unification of these two theories or outlooks. And
of course a coherent, unified theory ought not to have two radically
different views of spacetime.
* Einstein attempted to merge the two, but failed. Beginning in the
1970s, with the work of Ashtekar, Witten, Rovelli, Crane, Susskind,
Baez, and many others, progress was made toward unifying the models.
The quantum gravity program, as pursued by the several different
schools (strings and branes, spin foams, twistors, etc.), is to unify
these two fundamentally different outlooks. As of now, this hasn't
happened.
* Personally, I think there is much of interest in the "discrete at
Planck scales" relational approach.
--Tim May
