Re: Quantum mechanics without quantum logic
Dear Friends, I found the seventh paragraph on page 9 to be telling: "The conditions of the Kochen-Specker theorem are not carried out in the approach described in present paper. ..." This might be the locus upon which the fallacy of the paper turns. Stephen - Original Message - From: "Bruno Marchal" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Cc: <[EMAIL PROTECTED]> Sent: Saturday, April 17, 2004 11:28 AM Subject: Re: Quantum mechanics without quantum logic > At 11:42 15/04/04 +0200, Saibal Mitra wrote: > > > > >http://arxiv.org/abs/quant-ph/0404045 > > > > > >Quantum mechanics without quantum logic > >Authors: D.A. Slavnov > >Comments: 24 pages, no figures, Latex > > > >We describe a scheme of quantum mechanics in which the Hilbert space and > >linear operators are only secondary structures of the theory. As primary > >structures we consider observables, elements of noncommutative algebra, > >and the physical states, the nonlinear functionals on this algebra, which > >associate with results of single measurement. We show that in such scheme > >the mathematical apparatus of the standard quantum mechanics does not > >contradict a hypothesis on existence of an objective local reality, a > >principle of a causality and Kolmogorovian probability theory. > > > > > To talk frankly it seems to me that Slavnov is a little bit unfair > about Quantum Logic (QL), confusing it with some Hilbert Space idolatry. > It looks still more unfair when you remember that, in the process of > writing the QL founding 1936 paper (ref in my thesis), von Neumann > wrote to Birkhoff and said: > > "I would like to make a confession which may seem immoral: I do not > believe absolutely in Hilbert space any more." (quoted at length in the > formidable book by Miklos Redei : Quantum Logic in Algebraic > Approach , Kluwer, 1998). > > And so we can say that QL has been literally born from a first skeptical > move with respect to the Hilbert space worship. And as far as I > understand Slavnov his move seems similar to von Neumann's one. > Which I think is not a bad move at all. The reason why von Neumann > has abandonned the "obvious" orthomodular lattice of the closed linear > subspaces of an (infinite dimensional) Hilbert space was that he > wanted to keep *modularity* which is closer to the distributivity (of > the 'and' and the 'or') axioms of a Boolean Algebra, ... so close that > it makes it possible to define the unique > probabilities from the "probability one" logic, that is from Quantum > Logic (there would be some universal density operator). > > I do believe this has no bearing at all with any magical trick capable > of making vanishing the other relative worlds, histories, minds, > maximal consistent extensions, possibilities ... That seems to me > the most preposterous part of Slavnov paper. > In 1939 von Neumann still invokes a "magical" > role of consciousness in his singling out a "collapsed" reality. > > That Quantum logic *can* be a formidable tools is exemplified in > my thesis where I show that if we are turing-emulable then > physics (as a science of correct prediction) is necessarily > redefined as a measure on all the "computational histories" > going through our relatively actual states. > The "all" is managed by explicit appeal to Church thesis. > And then, translating this in the language of a sound > universal (lobian) machine I extract the logic of the > probability one (from and on all the maximal consistent > extensions) and got an (arithmetical) quantum logic (AQL*) > Is it modular, orthomodular? Open problems! > > Of course modularity would help for the sequel (the derivation > of physics from arithmetics/machine 'psychology'). You can > look at the last pages of the following document for the > precise definition of the arithmetical quantum logic which I > call AQL* now but is named QuelQL* in the following document: > http://iridia.ulb.ac.be/~marchal/bxlthesis/Volume1CC/4Recapitulation.pdf > > Bruno > > http://iridia.ulb.ac.be/~marchal/ > > > > > Yahoo! Groups Sponsor -~--> > Buy Ink Cartridges or Refill Kits for your HP, Epson, Canon or Lexmark > Printer at MyInks.com. Free s/h on orders $50 or more to the US & Canada. > http://www.c1tracking.com/l.asp?cid=5511 > http://us.click.yahoo.com/mOAaAA/3exGAA/qnsNAA/pyIolB/TM > -~-> > > > Yahoo! Groups Links > > <*> To visit your group on the web, go to: > http://groups.yahoo.com/group/Fabric-of-Reality/ > > <*> To unsubscribe from this group, send an email to: > [EMAIL PROTECTED] > > <*> Your use of Yahoo! Groups is subject to: > http://docs.yahoo.com/info/terms/ > > >
Re: The difference between a human and a rock
Hal Ruhl wrote: I see nothing in the rest of your post that makes my believe there is a difference of kind between rocks and humans. I believe it is a mistake to concentrate only on the reductionist theory of the "very small", and to assume that there is nothing else interesting about systems that are larger. Theories of spacetime and matter's "unit" composition are not the be all and end all. To explain emergent system behaviour, you have to have a theory whose language is a vocabulary of various kinds of complex properties. This is because emergent systems, as one of their interesting properties, do not depend on all of the properties of their substrate. They only depend on those properties of the substrate which are essential to the interaction constraints that determine the macro behaviour of the system. Thus, in theory, you can change the system's substrate and still have the same complex system, at its relevant level of description. However, that being said, I think, Hal, that we're on a similar wavelength re. "fundamental" "info" physics. Ref. my previous everything-list posts on the subject: Riffing on Wolfram http://www.escribe.com/science/theory/m4123.html Re: The universe consists of patterns of arrangement of 0's and 1's? http://www.escribe.com/science/theory/m4174.html Re: The universe consists of patterns of arrangement of 0's and 1's? http://www.escribe.com/science/theory/m4183.html Constraints on "everything existing" http://www.escribe.com/science/theory/m4412.html Re: Constraints on "everything existing" http://www.escribe.com/science/theory/m4414.html Re: Constraints on "everything existing" http://www.escribe.com/science/theory/m4427.html Re: Running all the programs http://www.escribe.com/science/theory/m4525.html Re: 2C Mary - How minds perceive things and "not things" http://www.escribe.com/science/theory/m4534.html Re: are we in a simulation? http://www.escribe.com/science/theory/m4566.html Re: Fw: Something for Platonists http://www.escribe.com/science/theory/m4594.html Re: Why is there something instead of nothing? http://www.escribe.com/science/theory/m4896.html Re: Why is there something instead of nothing? http://www.escribe.com/science/theory/m4900.html Re: Is the universe computable? http://www.escribe.com/science/theory/m4950.html Warning, my vocab in these posts is a little informal.Go for the fundemental concepts if you can get them out of the writing. Cheers, Eric
Re:The difference between a human and a rock
Hi Eric: At 03:03 AM 4/17/2004, you wrote: How does a human differ in kind from a rock? -Well both are well modelled as being "slow processes" (i.e. localized states and events) in spacetime. - A process is a particular kind of "pattern of organization" of some subregion of spacetime. - We share being made of similar kinds of matter particles that stay close to each other in spacetime for some finite time period, and some finite spatial extent. I am trying to stay at the level of the cells. Particles and spacetime would be emergent interpretations of the activity at the cell level. "Activity" as stated in earlier posts is a consequent of the effort to construct the system only from cf-counterfactuals. Oh, but you said "how do we differ?" Well, a human roganism is a sub-unit of a longer-lived "species" pattern within an "organic emergent system eco-system" pattern. A rock does not appear to have that much complexity of form and autopoietic function. Size, duration, and complexity are not a difference of kind in my description, but rather one of degree. Neither autopoietic nor sympoietic seems to fit well as an adjective here as near as I can tell. As to reproduction dances that are rocks shed small dances [sand and clay] that under the right progression become rocks again - dances that are humans do the same. A rock is one of those kind of local spacetime patterns or systems that "doesn't have much choice about how it is." The unit of a dance is that a cell polls its nearest neighbors and the result determines its next state. While some patterns and rules may result in larger scale emergent coordinations I do not see that "choice" can emerge. The laws of physics, and the nature of the rock's components and the thermodynamics of its vicinity are such that it pretty much collects into how it's going to be at some time, then is physically constrained to stay just that way, at macro scales anyhow, for a long period of time. Of course, being a big physical process pattern subject to the laws of thermodynamics, it is, actually, changing, and usually dissipating (disorganizing), just very, very slowly. Physics is just emergent from the unit of the dance. snip Dances can shed and absorb smaller dances. This process changes dances. It can cause dances to shift towards or away from another dance that is shedding dances. It can sustain or terminate dances. I see nothing in the rest of your post that makes my believe there is a difference of kind between rocks and humans. Yours Hal
Re: Computational irreducibility and the simulability of worlds
Hal Finney wrote: How about Tegmark's idea that all mathematical structures exist, and we're living in one of them? Or does that require an elderly mathematician, a piece of parchment, an ink quill, and some scribbled lines on paper in order for us to be here? It seems to me that mathematics exists without the mathematician. And since computer science is a branch of mathematics, programs and program runs exist as well without computers. Ok, but real computers are "math with motion". You have to have the program counter touring around through the memory in order to make a narrative sense of anything "happening". Mathematics, being composed of our symbols, is an abstract "re-presentation". I think what Tegmark must be saying is that "something" exists which is amenable to description by all self-consistent mathematical theories (logical sentence sets) , and by no inconsistent theories. To me, this is just equivalent to saying that "all possible configurations of differences exist" and that any SAS that represents its environment accurately (e.g. via abstract mathematics) is constrained, by its own being part of the information structure, to only perceive self-consistent configurations of differences as existing. Self-consistency of mathematical theory, as it translates from the representation level to the represented level, just means that things "perceived" can only be one way at a time, and that's the kind of thing that a consistent mathematical theory describes.
Re: Quantum mechanics without quantum logic
At 11:42 15/04/04 +0200, Saibal Mitra wrote: http://arxiv.org/abs/quant-ph/0404045 Quantum mechanics without quantum logic Authors: D.A. Slavnov Comments: 24 pages, no figures, Latex We describe a scheme of quantum mechanics in which the Hilbert space and linear operators are only secondary structures of the theory. As primary structures we consider observables, elements of noncommutative algebra, and the physical states, the nonlinear functionals on this algebra, which associate with results of single measurement. We show that in such scheme the mathematical apparatus of the standard quantum mechanics does not contradict a hypothesis on existence of an objective local reality, a principle of a causality and Kolmogorovian probability theory. To talk frankly it seems to me that Slavnov is a little bit unfair about Quantum Logic (QL), confusing it with some Hilbert Space idolatry. It looks still more unfair when you remember that, in the process of writing the QL founding 1936 paper (ref in my thesis), von Neumann wrote to Birkhoff and said: "I would like to make a confession which may seem immoral: I do not believe absolutely in Hilbert space any more." (quoted at length in the formidable book by Miklos Redei : Quantum Logic in Algebraic Approach , Kluwer, 1998). And so we can say that QL has been literally born from a first skeptical move with respect to the Hilbert space worship. And as far as I understand Slavnov his move seems similar to von Neumann's one. Which I think is not a bad move at all. The reason why von Neumann has abandonned the "obvious" orthomodular lattice of the closed linear subspaces of an (infinite dimensional) Hilbert space was that he wanted to keep *modularity* which is closer to the distributivity (of the 'and' and the 'or') axioms of a Boolean Algebra, ... so close that it makes it possible to define the unique probabilities from the "probability one" logic, that is from Quantum Logic (there would be some universal density operator). I do believe this has no bearing at all with any magical trick capable of making vanishing the other relative worlds, histories, minds, maximal consistent extensions, possibilities ... That seems to me the most preposterous part of Slavnov paper. In 1939 von Neumann still invokes a "magical" role of consciousness in his singling out a "collapsed" reality. That Quantum logic *can* be a formidable tools is exemplified in my thesis where I show that if we are turing-emulable then physics (as a science of correct prediction) is necessarily redefined as a measure on all the "computational histories" going through our relatively actual states. The "all" is managed by explicit appeal to Church thesis. And then, translating this in the language of a sound universal (lobian) machine I extract the logic of the probability one (from and on all the maximal consistent extensions) and got an (arithmetical) quantum logic (AQL*) Is it modular, orthomodular? Open problems! Of course modularity would help for the sequel (the derivation of physics from arithmetics/machine 'psychology'). You can look at the last pages of the following document for the precise definition of the arithmetical quantum logic which I call AQL* now but is named QuelQL* in the following document: http://iridia.ulb.ac.be/~marchal/bxlthesis/Volume1CC/4Recapitulation.pdf Bruno http://iridia.ulb.ac.be/~marchal/
Re: Re:The difference between a human and a rock
Eric, an apology: I just misplaced a remark to this post of yours into my response to Eugen as a PS. Please forgive John Mikes - Original Message - From: "Eric Hawthorne" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Cc: <[EMAIL PROTECTED]> Sent: Saturday, April 17, 2004 3:03 AM Subject: Re:The difference between a human and a rock > How does a human differ in kind from a rock? > > -Well both are well modelled as being "slow processes" (i.e. localized > states and events) in spacetime. > - A process is a particular kind of "pattern of organization" of some > subregion of spacetime. > - We share being made of similar kinds of matter particles that stay > close to each other in spacetime for > some finite time period, and some finite spatial extent. > > Oh, but you said "how do we differ?" > > Well, a human roganism is a sub-unit of a longer-lived "species" pattern > within an "organic emergent system eco-system" > pattern. > A rock does not appear to have that much complexity of form and > autopoietic function. > > A rock is one of those kind of local spacetime patterns or systems that > "doesn't have much choice about how it is." > The laws of physics, and the nature of the rock's components and the > thermodynamics of its vicinity are such that it > pretty much collects into how it's going to be at some time, then is > physically constrained to stay just that way, > at macro scales anyhow, for a long period of time. Of course, being a > big physical process pattern subject to > the laws of thermodynamics, it is, actually, changing, and usually > dissipating (disorganizing), just very, very slowly. > > A human organism pattern is existing at a thermodynamic range > internally, and in a thermodynamic regime in its > environment, that allows for more "options". for how (and e.g. where) to > be (over short time scales.) Interestingly, > this makes for the presence of all kinds of other similar organic > patterns with options, and interesting behaviours > (like eating you for dinner, or infecting you and eating your cell > structure.) In other words, this thermodynamic > regime, and the particular kinds of atoms and chemical bonds in > ecosystems, make for active competition for > which should be the dominant pattern of organization of matter and > energy in the vicinity. i.e. You can't always > just be a rock, because there might be a creature with a hammer wanting > to break you down into cement. > Or you can't live for ever, as an organism, because something else wants > to re-pattern your matter and energy; > that is, the matter and energy your pattern has competed successfully to > borrow for its form for a while. > > Clear as oozing primordial subterranean sulphur-vent mud? > > Ok but here's the interesting part of the story. Because there are > "options for how to be i.e. how to hold together" > at our organic ecosystem thermodynamic regime, there is > "pattern-competition" for who is the most auto-poietic > (i.e. what forms of matter and energy collection can hold together best, > at the expense of others). > > And it turns out that life-like ecosystem patterns, species patterns, > and organism patterns win out for a time, > precisely because their main function is autopoiesis, and they > eventually, through natural selection, get very > good at it. > > And it may turn out that the way you survive best as a pattern in > spacetime, assuming you have a certain > thermodynamic range to work with, is to store inside yourself > INFORMATION about "that which is > outside yourself and nearby. i.e. about your environment. In otherwords, > pattern, if you want to live, get > out there and start RE-PRESENTING aspects of your environment WITHIN > YOURSELF (in some > partly abstract form within some aspect of your own form.) > Eventually, if you do that, simple representation > of your environment. "Ouch that hurt. I'm going to flail the other way > outa here." or > "hmmm, my complex molecules like the smell and molecular fit of YOUR > complex molecules" > will give way to complex representation within the organism of its > environment, and complex action plans > to be carried out to protect the organism (and its kin's) pattern from > nastier aspects of the environment. > So we get "Hmmm. I think that guy and his army is out to get me and > mine." "I think I will pre-emptively > strike on that other guy's country because he vaguely looks like the > first guy." Ok, bad example. > or you get "Hmmm. What an intelligent (accurate > environment-representer), capable (effective environment > modifier and pacifier), and beautiful (pattern-form-average-conformant) > woman she is. I'll ask her to marry me. > > Or something like that. > > And that's the major difference between humans and rocks. Our > thermodynamic regime necessitates that > we navigate options for our existence/non-existence as stable patterns > by representing informationally, then > navigati
Re: Computational irreducibility and the simulability of worlds
Eugen, an outsider thought to your interesting attachment: We know about two parallel worlds (wit languages?): A. the 'physos'-observable one - som call material reality (I don't), B. mathematics I extend A into all white elephant/rabbit versions we can 'talk' about. B exists in the mind of mathematicians (including simpler levels existing in simpler minds one would not call 'a mathematician'. E.g. me. The problem starts when scientists start to apply one to the other, mostly B to A, forcing connections between the parallels. It leads to omissions, unnatural conclusions, I call it reductionism into those cases where it was (successfully???) done. I know this was not what you intended. John Mikes PS to your interesting "Rock" post: that is what your human mind says. Ask the rock, you may be surprised. - J - Original Message - From: "Eugen Leitl" <[EMAIL PROTECTED]> To: "Hal Finney" <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]> Sent: Saturday, April 17, 2004 4:25 AM Subject: Re: Computational irreducibility and the simulability of worlds
Re: Computational irreducibility and the simulability of worlds
On Sat, Apr 17, 2004 at 01:03:03AM -0700, Hal Finney wrote: > How about Tegmark's idea that all mathematical structures exist, and we're > living in one of them? Or does that require an elderly mathematician, > a piece of parchment, an ink quill, and some scribbled lines on paper in > order for us to be here? That wouldn't quite do. Just simulating this planet takes a lot of hardware. Just because you can write down Navier-Stokes it doesn't mean rivulets, streams and oceans spring into being. A little more work is required for that. > It seems to me that mathematics exists without the mathematician. To me it seems the opposite is true. As long as it's an unfalsifyable prediction, there's not much point to pursue it further. > And since computer science is a branch of mathematics, programs and > program runs exist as well without computers. While I'm open to existence of a metalayer, built from information or otherwise, I'm very much opposed to mysticism. -- Eugen* Leitl http://leitl.org";>leitl __ ICBM: 48.07078, 11.61144http://www.leitl.org 8B29F6BE: 099D 78BA 2FD3 B014 B08A 7779 75B0 2443 8B29 F6BE http://moleculardevices.org http://nanomachines.net pgp0.pgp Description: PGP signature
Re: Computational irreducibility and the simulability of worlds
Eric Hawthorne writes: > So does that mean we just say "think of the substrate of the universe as > being a turing machine equivalent", > any old turing machine equivalent. Ok, but still, you have to admit that > every "easy to think of" instantiation > of a turing machine (e.g. a PC with a lot of time on its hands) is a > terribly implausible universe substrate. > For heavens sake, the PC with a lot of time on its hands presupposes > time (and space (i.e. different localities, > with notions of adjacency), in which to write the tape). Classic > chicken and egg problem. > > Does anyone know the way out of that particular conceptual pickle? How about Tegmark's idea that all mathematical structures exist, and we're living in one of them? Or does that require an elderly mathematician, a piece of parchment, an ink quill, and some scribbled lines on paper in order for us to be here? It seems to me that mathematics exists without the mathematician. And since computer science is a branch of mathematics, programs and program runs exist as well without computers. Hal Finney
Re:The difference between a human and a rock
How does a human differ in kind from a rock? -Well both are well modelled as being "slow processes" (i.e. localized states and events) in spacetime. - A process is a particular kind of "pattern of organization" of some subregion of spacetime. - We share being made of similar kinds of matter particles that stay close to each other in spacetime for some finite time period, and some finite spatial extent. Oh, but you said "how do we differ?" Well, a human roganism is a sub-unit of a longer-lived "species" pattern within an "organic emergent system eco-system" pattern. A rock does not appear to have that much complexity of form and autopoietic function. A rock is one of those kind of local spacetime patterns or systems that "doesn't have much choice about how it is." The laws of physics, and the nature of the rock's components and the thermodynamics of its vicinity are such that it pretty much collects into how it's going to be at some time, then is physically constrained to stay just that way, at macro scales anyhow, for a long period of time. Of course, being a big physical process pattern subject to the laws of thermodynamics, it is, actually, changing, and usually dissipating (disorganizing), just very, very slowly. A human organism pattern is existing at a thermodynamic range internally, and in a thermodynamic regime in its environment, that allows for more "options". for how (and e.g. where) to be (over short time scales.) Interestingly, this makes for the presence of all kinds of other similar organic patterns with options, and interesting behaviours (like eating you for dinner, or infecting you and eating your cell structure.) In other words, this thermodynamic regime, and the particular kinds of atoms and chemical bonds in ecosystems, make for active competition for which should be the dominant pattern of organization of matter and energy in the vicinity. i.e. You can't always just be a rock, because there might be a creature with a hammer wanting to break you down into cement. Or you can't live for ever, as an organism, because something else wants to re-pattern your matter and energy; that is, the matter and energy your pattern has competed successfully to borrow for its form for a while. Clear as oozing primordial subterranean sulphur-vent mud? Ok but here's the interesting part of the story. Because there are "options for how to be i.e. how to hold together" at our organic ecosystem thermodynamic regime, there is "pattern-competition" for who is the most auto-poietic (i.e. what forms of matter and energy collection can hold together best, at the expense of others). And it turns out that life-like ecosystem patterns, species patterns, and organism patterns win out for a time, precisely because their main function is autopoiesis, and they eventually, through natural selection, get very good at it. And it may turn out that the way you survive best as a pattern in spacetime, assuming you have a certain thermodynamic range to work with, is to store inside yourself INFORMATION about "that which is outside yourself and nearby. i.e. about your environment. In otherwords, pattern, if you want to live, get out there and start RE-PRESENTING aspects of your environment WITHIN YOURSELF (in some partly abstract form within some aspect of your own form.) Eventually, if you do that, simple representation of your environment. "Ouch that hurt. I'm going to flail the other way outa here." or "hmmm, my complex molecules like the smell and molecular fit of YOUR complex molecules" will give way to complex representation within the organism of its environment, and complex action plans to be carried out to protect the organism (and its kin's) pattern from nastier aspects of the environment. So we get "Hmmm. I think that guy and his army is out to get me and mine." "I think I will pre-emptively strike on that other guy's country because he vaguely looks like the first guy." Ok, bad example. or you get "Hmmm. What an intelligent (accurate environment-representer), capable (effective environment modifier and pacifier), and beautiful (pattern-form-average-conformant) woman she is. I'll ask her to marry me. Or something like that. And that's the major difference between humans and rocks. Our thermodynamic regime necessitates that we navigate options for our existence/non-existence as stable patterns by representing informationally, then navigating and affecting, our surrounding space, time, matter, and energy forms. Eric Hal Ruhl wrote: Hi Stephen: Observers: In this venue dances interact and change each other discontinuously by mutual collision or by exchanging smaller dances. How then does a human differ in kind from a rock? Should we expect them to differ in kind? Yours Hal