Re: Many Fermis Interpretation Paradox -- So why aren't they here?
At 9:36 -0700 1/10/2002, Tim May wrote: MWI looks, then, like just another variant of modal realism. To wit, there IS a universe in which unicorns exist, and another in which Germany won the Second World War, but these universes are forever and completely out of touch with us. Not quite due to possible interferences. We do have empirical evidences for those worlds imo. (if only the two slits + Bell or better GHZ) BTW, Tim, I am discovering n-categories. Quite interesting. John Baez has written good papers on that, like his categorification paper. Have you read those stuff. Could be useful for the search of coherence condition in many world/observer realities ... I've been reading Baez for a while. An excellent teacher. I hear he's working on a book on n-categories. And Baez and my namesake, J. Peter May--unrelated to me, are leading a consortium to research n-categories more deeply. I confess that I have only vague ideas what they aresort of generalizations of natural transformations, I sense. A very natural generalisation (!). Just replace the hom Sets by hom Categories. In which you can again replace the hom sets by hom categories What is intriguing is the existence of coherence conditions making those constructions apparently very genuine for many stuff from quantum field theories. (I'm still studying categories at a more basic level, having jumped ahead to other areas, as is my wont.) His From Categories to Feynman Diagrams (co-authored with James Dolan) and several of his related papers are good introductions. Thanks. I didn't see this one. Very nice. http://arxiv.org/abs/math.QA/0004133 Chris Isham is also very good on drawing the connections between conventional quantum mechanics (i.e., stuff in the lab, not necessarily quantum gravity or quantum cosmology) and category/topos theory. (In particular, the collapse of the wave function and measurement looks like a subobject classifier, or, put another way, the usual transition from neither true nor false in a Heyting algebra to the one or the other we _always_ see once there is any chance to observe/measure/decide. That is, Heyting -- Boolean is what the mystery of QM centers around. Boolean or Heyting Toposes or cartesian closed categories have exponentials. They describes subjects (first or plural). They are distributive categories. You always seem to forget the non distributive categories (nicely introduced in Lawvere Shanuel book), which are akin to linear and quantum logic, and quantum algebra. Technically linearity seems to be a consequence of the non distributivity, I'm not sure I really grasp the idea yet. (I am intrigued to find that Jeffrey Bub, in his Interpreting the Quantum World, 1997, makes central use of possible worlds, lattices, and such. While he does not explicitly mention Heyting algebras, the connection is close, and is implicit in the math. Had I encountered this approach when I was studying QM, I might have pursued it as a career. Instead, I was bored out of my mind solving partial differential equations for wave functions inside boxes. Ugh.) I'm reading Graham Priest's An Introduction to Non-Classical Logic, 2001, which covers various modal logics, conditional logics, intuitionist logic, many-valued logics, and more (first degree entailment, relevant logic, etc.). I should read it. One day I will make a comment about its use of Godel in his book In contradiction. The tableaux approach is new to me. They look like the trees of Smullyan, and hence like semilattices. I have used the smullyan trees for the G and Co. theorem provers. The tableaux structure reflects in some way the Kripke structure. Posets appears with S4-like modal logic. You should study Gentzen presentation of logic which are naturally related to categories. An indigest but brilliant introduction to many (intuitionnist) logics is the North-Holland logic book by Szabo: Algebra of proofs. To bad he miss the braided monoidal categories ... For a categorician, knots theory is a branch of logic. (I'm also reading Davey and Priestley's Introduction to Lattices and Order, along with parts of Birkhoff's classic, and the lattice/poset approach continues to appeal to me greatly. Nice. They have chapters on the non distributive order structures. It's a vantage point which makes all of this heretofore-boring-to-me logic stuff look terribly interesting. I'm viewing most programs/trees/refinements/tableaux as branching worlds, as possible worlds (a la Kripke), to be further branched or discarded. Hence my focus on MWI and Everything remains more on the mathematics. (I just ordered my own copy of Goldblatt's Mathematics of Modality.) Possible worlds, something I only encountered in any form (besides Borges, Everett, parallel universes sorts of references) in the past several years, is my real touchstone. And, more mundanely, I think it applies to cryptography and money. I had a
Modal Realism vs. MWI
On Friday, October 4, 2002, at 09:13 AM, Bruno Marchal wrote: At 9:36 -0700 1/10/2002, Tim May wrote: MWI looks, then, like just another variant of modal realism. To wit, there IS a universe in which unicorns exist, and another in which Germany won the Second World War, but these universes are forever and completely out of touch with us. Not quite due to possible interferences. We do have empirical evidences for those worlds imo. (if only the two slits + Bell or better GHZ) While I find Deutsch fairly persuasive, the verdict is of course not yet in whether MWI is the correct interpretation. The double slit results had a traditional wave mechanics interpretation 75 years ago (wave-particle duality), and this remains a viable interpretation even today. (I'm not talking about popularity, either on this list or in the overall community, just technical viability.) However, I take your point that full Lewis-Stalnaker-D. Lewis modal realism is more disjoint than the less disjoint (initial interference of branching worlds) MWI. In terms of topology, one might say full modal realism is the discrete (perhaps Zariski) topology, while MWI has more notions of closeness, overlap, etc. (I think this could be worked out, but I haven't.) Certainly after a time interval where decoherence occurs, the interaction between macroscopically different worlds is essentially zero. So, I will amend my earlier statement to read: After the very early, entangled period, MWI looks, then, like just another variant of modal realism. To wit, there IS a universe in which unicorns exist, and another in which Germany won the Second World War, but these universes are forever and completely out of touch with us. And since the time of entanglement/coherence is small for most systems, most worlds in MWI are as far apart as modal realism worlds are. (Digression: I wonder what kind of work has been done on _evolution_ in topology, e.g., the transition of systems from overlapping open sets to the discrete topology? Looks like nucleation and growth out of a continuous medium, or formation of tree structures, perhaps.) A very natural generalisation (!). Just replace the hom Sets by hom Categories. In which you can again replace the hom sets by hom categories What is intriguing is the existence of coherence conditions making those constructions apparently very genuine for many stuff from quantum field theories. Baez (IIRC) has an anecdote about talking with a noted quantum field theorist at a conference. The theorist was highly skeptical of generalized abstract nonsense (i.e., category theory). Baez told him about some of the developments and the theorist went off to sleep on it. The next morning he buttonholed Baez and said Braided monoidal categories are really cool (I'm paraphrasing from memory). I have used the smullyan trees for the G and Co. theorem provers. The tableaux structure reflects in some way the Kripke structure. Posets appears with S4-like modal logic. You should study Gentzen presentation of logic which are naturally related to categories. An indigest but brilliant introduction to many (intuitionnist) logics is the North-Holland logic book by Szabo: Algebra of proofs. To bad he miss the braided monoidal categories ... For a categorician, knots theory is a branch of logic. I haven't gotten to knots yet, except for a look a few years ago at the Vaughan Jones stuff on classifications of knots (more related to string theory, which I did a little bit of reading on). Gentzen is referred to, of course, in the books on logic I'm reading, but I'm still absorbing the more basic stuff. Possible worlds, something I only encountered in any form (besides Borges, Everett, parallel universes sorts of references) in the past several years, is my real touchstone. And, more mundanely, I think it applies to cryptography and money. I had a meeting/party at my house a few weeks ago with about 50 people in attendance (gulp!). We had a series of very short presentations. I gave a very rushed 10-minute introduction to intuitionistic logic, mainly focused on my time as a poset, a lattice example, citing the natural way in which not-not A is not necessarily the same as A. If the past of an event is A, then not-A is its future. But the not-future is larger than the original past, as incomparable (in the poset/trichotomy sense) events influence the future. Or, put in relatitivity/cosmology terms, which many people are more familiar with, ironically, events outside the light cone of the present figure into the future. So the natural causal structure of spacetime is intuitionistic, a Brouwerian lattice. Very plausible. But be careful of the solipsist move here. Unless I miss something, like a universal first person may be, I really don't know. I'm not following you here. If you're commenting on my it applies to cryptography and money, we
Re: Romeo and Juliet and QS
Bruno Marchal wrote: At 23:53 -0700 27/09/2002, George Levy wrote: Here is a thought experiment illustrating a paradox involving the first and third person point of views. Romeo and Juliet, being very unhappy with their families, the Montague and the Capulet, decide to engage in QS. (By QS, I do not mean Quantum Sex, even though such an activity has intriguing possibilities indeed. This topic is beyond the subject addressed here so I will postpone it for a later posting) Neither is QS for Qualified Specialist, nor for Quantum Stupidity I suppose. Instead of telling what QS is not for, you could remind us what QS *is* for... Ah! Quantum Suicide. I remember. I was afraid to be censored for mentioning Quantum Suicide, so I just said it was not Quantum Sex. Diverging for a minute on Quantum Sex... I am intrigued by this idea... Quantum superposition is what makes Quantum Sex possible. Imagine all the possible simultaneous partners you could have. Forget menage-a-trois. The 70 virgins are insignificant compared to the huge number and diversity of partners... Not that Quantum Sex and Quantum Suicide are not related. One may lead to the other, but I am still trying to figure out which one Otherwise the machine terminates itself with both persons inside it in a microsecond. Anyone within a radius of 20 feet of the machine is also terminated. Even within 19,887642109 feet ? If physicists can talk about point particles then I can say 20 feet. However, if you want 19,887642109 feet you can have them. Just pay in cash! A few days later, after a series of successful tests demonstrating the non-operation of the machine, (otherwise the tests would destroy the machine) the device is ready to operate. Tearfully, Romeo and Juliet say their goodbyes to their dear friends. They kiss passionately, and slowly step into the machine. Balthasar moves away in a hurry afraid for his life. Romeo is sitting in front of the command panel. One last time, he looks at Juliet who gives him a nod. Romeo pushes the ignition button ... and nothing happens, Romeo and Juliet step out of the machine, and full of joy, run to their families to announce thier engagement and prepare their wedding... ...and a huge exposion shakes the ground... Balthasar is at a safe distance and is not hurt. However, Mercutio, who could not bear to lose his friends, had decided at the last minute to share their fate. He had moved within one foot of the machine when Romeo hit the iginition switch. Now here are a few questions involving first and third person points of views : Q1. What is the first person point of view of Juliet by Balthasar? What do you mean by the first person point of view of X by Y? Here I would say the (local) third person point of view is the description of the (genuine part) of the Schroedinger wave. No less. We are discussing *Quantum* S! Also, by definition I would say the the first person point of view of X is available to X, and nobody else. Oh, perhaps you mean someone, belonging to the same quantum branch, and who read Juliet (X) personal diary? OK. We agree on this. It's just a queston of adjusting our terms A1. He saw the machine explode. No more Juliet. In the (locally and even relatively) normal worlds *those* normal Balthazar saw the machine exploding. No more manifestation of Juliet relatively to *those* Balthazar, indeed. Q2. What is the first person point of view of Juliet by Romeo? A2. He sees his dear Juliet alive and well. And well? What about the vast set of quasi normal worlds (that is those worlds nearest to the normal world(*) where you relatively consistently survive) where Romeo and/or Juliette survive(s) but are wounded, and not so well? Those worlds where Mercutio can even no more put some new ignition button. What about those quasi normal worlds where the feud continue but Romeo and Juliette (and Mercutio, and Balthazar) get a brain disease and do no more really follow the drama? Both with comp and (pure) QM, violent self-annihilation send you to hell, I'm afraid. The amount of energy to annihilate yourself depends on the unknowable comp level of substitution. This is an unsupported remark. It may send you to hell but it may not. The actual probabilities must be worked out in light of the reliability of the machine versus the stubborness of the Montague and Capulet. It's just an engineering/psychological design problem. Just put enough redundancy in the machine to make sure the machine operates the way it is supposed to, and enough wine in the families stomachs to make sure they don't. Q3. What is the first person point of view of Juliet by Mercutio? A3. He sees Juliet alive and well. Same remarks. Same remarks Q4. What is the first person experience of Juliet by Juliet? A4 She is happy to be alive and in love with Romeo. OK
