On Sun, Jan 20, 2013 at 6:53 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:
> > On 19 Jan 2013, at 13:42, Telmo Menezes wrote: > > > > > On Thu, Jan 17, 2013 at 5:47 PM, Bruno Marchal <marc...@ulb.ac.be> wrote: > >> >> On 17 Jan 2013, at 16:01, Telmo Menezes wrote: >> >> >> >> >> On Thu, Jan 17, 2013 at 3:01 PM, Bruno Marchal <marc...@ulb.ac.be> wrote: >> >>> >>> On 17 Jan 2013, at 13:32, Telmo Menezes wrote: >>> >>> Hi all, >>>> >>>> Naive question... >>>> >>>> Not being a physicists, I only have a pop-science level of >>>> understanding of the MWI. I imagine the multi-verse as a tree, where each >>>> time there is more than one possible quantum state we get a branch. I >>>> imagine my consciousness moving down the tree. >>>> >>>> Suppose Mary performs the Schrodinger's cat experiment in her house and >>>> Joe does the same in his house. They both keep the animals in the boxes and >>>> don't take a peak. Don't tell PETA. They meet for a coffe in a nearby >>>> coffeeshop. >>>> >>>> So now we have four possible universes where Mary and Joe can meet. But >>>> from the double slit experiment we know that the cats are both still >>>> dead+alive in the current universe. Right? So are Mary and Joe meeting in >>>> the fours universes at the same time? >>>> >>> >>> Let a = alive, d = dead, and the subscript 1 and 2 distinguishes the two >>> cats, which are independent. Both cats are in a superposed state dead + >>> alive: >>> >>> (a1 + d1) and (a2 + d2), >>> >>> so the two cats configuration is given by (a1 + d1) * (a2 + d2), with >>> "*" the tensor product. >>> This products is linear and so this give a1*a2 + a1*d2 + d1*a2 + d2*a2. >>> Mary and Joe don't interact with any cats, so the global state is also a >>> direct tensor product M * J * (a1*a2 + a1*d2 + d1*a2 + d2*a2), which gives: >>> >>> >>> M * J *a1*a2 + M * J *a1*d2 + M * J *d1*a2 + M * J *d2*a2 >>> >>> You can add the "normalization" constant, which are 1/sqrt(2) times >>> 1/sqrt(2) = 1/2= >>> >>> 1/2 M * J *a1*a2 + 1/2 M * J *a1*d2 + 1/2 M * J *d1*a2 + 1/2 M * J *d2*a2 >>> >>> So the answer to your question is yes. >>> >> >> Nice. Thanks Bruno! >> >> >> Welcome! >> >> >> >>> >>> To be sure, the normalizing factor does not mean there are four >>> universes, but most plausibly an infinity of universes, only partitioned in >>> four parts with identical quantum relative measure. >> >> >> Sure, I get that. >> >> Am I a set of universes? >> >> >> You can put it in that way. You can be identified by the set of the >> universes/computations going through your actual states. But that is really >> a logician, or category theoretician manner of speaking: the identification >> is some natural morphism. >> >> Well I think Bohr made the trick for the atoms. I think he defines once >> an atom by the set of macroscopic apparatus capable of measuring some set >> of observable. >> >> That can be useful for some reasoning, but also misleading if taken >> literally, without making clear the assumed ontology. >> > > Ok. That mode of reasoning is weirdly appealing to me. Even Bohr's take. > > > It is common in algebra, logic and exploited in category theory. As long > as we identify identity and morphism it is OK, in the applied fields. > Don't confuse the price of a glass of beer with the set of all glass of > beers with the same price :) > > > > > > >> >> Logicians often identify a world with a set of proposition (the >> proposition true in that world). >> But they identify also a proposition with the a set of worlds (the worlds >> in which that proposition is true). >> Doing both identification, you can see a world as a set of set of worlds. >> That is useful for some semantics of modal logics. >> > > What textbook would you recommend on modal logic? (I'm relatively > confortable with first-order logic from studying classical AI and also from > Prolog). > > > The two books by George Boolos (1979, 1993), on the self-referential > logics (G, G*, S4Grz) contains a quite good introduction to modal logic. > > The best textbook on modal logic is in my opinion is the book by Brian > Chellas: "Modal logic an introduction". > > http://www.amazon.com/Modal-Logic-Introduction-Brian-Chellas/dp/0521295157 > > A recreative introduction to modal logic and self-reference (the logic G) > is "Forever Undecided" by Raymond Smullyan. > > > (A good book on first order logic, with the main theorems (deduction, > completeness and soundness, Löwenheim-Skolem, incompleteness) is Elliott > Mendelson.) > Thanks! I keep thinking that this list might benefit from a wiki. > > > > > >> >> Those are examples of dualities, which abounds in logic, and which can be >> very useful when used which much care, and very misleading when forgetting >> that a morphism is not an identity relation. >> >> >> >> >> >>> To get the exact "number" of universes, we should first solve the >>> marriage of gravity with the quantum. And with comp, we should also derive >>> the Quantum from arithmetic (but that's not true, actually: with comp we >>> have directly the infinities of "universes"). >>> >> >> Ok, sounds good but I have to dig deeper. (moving my own understanding of >> what you're saying beyond the mushiness that it currently is) >> >> >> I can recommend the reading of the book by David Albert "Quantum >> Mechanics and experience(*)". It is short and readable. >> > > Nice. I bought it and I'm enjoying it so far. > > > Nice. > > Best, > > Bruno > > > > > >> >> To get all the quantum weirdness, and quantum computation, you don't >> really need the Hilbert Space, a simple linear space, on the complex >> numbers, is enough, with a good scalar product. It is about infinitely >> easier to grasp quantum teleportation (and other very weird quantum things) >> than to derive the structure of the Hydrogen atom from the SWE. Quantum >> weirdness is simple! >> I don't follow David Albert on Bohm, and he could have been less quick on >> the Bell's inequality, ... and Everett, but it provides, imo, the best >> simplicity/rigor tradeoff to get the main "conceptual difficulties" of the >> QM theory. >> >> Bruno >> >> (*) >> http://www.amazon.com/Quantum-Mechanics-Experience-David-Albert/dp/0674741137 >> >> > > http://iridia.ulb.ac.be/~marchal/ > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to everything-list@googlegroups.com. > To unsubscribe from this group, send email to > everything-list+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. 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