On Sun, Jan 20, 2013 at 7:43 PM, Richard Ruquist <[email protected]> wrote:
> On Sun, Jan 20, 2013 at 12:53 PM, Bruno Marchal <[email protected]> wrote: > > > > On 19 Jan 2013, at 13:42, Telmo Menezes wrote: > > > > > > > > > > On Thu, Jan 17, 2013 at 5:47 PM, Bruno Marchal <[email protected]> > wrote: > >> > >> > >> On 17 Jan 2013, at 16:01, Telmo Menezes wrote: > >> > >> > >> > >> > >> On Thu, Jan 17, 2013 at 3:01 PM, Bruno Marchal <[email protected]> > 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.) > > > > > > Here is a link to what seems to be a very complete set of tutorials on > logic: > https://sites.google.com/site/theoremeorg/ > Richard > Thanks Richard! Very nice. > > > > > > > >> > >> > >> 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 [email protected]. > > To unsubscribe from this group, send email to > > [email protected]. > > 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 [email protected]. > To unsubscribe from this group, send email to > [email protected]. > 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. 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