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 ofunderstanding of the MWI. I imagine the multi-verse as a tree,where each time there is more than one possible quantum state weget a branch. I imagine my consciousness moving down the tree.Suppose Mary performs the Schrodinger's cat experiment in her houseand Joe does the same in his house. They both keep the animals inthe boxes and don't take a peak. Don't tell PETA. They meet for acoffe 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 bothstill dead+alive in the current universe. Right? So are Mary andJoe meeting in the fours universes at the same time?Let a = alive, d = dead, and the subscript 1 and 2 distinguishesthe two cats, which are independent. Both cats are in a superposedstate 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 isalso 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*a2You can add the "normalization" constant, which are 1/sqrt(2) times1/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*a2So the answer to your question is yes. Nice. Thanks Bruno!Welcome!To be sure, the normalizing factor does not mean there are fouruniverses, but most plausibly an infinity of universes, onlypartitioned 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 theuniverses/computations going through your actual states. But that isreally a logician, or category theoretician manner of speaking: theidentification is some natural morphism.Well I think Bohr made the trick for the atoms. I think he definesonce an atom by the set of macroscopic apparatus capable ofmeasuring some set of observable.That can be useful for some reasoning, but also misleading if takenliterally, without making clear the assumed ontology.Ok. That mode of reasoning is weirdly appealing to me. Even Bohr'stake.

`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 (theproposition true in that world).But they identify also a proposition with the a set of worlds (theworlds in which that proposition is true).Doing both identification, you can see a world as a set of set ofworlds. That is useful for some semantics of modal logics.What textbook would you recommend on modal logic? (I'm relativelyconfortable with first-order logic from studying classical AI andalso 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, LĂ¶wenheim-Skolem, incompleteness) is`

`Elliott Mendelson.)`

Those are examples of dualities, which abounds in logic, and whichcan be very useful when used which much care, and very misleadingwhen forgetting that a morphism is not an identity relation.To get the exact "number" of universes, we should first solve themarriage of gravity with the quantum. And with comp, we should alsoderive 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 ownunderstanding of what you're saying beyond the mushiness that itcurrently is)I can recommend the reading of the book by David Albert "QuantumMechanics 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'treally need the Hilbert Space, a simple linear space, on the complexnumbers, is enough, with a good scalar product. It is aboutinfinitely easier to grasp quantum teleportation (and other veryweird quantum things) than to derive the structure of the Hydrogenatom from the SWE. Quantum weirdness is simple!I don't follow David Albert on Bohm, and he could have been lessquick on the Bell's inequality, ... and Everett, but it provides,imo, the best simplicity/rigor tradeoff to get the main "conceptualdifficulties" of the QM theory.Bruno (*) http://www.amazon.com/Quantum-Mechanics-Experience-David-Albert/dp/0674741137

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