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. > > 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). > > 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. > > 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]. 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