On Sun, Jan 20, 2013 at 7:43 PM, Richard Ruquist <yann...@gmail.com> wrote:

> On Sun, Jan 20, 2013 at 12:53 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.)
> >
> >
>
> 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/
> >
> >
> >
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