# Re: Two Schrodinger cats

`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:
>
>
>
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> 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 :)
>
>
>
>
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>
>>
>> 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, LĂ¶wenheim-Skolem, incompleteness) is Elliott
> Mendelson.)
>

Thanks! I keep thinking that this list might benefit from a wiki.

>
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>>
>> 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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