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.


>
> 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/
>
>
>
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