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.
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.
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.
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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