On 17 Jan 2013, at 13:32, Telmo Menezes wrote:
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
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
So the answer to your question is yes.
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. 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").
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