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.

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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