From: <[email protected] <mailto:[email protected]>>
On Sunday, June 3, 2018 at 2:23:46 AM UTC, [email protected] <mailto:[email protected]> wrote:On Saturday, May 26, 2018 at 12:06:53 AM UTC, Bruce wrote: From: <[email protected]On Wednesday, May 23, 2018 at 8:16:07 AM UTC, Bruce wrote: From: <[email protected]OK, but how does one jump to the assumption of other worlds? Doesn't each "branch" exist in this world? AGInitially yes. But decoherence diagonalizes the density matrix FAPP, so the other branches become unreachable. That is what one means by separate worlds. *I am tentatively OK with this conclusion (tentatively until I examine the mathematics and verify it), as long as these separate "worlds" do NOT contain copies of THIS world. It's the copying that I find hugely extravagant, ridiculous, and erroneous! Can decoherence theory be consistent without the "copying" claim? Is this the view you adopt to keep your sanity? TIA, AG*The fact that the whole world is copied in each branch of the MWI is a simple consequence of the mathematics. If one has a state |psi> = (|+> + |->) that one measures, which is a superposition of two possible outcome states, |+> and |->, then schematically this measurement process looks like |psi>|A>|O>|e>, where |A> is the apparatus, |O> is the observer, and |e> is everything else, namely the environment. Unitary evolution takes this to: (|+>|A+>|P+>|e+> + |->|A->|O->|e->) where |A+> means the apparatus register the |+> result, |O+> means the observer sees the |+> result, and |e+> means that information about the |+> result leaks into the environment by decoherence and is effectively recorded there many times. Similarly for the other |-> branch. *As previously noted, the formula you meant to write is: (|+>|A+>|O+>|e+> + |->|A->|O->|e->). What thought experiment would be appropriate to understand either of the environmental states? AG**Does |e+> represent the eigenstate of the universe, excluding the particle being measured, the apparatus and the observer, when the spin is measured UP? That is, what is the physical content and meaning of |e+> within the standard formalism of QM? AG*
You are right, I meant |O+> for the observer who sees |+>. But the environment states, |e+> and |e->, are not necessarily eigenvalues of any particular simple operator. They are, rather, a schematic representation of the total environment (excluding apparatus and observer) that, by decoherence, contains multiple copies of the result (|+> or |->, respectively). By construction, these environmental states are orthogonal.
Remember that the analysis I have given above is schematic, representing the general progression of unitary evolution. It is not specific to any particular case, or any particular number of possible outcomes for the experiment.
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