On 1/4/2012 12:34 PM, Stephen P. King wrote:
On 1/4/2012 3:03 PM, meekerdb wrote:
In the MW interpretation there is no collapse, but there is a split into (almost) orthogonal "worlds" or each person splits into orthogonal "minds". These are just projections onto different quasi-classical subspaces corresponding to different measurement values. The projection is a mathematical, not a physical, operation.


Could you elaborate on the meaning of the word "almost" as it is used here? How do we go from the implicit "always" of orthogonal relations between state vectors of the linear algebra of Hilbert spaces to an "almost" orthogonal relation? Is this a definable function/morphism?



In the usual density matrix formalism, the cross terms in the system being measured never go exactly to zero and the world is never exactly classical. Decoherence provides a physical description of the evolution to almost orthogonal, c.f. Schlosshauer's review paper.


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