On 8/25/2012 8:35 AM, Bruno Marchal wrote:

Decoherence theory provides a mechanism, although the basis problem is open. It is of a piece with the problem of deriving the classical from the quantum.

I have never understood the basis problem. It is quite similar to comp. You have to fix a base to do the math, and then you can show that all appearances, from the first person perspective are independent of the choice of the basis. then we can understand empirically why some bases will seem more important, as natiure did a choice of measuring apparatus for us a long time ago, but all this can be described in any basis. My feeling is that Everett got this right at the start.

But decoherence is not independent of the basis. It is only in particular bases that one can average over the environment and make the density matrix diagonal. Suppose you did that and then chose a different basis to express the result. In general the transformation to the different basis would generate cross-terms in the density matrix. That the classical world appears as it does must be due to what Zurek calls an ein-selection principle; i.e. that the world only appears stable/classical in certain bases. Everett just accepts that we can choose a measuring instrument that defines a certain basis - but that is equivalent to assuming that a quasi-classical world exists.


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