Bruno Marchal wrote:
On 25 Feb 2015, at 12:28, Bruce Kellett wrote:
In particular one has to solve the basis problem
I disagree. It seems to me that Everett already solved it. The relative
subjective state does not depend on the base.
That is precisely the problem. There are an infinite number of possible
bases for any Hilbert space and the Everett relative state formulation
does not distinguish between them -- but experience does. Why?
Of course the history of
our body and brains shows that our consciousness is selected with
remlative states distinguishible in the position base, but that is more
historical than fundamental (except Zurek porvides some explanation why
position was well suited for having something like interacting machines).
There is a common misconception that the basis problem is resolved by
saying that the interaction Hamiltonian singles out the position basis.
But that is not the problem. The position operator, even in one
dimension, acts in an infinite dimensional Hilbert space. The issue is
how do we choose a basis in this space? Not whether we choose this space
rather than another.
An eigenfunction in one basis is a superposition (potentially an
infinite superposition) in any other basis. Why do we not see
superpositions of positions?
Bruce
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