On 25 Feb 2015, at 23:31, Bruce Kellett wrote:
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?
Because when we do an experience, in a lab, or with our eyes, we
*choose* a base. (in the case of our eyes, of course, nature made the
choice of the base for us, through our history).
It is not different than "there are many planet, why are we on Earth".
That is the problem which is solved by the notion of indexical, and
that computationalism generalizes.
But the global phenomenon lead to the same subjective experience,
whatever the base is chosen.
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.
I agree. That is not the solution. The solution is what I say above.
The interaction hamiltonian does not impose a principal base, it
explains only why brains relativize a base with respect to us.
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?
The answer is: we don't.
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?
Because seeing is expressed much more easily in the base position. But
we don't need to give any special importance to the base position, or
any base. They all give the same universal evolution, and the same
relative state impressions. Then, when we choose some special
measuring apparatus, we just select the relative state accessible to
us, and express them in the base which limit the most the calculus.
All we need are state enough orthogonal for not burying the digital
information. In the case of the brain, our consciousness has only
selected the base in which it is related to digital information
processing. So from our perspective, it looks like some base are more
important than other, but that is only an indexical, like it looks
that here-and-now is more important, but that is not fundamental. It
is only due to the necessity of having *some* point(s) of view.
Bruno
Bruce
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