On 02 Nov 2015, at 11:23, Bruce Kellett wrote:
On 2/11/2015 7:10 pm, Bruno Marchal wrote:
On 02 Nov 2015, at 06:17, Bruce Kellett wrote:
Which is just your idiosyncratic way of saying that we have to
apply a projection operator.
No, we have to recover the "projection operator" from the
computationalist quantization. It is a math problem.
So do it.
That has been the subject of the PhD thesis. I can explain all the
detail, but you will need to invest more time in computer science/
mathematical logic. It is not a simple problem. UDA took a flash in my
childhood, AUDA took 30 years of works (in part because some people
makes me doubt of some results or conjecture I made for years, until I
saw them solved and published by others, to which I refer. The problem
now is that those interested in metaphysics seem to be not enough
patient to do the math. Philosophy attracts often people who dislike a
lot math and "exact" science. My whole main point is that with
computationalism, the mind body problem is translated into a problem
in math.
And the solution is given by the
[i]<i>p, p sigma_1, with i = 1, 2, 3, and [1]p = []p & p, [2]p = []p &
<>t,
and [3]p = [2]p & p (and [] is Gödel's beweisbar, and <>t = ~[]~t =
~[]f).
The trouble with your FPI approach is that it does not explain the
inter-subjective agreement that is an essential part of our
experience. All people experience the same "classical" world (in
which they agree about the observed basis vectors that are robust
against environmental decoherence)
The indexical quantization provides the path toward the solution or
the lack of solution. Don't confuse the intuitive FPI of the UDA,
and its translation in math based on the Gödel-Post-Turing-Kleene
technic which makes the self-reference mathematically precise.
Don't confuse it with what?
Sorry, it is my bad english. Don't confuse the intuitive FPI of the
UDA *with* its translation in math (based on the Gödel-Post-Turing-
Kleene technic which makes the self-reference povs mathematically
precise).
The full space might well still be 'there' (in whatever sense
you like), but the fact that the observer is conscious of only
part of that space involves a projection operator. And
projection operators are not time symmetric or unitary. This is
the partial trace problem, and it remains unsolved.
It is exactly what Everett solved, assuming mechanism, by taking
into account the personal point of view of the isolated system
with respect to what it is isolated and not isolated. Everett
shows this does not depend on the bases.
He showed no such thing. The basis according to which the
"classical" world is projected out is absolutely crucial. We would
not observe the same world in any other basis. The basis we do
observe is the one that is robust against environmental
decoherence -- any other basis is not robust, so rapidly devolves
into the robust (einselected) basis.
The choice of the bases is what Zurek have explained. That extends
Everett.
I think you should study Zurek at little more closely. He did not
actually explain the choice of basis. His result was that the basis
had to be robust against environmental decoherence -- which is true,
but does not give the actual basis. Position space is a Hilbert
space, not a basis for a Hilbert space.
?
Position provides a basis for the Hilbert space, which is independent
of the choice of that basis. we could use momentum instead, and
described the position by linear combination of momentum, and Zurek
wil still justify that the subject with a brain will handle the
position more easily than using the momentum.
I am not sure I can make sense of "Position space is a Hilbert space".
An Hilbert space is closed for linear combination (even infinite) of
any element belonging to any bases chosen in the Hilbert space.
Bruno
http://iridia.ulb.ac.be/~marchal/
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