[time 386] Re: [time 385] The Universe, \Phi and Inner Products

Stephen P. King (stephenk1@home.com)
Sun, 06 Jun 1999 11:35:28 -0400

Dear Hitoshi and Matti,

Hitoshi Kitada wrote:
> Dear Stephen,
> If you argue in LS theory, the inner products are of an infinite
> number, proper to each Local System. I.e. LS theory considers an
> infinite number of Hilbert spaces describing the inner state of each
> observer's system. The outside of an observer's system is not
> described by Hilbert spaces. Only a part of the outside that is an
> object of an observation is described by a Hilbert space structure.

        I am very much interested on how acts of observation select a finite
partially ordered subset of the infinite number of Hilbert spaces. I am
wondering if the 4-vectors of GR are contractible from some part of
these Hilbert spaces. Perhaps my words are incorrect here, I am trying
to understand how consciousness, as a specific type of measurement, can
be modeled. :)
> In LS theory, the phenomena arise by the participation of the
> observer. In this sense, my standpoint is the same as the Wheeler's
> "participatory universe."

        Yes! This is my understanding. :) I am wondering how to model the
"clocking" and "gauging" behavior of the LSs, e.g. the mechanisms of
observation. It looks like a mapping between sets, but one that has
hierarchical orderings involved.
> The total state \phi of the universe is not considered in a Hilbert
> space. It represents just the state of the total universe, which
> does not evolve. No inner product is considered regarding \phi.

        Thus by definition there are no measurements of this \phi, no
projection postulates in the ordinary sense? It is only the All...?

> Neither the "observer" nor the "jumps" are "fundamental", as I see it;
> they are complementary. Having one without the other renders
> them meaningless! Existence is the grundlagen.

> I think that I disagree. The use of single phi means
> materialistic (sorry!(;-)) world view with single objective reality.
> Materialism leads to problems with inner product besides all these social
> problems(:-).
> Single \phi does not need any inner product. By materialism, what do
> you mean?

        To me, materialism means that the Universe is made up of a single
substance and that information is merely patterns of matter. I question
the root notions of "substance" since it tacitly posits the properties
of a priori synthetics (existing with definite properties independent of
observation). Thus I agree with Matti! ;) This is a very subtle issue
that we do need to discuss further. :)

URLs on materialism:


compare to idealism (information monism):


        I think that the Universe U is, in it-self, Existence and as such it is
One. Any subset of U that is distiguishable from the whole, is so
because it is dual by the definition of distinguishability. This duality
it the duality of complementarity, the duality of the subject-object

> In TGD I allow all possible phis, quantum histories. TGD is
> nonmaterialistic theory in strong sense.

        Matti, do you mean that TDG is not a model based on "atoms" in the
origional sense?

> In the observable world for an observer, all histories are possible.
> \phi does not appear in observations. The universe \phi is different
> from the observed universe.

        Histories might be considered as finite portions (subsets) of streams.
This is were I think that we need to understand Peter's work better...
> > Thus I am proposing many \phi! :)
> To each obsevation, there corresponds a proper universe. In this
> sense, there are many \phi, where \phi is used in different meaning
> from the \phi in the above.
        Have you ever taken a look at the infinitesimals in non-standard
analysis as a means to model the relationships between the \phi_U^T (the
Totality) and the \phi_U^i: i = 1, 2, ..., N? They are "actual" and
opposed to the "potential" infinitesimals of normal maths....
        I will try to write up a note on this...



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