Matti Pitkanen (matpitka@pcu.helsinki.fi)
Mon, 7 Jun 1999 08:21:00 +0300 (EET DST)
On Sun, 6 Jun 1999, Hitoshi Kitada wrote:
> Dear Stephen,
snip
> > > The inner product for configuration space spinor fields reduces
> to inner
> > > product ofm configuration space spinors integrated over entire
> > > configuration space of 3-surfaces. Inner product of spinors is
> just Fock
> > > space inner product for fermions (oscillator operators create
> the state).
> > >
> > > In your case you have single phi and inner product must be inner
> product
> > > for some subsystem (LS?). Hence situation is different from that
> > > in TGD.
> >
[Stephen]
> > I am getting confused. :( We need to ask Hitoshi about these
> details...
>
[Hitoshi]
> 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.
>
> 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."
>
> 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.
Yes. I understand. This resembles the approach of Joel Henkel
to the quantum description of biossystems. He also considers collection
of Hilbert spaces in his nonunitary QM. I had long discussions with
Joel for some time ago. We found that the decomposition of
Hilbert space to 'pieces' corresponds in TGD to the decomposition
of quantum TGD to padic quantum TGD:s. Breaking of real unitarity
is possible test for Joel's approach as also for TGD
(but for different reasons) and probably any
theory giving up the idea about the quantum state of entire
universe.
>
> >
> > > > snip
> > > >
> > > > [SPK]
> > > > > > Making "'our minds' as outsider" is modeling our minds, it
> does not
> > > > > > give a complete knowledge of the subjective stance, but we
> can use it as
> > > > > > information from which to infer sets of observables and
> the
> > > > > > superselection rules that order them. I call this
> "contextual
> > > > > > definiteness". I can not say with probability 1 what you
> see, but I can
> > > > > > calculate what you might see that I can also see. Does
> this make sense?
> > > > > > It is like figuring out if a distant observer that I can
> talk to on a
> > > > > > radio can observe something similar to what I do. I can
> not "see" what
> > > > > > he sees, but I can say with high certainty (low error)
> that we observer
> > > > > > "the same thing".
> > > > [MP]
> > > > > Your argument certainly makes sense. What I am however
> troubled is the
> > > > > introduction of observers as fundamental (the concept is of
> course very
> > > > > practical approximation). Introduction of observers at
> fundamental
> > > > > level leads to consistency conditions on the observations
> if they
> > > > > correspond to quantum jumps.
> > > >
> > > > 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.
> > >
> [MP]
> > > 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?
>
> In
> > > TGD I allow all possible phis, quantum histories. TGD is
> nonmaterialistic
> > > theory in strong 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.
>
> >
> > 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.
>
Yes. This resembles Henkel's approach.
Best,
MP
> >
> > More later,
> >
> > Stephen
> >
>
> Best wishes,
> Hitoshi
>
>
>
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