Hitoshi Kitada (firstname.lastname@example.org)
Mon, 7 Jun 1999 15:43:37 +0900
----- Original Message -----
From: Matti Pitkanen <email@example.com>
To: Hitoshi Kitada <firstname.lastname@example.org>
Cc: Stephen P. King <email@example.com>; <firstname.lastname@example.org>
Sent: Monday, June 07, 1999 2:21 PM
Subject: [time 388] Re: [time 384] Re: [time 380] Re: [time 376] What are
> On Sun, 6 Jun 1999, Hitoshi Kitada wrote:
> > Dear Stephen,
> > > > 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.
> > >
> > > I am getting confused. :( We need to ask Hitoshi about these
> > details...
> > 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
My theory considers an LS, say L, as being equipped with the Hamiltonian H_L
of L itslef. With respect to this Hamiltonian H_L, the local system L evolves
according to exp(-iH_L) and thus this evolution preserves the unitarity
insofar as that local system is the object of observation. Namely an observed
system is always considered as a closed system.
Breaking of the unitarity when considered in a larger LS, L', would occur but
it occurs only when the observer could detect the larger system L'. Unless the
observer knows L', he has to assume that the unitarity of the evolution
exp(-itH_L) of the system L under consideration holds because his concerns are
not extended beyond the observed system L. In other words, any observer
observes an object with assuming the "ideal" unitarity of the observed
system's evolution. This is a restatement of the usual assumption in actual
observations/experiments, which is necessary for any theoritical
considerations to be possible.
> > > 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.
It seems resembling, but I consider a theoretical framework applicable to the
actual situation of observations. Explanation of actual situations seems
requiring us/me to assume that there exist many universes which vary in
accordance with each observation.
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