Hitoshi Kitada (hitoshi@kitada.com)
Tue, 8 Jun 1999 14:14:57 +0900
Dear Matti,
This is a supplementary remark with some questions.
----- Original Message -----
From: Matti Pitkanen <matpitka@pcu.helsinki.fi>
To: Hitoshi Kitada <hitoshi@kitada.com>
Cc: <time@kitada.com>
Sent: Monday, June 07, 1999 6:05 PM
Subject: [time 391] Re: [time 388] Re: [time 384] Re: [time 380] Re: [time
376] Whatare observers
>
>
> On Mon, 7 Jun 1999, Hitoshi Kitada wrote:
>
> > Dear Matti,
> >
> >
> >
> > >
> > >
> > > 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.
> >
> > 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.
Here t must be considered as the time t_L of the local system L.
> >
> > Breaking of the unitarity when considered in a larger LS, L',
This occurs only if one cosiders the system L as obeying the time t_L' of
the larger system L'. Insofar as the system L is considered obeying its own
time t_L, the breaking of unitairy does not occur.
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.
>
>
> In Henkel's theory there are also 'local systems' obeying unitary time
> development. But there is also nonunitary time development.
I think this would occur maybe because he thinks the time as common to all
systems.
> This is related to symmetry breaking. For instance, different vacuum
> expectations of Higgs field or some order parameter would correspond
> to nonequivalent Hilbert spaces and non-unitary time development can
> lead from realization to another. The interaction with surroundings
> somehow induces the nonunitary time development. The weak point of
> Henkel's approach is how to realize this time development concretely.
Does Henkel assume the total universe evolve along with a global time?
>
>
>
> In TGD approach different sectors D_p of configuration space (p prime)
> correspond to quantum theories in different p-adic number fields and
> at first it seems that unitarity is broken down dramatically!
Do you also think the universe evolves along a common time?
> One can however define generalized S-matrix which obeys generalized
> unitarity. S-matrix for transitions leading
> from any D_p1 to D_p is C_p valued.
>
> The restriction of S-matrix to transitions D_p to D_p IS unitary!
> Despite the fact that S-matrix elements D_p to D_p1 , p_1 neq p can
> be nonvanishing!! Sounds highly paradoxical!
>
> The point is that total p-adic probability for transition D_p to D_p1, p_1
> neq p can *vanish*! This is something genuinely p-adic and highly
> paradoxal and nonsensical from the real point of view.
> Therefore p-adic unitarity allows something which
> is not unitary in real context.
I question what necessitates the unitarity. Unitarity is a notion which is
introduced to assist the human reasoning in regards to the understanding of
nature. This is an idealistic notion, which gives us some balance sheets of
probabiltiy as the law of conservation of energy, etc. give. From the
viewpoint that the observer is fundamental that is contrast to your view,
the observer has some implicit assumption about what he sees, without which
he can not make any judgements/estimates about nature. As Einstein has ever
said, we have an image of nature in mind already before we observe nature.
What remains is how the image can be applicable and adjustable to nature.
>
> There is however question of interpretation. One can consider
> either p-adic sums of p-adic probabilities or sums of real
> counterparts of p-adic probabilities as predictions of theory.
> How the physical situation determines which definition of
> probabilities one must use? The answer to this question
> leads to the concept of monitoring and resolution of monitoring.
>
>
>
> Concrete example about conceptual beauty of p-adics illustrating the
> concept of monitoring.
>
>
> a) Elementary particle can have S-matrix for which
> the total *p-adic* decay rate is vanishing. Elementary particle
> is p-adically stable: individual p-adic probabilities
> for decays to various many particle states can be nonvanishing
> and only their *p-adic* sum vanishes.
>
> b) The interpretation is
> that the p-adic sum of p-adic decay probabilities measures the decay rate
> of elementary particle when the *resolution of monitoring of
> final states is not able to distinguish between final states*.
>
> b) When monitoring is able to distinguish between subspaces
> of final states situation changes. For instance,
> one could be able to measure charges of final state
> particles or measure momenta with some resolution.
> Optimal resolution
> is able to distinguish between all final states.
> The measured decay rate, which is *sum over the real counterparts of
> p-adic decay probabilities* to those subspaces of the Hilbert space of
> final states defined by resolution and is *nonvanishing* in general.
> Breaking of unitarity in real level means that real probabilities
> are not derivable from unitary S-matrix.
>
>
> c) Thus p-adics make possible to avoid the introduction of decay widths
> and complex energies, which are mathematically ugly
> concepts. Elementary particles could be
> stable in absence of monitoring not able to
> resolve between various final states.
>
>
>
>
>
>
>
>
> >
> > [snip]
> >
> > > > > 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.
and each observer's time.
> >
>
> Best,
> MP
>
>
Best wishes,
Hitoshi
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