**Hitoshi Kitada** (*hitoshi@kitada.com*)

*Thu, 9 Sep 1999 06:16:06 +0900*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Stephen P. King: "[time 717] Re: [time 716] Time operator => Ensembles of clocks?"**Previous message:**Hitoshi Kitada: "[time 715] Re: [time 710] Re: [time 709] FTL propagations"**In reply to:**WDEshleman@aol.com: "[time 710] Re: [time 709] FTL propagations"**Next in thread:**Stephen P. King: "[time 717] Re: [time 716] Time operator => Ensembles of clocks?"

Dear Stephen,

stephen p. king <stephenk1@home.com> wrote:

Subject: [time 711] Re: [time 708] Time operator => Ensembles of clocks?

*> Dear Hitoshi et al,
*

*>
*

*> Hitoshi Kitada wrote:
*

*> >
*

*> > Dear Stephen,
*

*> >
*

*> > Stephen P. King <stephenk1@home.com> wrote:
*

*> >
*

*> > Subject: [time 706] Re: [time 702] Time operator?
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*> > > [HK]
*

*> > > > You are right again. I completely agree. This is the same problem if
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it is

*> > > > possible to construct a four dimensional version of the Hilbert space.
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*> > > > What I
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*> > > > proposed is that if the space of states could be thought as the
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totality

*> > > > of
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*> > > > the QM orbits exp(-itH/h)Psi(x,t), then the conjugateness of t to H is
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*> > > > trivial. This is an identical propsoition by nature of positing the
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*> > > > problem.
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*> [SPK]
*

*> > > Matti, are you saying that the dynamical law is a priori to time? How?
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*> > > I see the "dynamical law" as defining a pattern of behavior of a system
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*> > > as it evolves in its time. When we say that we localize it in time, we
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*> > > are refering, to be consistent, to the time of the localizing agent, not
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*> > > the system in question's time. There is no "time" for all unless we are
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*> > > merely considering the trivial case when all systems are synchronized...
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*>
*

*> Did this make sense?
*

Yes, but sounds obvious.

I see LS's as fundamental clocks, and thus it

*> should be possible to consider an "ensemble of clocks" as given by a
*

*> ensemble of LSs. But, I am very sketchy in my thinking of this. :-(
*

*>
*

*> > > Hitoshi, are the QM orbits constructed in a Hilbert space such that
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*> > > they are strictly orthogonal to each other? This, to me, says that the
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*> > > LS are independent and thus have independent space-time framings of
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*> > > their observations. Does this affect your argument?
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*> [HK]
*

*> > No. E.g., consider two orbits Psi(x,t) = exp(-itH/h)Psi(x,0) and Phi(x,t)
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=

*> > exp(-itH/h)Phi(x,0) in the same LS. The inner product of these wrt the
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usual 3

*> > dimensional Hilbert space is
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*> >
*

*> > (Psi(t), Phi(t)) = (Psi(0), Phi(0)).
*

*> >
*

*> > This is not equalt to zero unless the initial states are orthogonal.
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*> >
*

*> > But two orbits in different LS's are of course orthogonal by definition.
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*>
*

*> Ok, this is that I suspected. I am trying to work backwards from the
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*> notion that the ordits of LS's are orthogonal to each other. I am
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*> wondering if it is possiple to think of LS's as subjective observers and
*

*> the orthogonality condition as making them independent of each other.
*

Yes, this is the assertion of my axiom 1.

*> This implies to me that a space of n-dimensions can be defined by the
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*> set of LS's, where each LS defines a dimension.
*

Each LS defines some finite dimenstions according to the numebr of particles

it contains.

Question: Would this

*> space have "continuous" dimensions like a Von Neumann space?
*

I do not think so.

*> Now, as to your question about how we have a subject/object dichotomy,
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*> re: "So I am interested in how/why the two different views could be
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*> possible." I believe that each LS defines an observer, specifically a
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*> "subject". This "subject" has something that it is not as an "object".
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*> This is very important. So the "object" of the "subject" is the
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*> "~subject". Does this make sense?
*

Again sounds obvious/trivial.

It follows that ~(~subject) = subject.

*> I am seeing the scattering propagator (orbit?)of the LS as defining the
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*> subjective actions of an LS and that the mapping of such to that of the
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*> ~(orbit) as defining the objective actions, e.g. the LS observes
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*> situations that are "not" the behaviour of the scattering propagator or
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*> orbit.
*

Neglecting some of your abuse of words, I agree.

The trick is to see how it is that the class or set of {~(orbit)}

*> is finite.
*

If {~(orbits)} means the complement of the set of "orbits," it would be

infinite.

*> All I have right now is a metaphor, the metaphor of a dictionary. I see
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*> the "meaning" as given by the n-ary relations that exist between
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*> objects. In a dictionary, the meaning of each word is given by the
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*> relationship it has with a finite number of other words. Particularly,
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*> the relational structure that the words in the set "{definition}" have
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*> with each other. I think that Pratt's CABAs are a formal way of thinking
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*> of this notion.
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*> Now, how do we think of the communication or interaction or, qua Bill's
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*> thinking, interference, between LSs? In order for two systems to
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*> communicate there must be at least one aspect of the systems that they
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*> share or have in common.
*

The common part can be played by an observer of the two systems.

We can think of this as a common element in

*> their poset of their observations.
*

*> (BTW, Hitoshi, does the notion of a poset of observations make sense to
*

*> you?
*

What order do you define among the observations? The class of LS's is a

partially ordered set (poset) with respect to the set inclusion relation. In

this sense, i.e. in the sense that the order is a partial order, the totality

of LS's in my sense does not have a clear hierarchy as Matti's world seems to

have.

*> Also, do you see any big problems with Schommers work?)
*

No, as far as I saw it. It is an interesting book containing speculative

thinkings.

*>
*

*> I'll continue this next time...
*

*>
*

Best wishes,

Hitoshi

**Next message:**Stephen P. King: "[time 717] Re: [time 716] Time operator => Ensembles of clocks?"**Previous message:**Hitoshi Kitada: "[time 715] Re: [time 710] Re: [time 709] FTL propagations"**In reply to:**WDEshleman@aol.com: "[time 710] Re: [time 709] FTL propagations"**Next in thread:**Stephen P. King: "[time 717] Re: [time 716] Time operator => Ensembles of clocks?"

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