Hitoshi Kitada (hitoshi@kitada.com)
Thu, 9 Sep 1999 06:16:06 +0900
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?
> > > [HK]
> > > > You are right again. I completely agree. This is the same problem if
it is
> > > > possible to construct a four dimensional version of the Hilbert space.
> > > > What I
> > > > proposed is that if the space of states could be thought as the
totality
> > > > of
> > > > the QM orbits exp(-itH/h)Psi(x,t), then the conjugateness of t to H is
> > > > trivial. This is an identical propsoition by nature of positing the
> > > > problem.
> [SPK]
> > > Matti, are you saying that the dynamical law is a priori to time? How?
> > > I see the "dynamical law" as defining a pattern of behavior of a system
> > > as it evolves in its time. When we say that we localize it in time, we
> > > are refering, to be consistent, to the time of the localizing agent, not
> > > the system in question's time. There is no "time" for all unless we are
> > > merely considering the trivial case when all systems are synchronized...
>
> 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
> > > they are strictly orthogonal to each other? This, to me, says that the
> > > LS are independent and thus have independent space-time framings of
> > > their observations. Does this affect your argument?
> [HK]
> > No. E.g., consider two orbits Psi(x,t) = exp(-itH/h)Psi(x,0) and Phi(x,t)
=
> > exp(-itH/h)Phi(x,0) in the same LS. The inner product of these wrt the
usual 3
> > dimensional Hilbert space is
> >
> > (Psi(t), Phi(t)) = (Psi(0), Phi(0)).
> >
> > This is not equalt to zero unless the initial states are orthogonal.
> >
> > But two orbits in different LS's are of course orthogonal by definition.
>
> Ok, this is that I suspected. I am trying to work backwards from the
> notion that the ordits of LS's are orthogonal to each other. I am
> 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
> 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,
> re: "So I am interested in how/why the two different views could be
> possible." I believe that each LS defines an observer, specifically a
> "subject". This "subject" has something that it is not as an "object".
> This is very important. So the "object" of the "subject" is the
> "~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
> subjective actions of an LS and that the mapping of such to that of the
> ~(orbit) as defining the objective actions, e.g. the LS observes
> situations that are "not" the behaviour of the scattering propagator or
> 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
> the "meaning" as given by the n-ary relations that exist between
> objects. In a dictionary, the meaning of each word is given by the
> relationship it has with a finite number of other words. Particularly,
> the relational structure that the words in the set "{definition}" have
> with each other. I think that Pratt's CABAs are a formal way of thinking
> of this notion.
> Now, how do we think of the communication or interaction or, qua Bill's
> thinking, interference, between LSs? In order for two systems to
> communicate there must be at least one aspect of the systems that they
> 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
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