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

stephen p. king (stephenk1@home.com)
Wed, 08 Sep 1999 13:00:54 -0400

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.
> > 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? 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?
> 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.
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. Question: Would this
space have "continuous" dimensions like a Von Neumann space?
        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? 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. The trick is to see how it is that the class or set of {~(orbit)}
is finite.
        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. 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? Also, do you see any big problems with Schommers work?)
        I'll continue this next time...

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