[time 732] Re: [time 728] Time operator => Ensembles of clocks?

Stephen P. King (stephenk1@home.com)
Thu, 09 Sep 1999 12:37:59 -0400

Dear Hitoshi,

Hitoshi Kitada wrote:
> Dear Stephen,
> Stephen P. King <stephenk1@home.com> wrote:
> > Can we use the concepts of entrainment and phase locking to think of
> > how LS's interact?
> I do not understand what your question is.
        Could we think of LS's as quantum mechanical oscillators capable to
becoming phase locked or entrained with each other?

> > Yes, I am trying to see how we can recover a local approximation of
> > Riemannian geometry as the way that the individual posets of
> > observations of each of the LS's are "ordered". We need to show that it
> > is necessary and sufficient that the observations of any LS, e.g. a set
> > of classical center of mass particles, are arranged in a way that we can
> > think of relations among them in terms of a Riemannian metric. It could
> > be that we only need a Minkowski metric, because, I think that gravity
> > is defined in terms of the differences between the local space-times of
> > different LS's.
> > Remember that I am thinking of space-time in a way that is very similar
> > to how Schommers thinks of it: "...we have argued that physically real
> > processes do not take place $in$, but are $projected on$ space-time. The
> > coordinated [metrics, connections, etc.] and time are not accessible to
> > empirical tests and we can only observe distances between bodies and
> > time intervals in connection to processes: There is no exception to this
> > law. Thus, we can conclude that the phenomenon space-time comes into
> > being through bodies and processes. ... Objects and processes of the
> > real world [the poset of observations that a finite number of LS's can
> > agree upon] are perceived by an interaction process with our sense
> > organs; this reality is pictured by our perceiving apparatus, and the
> > phenomenon space-time belongs to the perceiving apparatus."
> > pg. 263, Quantum Theory and Pictures of Reality...
> >
> > I am going further than Schommers in that I am saying that the
> > so-called "real world" is not an absolute, it is a relative concept,
> > e.g. a given set of LS's that share a common metric such that a
> > synchronized frame of motions can be defined among them constitutes a
> > "world". In information theoretical terms we can think of a world as
> > that a given set of LS's can agree upon within the information encoded
> > in the configurations of their QM orbits. (This is tentative and maybe
> > very wrong!)
> In a rough sense, I agree. You need to formulate your thought if you wanted to
> be understood by others, i.e. by the so-called scholars or physicists, but
> this might be unnnecessary/useless, seeing them being involved only in their
> own special thoughts. (I do not mean speciality is good or should be
> evaluated, but the reverse ;-) )
        I agree!

> > [SPK]
> > > > 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.
> > [HK]
> > > Each LS defines some finite dimensions according to the number of
> > > particles it contains.
> > Ok, but can be define a space were each orthogonal "dimension" or
> > independent basis vector is an LS?
> >
> > [SPK]
> > > > Question: Would this
> > > > space have "continuous" dimensions like a Von Neumann space?
> > [HK]
> > > I do not think so.
> > So the dimensionality of a LS space would have integer valued
> > dimensions, not Real valued dimensions, each orthogonal?
> Yes.
        Umm, this, to me, seems to imply that the are restricted to dimensions
that are rational rations a/b. This is part of my reasoning as to why I
am asking about entrainment and phase locking!

> > > 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 word "scattering propagator" does not seem to exist: it should be replaced
> by the word "unitary propagator" like exp(-itH/h). There is a word "scattering
> operator" S that is defined by
> S = W_{+}^* W_{-},
> where
> W_{+ or -} = lim_{t -> + infinity or - infinity} exp(itH/h) exp(-itH_0/h).
> Here H is the Hamiltonian of the system
> H = H_0 + V,
> where H_0 is the unperturbed Hamiltonian and V is the perturbation.

        Is the perturbation given in increments related to the clocking action
of the unitary propagator? How is the quantity restricted to integer
valued amounts, if it is?
> Then the first part of your statement may be
> > I am seeing the unitary propagator exp(-itH/h) of the LS as defining the
> > subjective actions of an LS.
> On the second part:
> > and that the mapping of such to that of the
> > ~(orbit) as defining the objective actions,
> you may need to articulate what the mapping is. But seeing the following part:
> e.g. the LS observes
> > situations that are "not" the behaviour of the scattering propagator or
> > orbit.
> I think that you mean by "objective actions" the phenomena outside an
> observer.

        Yes, it is the poset of observations of the LS, the geometry of the
relations of the centers of mass of other LS's. I am thinking of a
generalization of Markopoulou's ideas and Matti's similar ideas...
> I thus think that you just rephrased what we have been discussing about the
> inside of an LS and the observation of the outside of an LS. I.e., this
> statement of yours does not seem to add any new to the previous arguments.
        Yes, but it does lets me know that I am understanding (bisimulating)
your ideas well! :-) What needs our special attention is how the
geometry of relations in constructed!

> > [SPK]
> > > The trick is to see how it is that the class or set of {~(orbit)}
> > > > is finite.
> > [HK]
> > > If {~(orbits)} means the complement of the set of "orbits," it would be
> > > infinite.
> > Would it be finite if we only consider orbits that we can think as
> > synchronized with each other?
> How are these systems synchronized? The number of the LS's is countable if the
> totality of the particles inside the universe is countable, but there is no
> definite finite limit to it as you say:
> Umm, this does not seem to limit the set
> > to a finite number! Perhaps it is the information theoretic aspect that
> > does this...
        Umm, Peter's paper http://www.cs.brown.edu/~pw/papers/math1.ps mentions
something that may help us:

"B(M), the behavior of a machine M defined earlier in this section, only
contains finite sequences. However, it can be shown that whenever two
SIMS are not equivalent, there will be a finite length
distinguishability certificate for them. [I see this, tentatively, as a
sequence that enumerates the sequence of permutations or operations
necessary to generate equivalence] The infinite hierarchy of strictly
better approximations via progressively longer sequences is analogous to
the hierarchy of finite models that approximate an infinite model, or to
the hierarchy of approximations to real numbers obtained by lengthening
the number of decimal digits." pg. 19.

        Also this relates to the Lexicon idea that I discussed in [time 636]
for example ...

> > > > 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.
> > Do you think that his redefinition of SR and QM to be useful?
> I need to remember what his redefinition was. Would you let me remember? It is
> a cumbersome task to resee the book :-) My impression was what he wrote is not
> new. Just a kind of review of QM and relativity written as a good reading like
> a good novel.

        Ok, perhaps I will post a big quote in a upcoming post. :-)



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