[time 1023] Re: [time 1021] Thoughts

Stephen Paul King (stephenk1@home.com)
Tue, 23 Nov 1999 15:35:39 -0500

Dear Hitoshi and Friends,

        I have interleaved my comments...

Hitoshi Kitada wrote:
> Dear Stephen and All,
> My aunt is dead 13 days after his husband's death and I had to attend the
> funeral. I felt there is certainly an unknown world for us.

        I offer my sincere condolences on your loss. It is events like these
that can serve to help us focus on the finite nature of our experience
and realize the urgency of our work. :-)
> I apologize for my delay in response, but I hope you all to be patient. A member
> unsubscribed today. I do not detain them who do not try to be patient, but I
> feel some difference between the westerners and asians. The asians are not too
> hurry to lose something that might be gotten by being patient, while the
> westerners seem not like to be patient. I should state that this difference is
> not a result of observation of short term. Does anyone have anti-opinions or any
> other opinions?

        It is my experience that we must balance our need for a quick answer to
our questions and the completeness thereof. I personally find the Asian
approach to be more beneficial than the Western, but this is just a
subjective judgment... The development of applications of Fuzzy Logic in
electronic appliances can provide an example of this dichotomy.
> Stephen Paul King <stephenk1@home.com> wrote:
> Subject: [time 1018] Re: [time 1017] Re: [time 1013] [Fwd: Simpson's Paradox and
> Quantum Entanglement]
> > Dear Hitoshi, Tito, Robert and Friends,
> >
> > This is a cause for happiness! We still have much work to do in the
> > area of figuring out the way to model the classical environment E of a
> > quantum mechanical Local System.
> I agree. The unknown world or the environment E would certainly contain things
> which are worth being attempted to know. The things to which we address the word
> "mystic" would be just the things belonging to the unkown environment E because
> the universe includes the whole and therefore must include the mystic things
> also. Newton's investigation into mystic things might not mean his hobbies in
> his later years.

        Umm, perhaps Newton's behavior is similar to Tippler's. It seems that
as the thinker ages, their urgency and willingness to appeal to mystic
things increases. Unfortunately this tends to create more obscurity than
understanding. In contrast, the hard-nosed approach of young thinkers
gives us an example of how the blinkering effect of ignoring subtleties
can, in the short term, give concrete results. This line of thought
reminds me of Robert's essay:
http://www.bestweb.net/~ca314159/WISDOM.HTM and his other essays on
> >
> > Hitoshi Kitada wrote:
> > >
> > > Dear Robert, Stephen, et al.,
> > >
> > > I was informed from a person in Israel (see attachment) that an idea similar
> to
> > > mine is in
> > >
> > > http://xxx.lanl.gov/abs/quant-ph/9902035
> > >
> > > The abstract is:
> > >
> > > > Quantum Physics, abstract
> > > > quant-ph/9902035
> > > > From: Jan M Rost <rost@tqd1.physik.uni-freiburg.de>
> > > > Date: Tue, 9 Feb 1999 17:43:43 GMT (12kb)
> > > >
> > > > Time Dependence in Quantum Mechanics
> > > > Authors: John S Briggs, Jan M Rost
> > > > Comments: 7 pages, no figures
> > > >
> > > >
> > > > It is shown that the time-dependent equations (Schr\"odinger and Dirac)
> > > > for a quantum system can be always derived from the time-independent
> > > > equation for the larger object of the system interacting with its
> > > > environment, in the limit that the dynamical variables of the
> > > > environment can be treated semiclassically. The time which describes
> > > > the quantum evolution is then provided parametrically by the
> > > > classical evolution of the environment variables. The method used
> > > > is a generalization of that known for a long time in the field of
> > > > ion-atom collisions, where it appears as a transition from the full
> > > > quantum mechanical {\it perturbed stationary states} to the
> > > > {impact parameter} method in which the projectile ion beam is
> > > > treated classically.
> > > In the paper Briggs and Rost introduce a decomposition of the total Hamiltonian
> > > H similar to that of http://kims.ms.u-tokyo.ac.jp/time_VI.tex ; a decomposition
> > > of H into a sum of H_S of the system S under discussion and H_E of the
> > > environment E with a non-zero interaction term H_{ES} between them. They derive
> > > the existence of time for the system S from the *time-independent* Schroedinger
> > > equation (E-H) Psi = 0 for the total system. The argument is different from mine
> > > in the point that my argument that derives the nonzero interaction is a top-down
> > > argument from Goedel's incompleteness theorem, while they seem to derive it from
> > > the apparent existence of time for the system S (see section IV). In this point
> > > their argument seems circular, but the main point of their arguments is in
> > > showing that time is a (semi-)classical notion that arises from the interaction
> > > of the system S with the *classical* environment E, which is very similar to
> > > mine.

        I have been reading this paper slowly and several ideas and questions
popped out at me:

1) Does the discussion of a time-energy uncertainty operator agree with
Schommers thinking about time operators?

2) Is it merely the "size" of the environment of a quantum system that
allows it to be treated "semiclassically"?

3) It seems that the authors have not gotten past the assumption that
time is "external"; but there is some hope. They say "...the
$parametric$ time derivative arises from the expectation values of the
environment $operators$" and "...the time which arises is precisely the
time describing the classical motion of $E$, i.e. the classical
environment provides the clock for the quantum system."
        Here we have a situation that reminds me of the mind/body dichotomy!
Does time arise from classical motions or from quantum scattering, like
is mind epiphenomena of body [matter] or matter epiphenomena of mind
[information]? I see that in the dualistic view that I am advocating the
two are complementary, not dichotomous e.g. XOR, in a fundamental sense.
The key is to understand that any object that can be considered as being
a "part" of a "whole" will have a dual complement. The Universe, as the
totality of Existence, has no complement, and thus is not dual in
        I think that we should consider how the relational structures of both
LSs and their classical environments ot "outsides" can be modeled and
how can be define such concepts as mappings, equivalencies, fixed
points, etc. I do believe that we need to use non-well founded ZFA set
theory instead of the usual well-founded ZFC theory. Does this last
point make sense?

4) What is the connection between the Phi_n being complex valued and the
dynamical coupling terms giving geometric (Berry) phases? This notion
has been popping up in my studies and conversations with Paul Hanna and
Matti! I have an intuition that there is some clue to our problem hiding
here! :-) See, for instance:
http://www.aps.org/BAPSMAR98/abs/S3970005.html ("dangerously irrelevant"

> > > In showing this, they use an " 'entangled' wave function for the complete object
> > > composed of system and environment."
> > >
> > > I am not sure if their usage of the word "entangled" is the same as Robert's.
> > > But seeing their definition, the entangled state seems to be a (infinite and
> > > convergent) sum of tensor products of vectors (wavefunctions) belonging to
> > > Hilbert spaces HH_S and HH_E describing the interior and exterior systems S and
> > > E. If this is the case with Robert's thought I can understand what Robert wrote
> > > before.
> > Could Bill's infinite products be the classical (external) reflection
> > of this sum of wavefunctions? My idea, metaphorically rendered, is that
> > for every wave function there exists a space-time Minkowskian manifold
> > that has embedded within itself the trajectories of classical particles
> > that the wave function describes. Does this make any sense? :-)
> I assume you discuss a wave function of a local system. Then it is known that
> there corresponds a classical trajectory that describes the orbit where the QM
> particle condenses mostly. But in this case the space-time is Euclidean.
> Mikowskian or Riemannian manifold would be a consequence of observation IMO. And
> as understood as a observational manifold, I think your statement makes sense.

        Could we review the key differences between Euclidean and Minkowskian
manifolds? I see Euclidean manifolds as being strictly simply connected
topologically and Minkowskian manifolds as having null subspaces (light
cone structures) that divide the manifold into areas that are simply
connected (time-like) and multiply-connected (space-like).
        Since, the notion of a "observation manifold" seems to me to imply that
such is simply connected, we could identify (up to isomorphism!?) the
simply connected regions of a given Minkowskian manifold to a Euclidean
manifold of the same dimensionality. BTW, the algebraic {cohomology)
properties of these regions needs to be considered carefully! The
non-commutativity related to quantum mechanical canonical conjugates may
be related to the non-commutativity that exists in the multiply
connected regions of the Minkowskian manifolds. Umm, the spaces that
are complements of knots have similar properties! Is the statistical
connection the "missing link"?
        Do these words trigger any thoughts? :-)



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