**Stephen Paul King** (*stephenk1@home.com*)

*Tue, 23 Nov 1999 15:35:39 -0500*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Stephen Paul King: "[time 1024] Johan van Benthem"**Previous message:**Hitoshi Kitada: "[time 1022] Re: [time 1020] Power in the control of Time"**In reply to:**Stephen Paul King: "[time 1009] [Fwd: Simpson's Paradox and Quantum Entanglement]"**Next in thread:**ca314159: "[time 1026] Simpson's Paradox"

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
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*> 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
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*> unsubscribed today. I do not detain them who do not try to be patient, but I
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*> feel some difference between the westerners and asians. The asians are not too
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*> hurry to lose something that might be gotten by being patient, while the
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*> westerners seem not like to be patient. I should state that this difference is
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*> not a result of observation of short term. Does anyone have anti-opinions or any
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*> 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
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*> Quantum Entanglement]
*

*>
*

*> > Dear Hitoshi, Tito, Robert and Friends,
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*> >
*

*> > This is a cause for happiness! We still have much work to do in the
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*> > area of figuring out the way to model the classical environment E of a
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*> > quantum mechanical Local System.
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[HK]

*> I agree. The unknown world or the environment E would certainly contain things
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*> which are worth being attempted to know. The things to which we address the word
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*> "mystic" would be just the things belonging to the unkown environment E because
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*> the universe includes the whole and therefore must include the mystic things
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*> also. Newton's investigation into mystic things might not mean his hobbies in
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*> 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

duality.

*> >
*

*> > Hitoshi Kitada wrote:
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*> > >
*

*> > > Dear Robert, Stephen, et al.,
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*> > >
*

*> > > I was informed from a person in Israel (see attachment) that an idea similar
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*> to
*

*> > > mine is in
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*> > >
*

*> > > http://xxx.lanl.gov/abs/quant-ph/9902035
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*> > >
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*> > > The abstract is:
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*> > >
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*> > > > Quantum Physics, abstract
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*> > > > quant-ph/9902035
*

*> > > > From: Jan M Rost <rost@tqd1.physik.uni-freiburg.de>
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*> > > > Date: Tue, 9 Feb 1999 17:43:43 GMT (12kb)
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*> > > >
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*> > > > Time Dependence in Quantum Mechanics
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*> > > > Authors: John S Briggs, Jan M Rost
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*> > > > Comments: 7 pages, no figures
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*> > > >
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*> > > >
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*> > > > It is shown that the time-dependent equations (Schr\"odinger and Dirac)
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*> > > > for a quantum system can be always derived from the time-independent
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*> > > > equation for the larger object of the system interacting with its
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*> > > > environment, in the limit that the dynamical variables of the
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*> > > > environment can be treated semiclassically. The time which describes
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*> > > > the quantum evolution is then provided parametrically by the
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*> > > > classical evolution of the environment variables. The method used
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*> > > > is a generalization of that known for a long time in the field of
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*> > > > ion-atom collisions, where it appears as a transition from the full
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*> > > > quantum mechanical {\it perturbed stationary states} to the
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*> > > > {impact parameter} method in which the projectile ion beam is
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*> > > > treated classically.
*

[HK]

*> > > In the paper Briggs and Rost introduce a decomposition of the total Hamiltonian
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*> > > H similar to that of http://kims.ms.u-tokyo.ac.jp/time_VI.tex ; a decomposition
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*> > > of H into a sum of H_S of the system S under discussion and H_E of the
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*> > > environment E with a non-zero interaction term H_{ES} between them. They derive
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*> > > the existence of time for the system S from the *time-independent* Schroedinger
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*> > > equation (E-H) Psi = 0 for the total system. The argument is different from mine
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*> > > in the point that my argument that derives the nonzero interaction is a top-down
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*> > > argument from Goedel's incompleteness theorem, while they seem to derive it from
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*> > > the apparent existence of time for the system S (see section IV). In this point
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*> > > their argument seems circular, but the main point of their arguments is in
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*> > > showing that time is a (semi-)classical notion that arises from the interaction
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*> > > of the system S with the *classical* environment E, which is very similar to
*

*> > > mine.
*

snip

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

it-self.

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.nando.net/newsroom/ntn/health/060198/health10_20653_body.html

http://www.cds.caltech.edu/cds/seminars/old/1996/96-01-22.Newton.html

http://gandalf.iap.physik.uni-tuebingen.de/hasselbach/interfer/frha/frhasagn.html

http://physicsweb.org/article/news-1998-01-01-02-01-01

http://www.aps.org/BAPSMAR98/abs/S3970005.html ("dangerously irrelevant"

????)

*> > > In showing this, they use an " 'entangled' wave function for the complete object
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*> > > composed of system and environment."
*

*> > >
*

*> > > I am not sure if their usage of the word "entangled" is the same as Robert's.
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*> > > But seeing their definition, the entangled state seems to be a (infinite and
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*> > > convergent) sum of tensor products of vectors (wavefunctions) belonging to
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*> > > Hilbert spaces HH_S and HH_E describing the interior and exterior systems S and
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*> > > E. If this is the case with Robert's thought I can understand what Robert wrote
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*> > > before.
*

[SPK]

*> > Could Bill's infinite products be the classical (external) reflection
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*> > of this sum of wavefunctions? My idea, metaphorically rendered, is that
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*> > for every wave function there exists a space-time Minkowskian manifold
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*> > that has embedded within itself the trajectories of classical particles
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*> > that the wave function describes. Does this make any sense? :-)
*

[HK]

*> I assume you discuss a wave function of a local system. Then it is known that
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*> there corresponds a classical trajectory that describes the orbit where the QM
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*> particle condenses mostly. But in this case the space-time is Euclidean.
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*> Mikowskian or Riemannian manifold would be a consequence of observation IMO. And
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*> 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? :-)

Later,

Stephen

**Next message:**Stephen Paul King: "[time 1024] Johan van Benthem"**Previous message:**Hitoshi Kitada: "[time 1022] Re: [time 1020] Power in the control of Time"**In reply to:**Stephen Paul King: "[time 1009] [Fwd: Simpson's Paradox and Quantum Entanglement]"**Next in thread:**ca314159: "[time 1026] Simpson's Paradox"

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