# [time 1021] Re: [time 1018] Re: [time 1017] Re: [time 1013] [Fwd: Simpson's Paradox and Quantum Entanglement]

Tue, 23 Nov 1999 21:41:08 +0900

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 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?

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.

>
> 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.
>
> Circularity, per say, is not a problem if we are working within
> Non-well founded set theory (ZFA)... The main problem that I have run
> into is that thinking about time (viz. Van Benthem, et al) is confined
> to the ordinary ZFC system and thus we will need to think about this. I
> will be looking for persons interested in this area of research...
>
> > 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.

Best wishes,
Hitoshi

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