Stephen Paul King (stephenk1@home.com)
Sun, 21 Nov 1999 14:54:20 -0500
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.
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? :-)
> Their work suggests that the investigation of time becomes within a reach of
> concrete physics, i.e. one can produce papers on time as one of the usual
> researches as other physical areas. The period for paradigm shift might have
> ended, and a time industry seems to be starting.
Hurray!
> Best wishes,
> Hitoshi
>
> ----- Original Message -----
> From: ca314159 <ca314159@bestweb.net>
> To: <vecchi@weirdtech.com>
> Cc: Stephen Paul King <stephenk1@home.com>; Time List <time@kitada.com>
> Sent: Saturday, November 20, 1999 11:22 AM
> Subject: [time 1013] Re: [time 1010] Re: [time 1009] [Fwd: Simpson's Paradox and
> Quantum Entanglement]
>
> > I.Vecchi wrote:
> > >
> > > Stephen Paul King wrote:
> > > >
> > > > Hi All,
> > > >
> > > > Robert Fung is making some great points!
> > > >
> > > > Later,
> > > >
> > > > Stephen
> > > >
> > > > ... entanglement is an additional problem when you consider
> > > > not just the state-space of a single particle, but the
> > > > state space of two particles that interacted and so their
> > > > PD's and PDF's have some memory of that event as if they
> > > > were two bell's (or impulse response functions[1]) that
> > > > once clanged together and when separated, they maintained
> > > > a "memory" of that event in their separate sets of PDs and PDFs.
> > > > Those separate memorys are what allow the two particles
> > > > to be non-locally correlated, or "entangled".
> > > >
> > > > Those memories however tend fade away (decohere) after a while.
> > > > But they should be maintainable, by a _local_ resonant
> > > > communications between the entangled particles.
> > > >
> > > > Of what use that may be to quantum cryptography &c.,
> > > > I am not concerned with, as I think there are more significant
> > > > implications than that.
> > > >
> > >
> > > Decoherence is indeed a slippery concept, often used in an improper way.
> > > The above statement about "fading memories" is in my opinion confusing.
> > > The point is that decoherence does not destroy long-range quantum
> > > superpositions. Decoherence just limits the ability of an observer
> > > subject to the second principle of thermodynamics to keep track of such
> > > superpositions.
The idea of memory seems to point to the metaphor of a dependence of an
objects properties on some particular history. As interactions continue,
the possible histories of the object tends to become multivalued, so the
relationship that you point out here is very valid. What we perhaps need
to look at more closely is the relationship between thermodynamic
entropy and information!
> > Superpositions are not necessarily entanglements.
> > A superposition is what happens at a beam splitter.
> > An entanglement is what happens in a non-linear crystal.
> >
> > Zeilinger et al, don't use beamsplitters to make entangled
> > particle pairs. Superpositions and entanglements are different.
> >
> > Wavefunction collapse can be alot like tapping a computer
> > programmer on the shoulder while s/he is in deep superposition
> > of many associated concepts; destoying their concentration.
> >
> > Decoherence is like you say, a loss of the ability to
> > make meaningful distinguishments, or the loss of the ability
> > to maintain a record of a past event (entanglement) and
> > this diffusion or dispersion does not destroy all record
> > of the past event but makes it increasingly unrecoverable
> > in a theromdynamic sense, which itself can probably be modelled
> > as a damping in an impulse-response (Green's functions) sense,
> > like a pair of bells having clanged against each other
> > and that ringing of each bell, fading like a memory of
> > the past as the energy of the event disperses within the bell.
> >
> > Single-moded spatio-temporal solitons (light-bullets)
> > are recognized for their ability to resist such dispersion
> > and are proposed for this reason as candidates for qubits
> > which resist decoherence. Other possibilities for
> > decoherence resistent qubits might be BE condensates,
> > superconductors, and superfluids, and extremely stabilized
> > laser-light (non-interaction experiments); all of which
> > effectively seem to homogenize their component units to the
> > point where they act in extreme unison (coherence).
> >
> > Pure coherence, unadulterated, is apparently not possible
> > in any finitely bounded system. But we none-the-less have
> > computers, which function almost completely as if this
> > idealism of both continuity and closure were attainable in a
> > finite system.
> >
> > The Zen master will tap the meditating student on the shoulder
> > to remind him that closures are indeed just as much a part of
> > life as coherence. Decisions have to be made.
> >
> > An electric battery represents distinguishment. Its potential
> > energy is meaningless without continuity (a circuit).
> > But shorting out the terminals of the battery and explosively
> > releasing all its energy is also meaningless.
> >
> > We build an electric circuit with resistance (decoherence) and
> > yet it can still have meaning, but that meaning is (as Stephen
> > minds me) is generally derived from outside the energy
> > economy of that circuit.
> >
> > The battery's energy is eventually depleted and it fails
> > to serve its purpose to make some form of distinguishment.
> >
> > In order for its purpose to survive, the energy must
> > be replenished from the outside, but not with excessive
> > greed (we live off the land and should respect the Time
> > it takes to feed us and itself).
Kindest regards,
Stephen
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