Stephen Paul King (stephenk1@home.com)
Wed, 24 Nov 1999 15:08:48 -0500
Dear Hitoshi and Friends,
I sniped to save space...
Hitoshi Kitada wrote:
snip
> > > > 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
snip
[SPK]
> > 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?
[HK]
> In the sense of section 5.3.5 of "Quantum Theory and Pictures of Reality" edited
> by Schommers, Schommers' thinking seems to agree. But the formulation in the
> former section of the book looks different.
Yes, I was wishing that we could take a look at this difference. The
problem I see is that it is very hard to do this within the narrow
window of these posts... The ontological assumptions that Briggs & Rost
use are very different from that of Schommers. I think that this is
significant, but they both seem to be stuck in the Priorian mode of
thinking, e.g. that the space-time manifolds exist a priori, as
illustrated in the 4-dimensional block universe metaphor. This is that I
call the initiallity assumption, which I believe to be a key problem
that we can overcome by using a non-well founded set theoretical
formalism and thinking methods. This is the reason for my mention of
Peter Wegner's papers.
[SPK]
> > 2) Is it merely the "size" of the environment of a quantum system that
> > allows it to be treated "semiclassically"?
[HK]
> In Briggs and Rost paper they seem to think so, but there might be a question on
> this point.
Yes! I am reminded of a post by Paul Snyder on sci.physics.research
that seems to back up our claim that clocking and observing in general
is a subjective activity.
Re: Is there a fundamental distance in GR?
On Tue, 23 Nov 1999 02:34:22 GMT, in sci.physics.research "Paul Stewart
Snyder" <ps@ws5.com> wrote:
>There is good reason to believe that "time" is
>not a fundamental variable in GR, that in fact it is
>derived from other observables. This raises the
>question, does distance exist as a fundamental
>variable in GR? Popular text books describe
>rulers shrinking as one approaches the speed
>of light, suggesting that an absolute distance at
>rest is somehow squished by increased speed.
>Of course relativity tells us that we cannot prefer
>the measurement of the length of the ruler at one
>speed to the measurement at any other speed.
>So are we not left with a relative measure of
>distance that has no single value, or meaning?
>
>Several writers have noted that, for example, in
>a three particle (A,B,C) universe, the "distance"
>from A to C can only be measured by reference
>to the distance from A to B. Yet, if the distance
>separating all the particles doubles, there is no
>measurement or experiment that can be
>performed that will establish that fact. So long
>as all "distances" increase or decrease by the
>same factor it is impossible to detect the change.
>
>This leads me to believe that there is no such
>thing as "distance" or "length" between the
>particles. It looks like the spatial separation from
>A to B can only be given as a proportion of the
>separation from A to C. A to B may have twice the
>separation of A to C, however we simply cannot
>say in any meaningful way what that separation is.
>
>Does this mean that there is no such thing as
>distance, or does it simply mean that we cannot
>measure the inherent distance between objects?
>It seems to me that relativity tells us that there is
>no such thing as distance/length, that in fact there
>is only proportional separation between objects.
>If true, this might be significant. Is it possible that
>the spatial separation of objects is truly relative,
>and that there is no such thing as "distance"?
>
>PS
[SPK]
> > 3) It seems that the authors have not gotten past the assumption that
> > time is "external";
[HK]
> Do you mean t in equation (18)?
Yes, the use of the t term in the "$classical$ momentum vector of the
environment $E$" is the case in point. I think that it is the way that
the space-time framing of observations is given that causes confusion.
Matti's use of at least two different "times" (geometric and subjective)
I see as an attempt to clear things up.
> >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!
[HK]
> Could you explain more about the relation between the mind/body dichotonomy and
> the sentences you quoted from Briggs and Rost?
The mind/body dichotomy arises when we try to force a monistic paradigm
on the subsets of the Universe. Since choosing either materialism or
idealism still requires an accounting of time and humans have an
predisposition toward the tacit assumption that time is external, it is
no surprise that Briggs and Rost identify the two times. We need to
understand that the classical Environments of each observer are not one
and the same! It is their similarity that creates this illusion. If we
are to consider that the internal Euclidean R^6 spaces of LS are, in
general, orthogonal, then so too would their external Minkowskian
space-time framings! This is why I advocate a bisimulation type of model
for interactions.
The synchronization of the internal clocking of the quantum system (LS)
and the external event ordering ("geometric time") is the key. This is,
I believe, the long sought Cartesian connection.
This is perhaps interesting:
http://www.zrc-sazu.si/www/fi/vestniki/sinop396.htm
and
for reference:
http://www.funkandwagnalls.com/encyclopedia/low/articles/m/m016002379f.html
If we think of the Mind of an observer as a structure M (like a
n-dimensional graph were individual qbits are the nodes and logical
precedence relations are the edges) and consider the consciousness of
such as the "center of mass" of M, then, perhaps, we can consider the
"flow" of consciousness as the result of changes in the overall
structure M. As M evolves (exponential decay of the scattering?) the
expectation values change thus the edge connections change.
> > 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!
[HK]
> I have to ask you more explanation of your idea you mention here.
This evolved from the reading of papers by Aharonov et al:
http://xxx.lanl.gov/abs/quant-ph/9909072
http://xxx.lanl.gov/abs/quant-ph/9708043
http://xxx.lanl.gov/find/quant-ph/1/au:+Aharonov_Y/0/1/0/all/0/1
and the mention of the Berry phase in:
http://xxx.lanl.gov/abs/quant-ph/9902037
My thought are still very vague at this stage... I am wondering about
the reasons why there is a choice between real and complex valuations of
\Phi_m in equation (A6) and in the equations representing quantum
systems in general...
snip
SPK]
> > > > 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? :-)
[HK]
> > > 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.
[SPK]
> > 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.
[HK]
> There is topological difference but it is possible to identify them at least
> formally by replacing t by it as is sometimes done in QFT.
Yes, over all there is a topological difference in the manifolds
overall, but I was thinking that we could identify the simply connected
submanifold of the Minkowskian Manifold with the Euclidean manifold,
e.g. is there an isomorphism between the time-like region of a
Minkowskian manifold and a Euclidean manifold.
> > 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
This archive was generated by hypermail 2.0b3 on Wed Dec 01 1999 - 01:15:40 JST