From: Arkadiusz Jadczyk (ark@...)
Subject: Re: second tangent map
Newsgroups: sci.physics.research
Date: 2002-01-06 14:13:23 PST
On Mon, 31 Dec 2001 00:13:24 +0000 (UTC), "bruno lemeri"
<blemeri@noos.fr> wrote: [unnecessary quoted text mercilessly eliminated by grumpy moderator] >I would like to know if the second tangent map F**:TTM->TTN has some
>interesting properties.
>
>Specifically,is it possible to define the acceleration of a curve in
>a manifold with a second tangent map ?

Though not directly answering your question, here is a hint:
second order frames allow us to define second order
objects. A connection is a such an object. And an affine connection,
in general relativity, tells us about acceleration. A conformal
connection is another second order object. Conformal transformations
involve accelerations. See Kobayashi, "Transformation groups
in differential geometry", Springer 1972.

ark

From: Arkadiusz Jadczyk (ark@...)
Subject: Re: Phase space
Newsgroups: sci.physics.research
Date: 2002-01-11 13:43:25 PST
On Fri, 11 Jan 2002 03:54:46 GMT, ultraman2002@hotmail.com (mandro)
wrote: >If configuration space C is a manifold, and a "momentum" is just
>
>the tangent vector of a curve in C,
>
>why is phase space P the cotangent bundle of C and not the tangent bundle?

The canonical symplectic form is on the cotangent bundle, not on the
tangent bundle. Lagrangian formalism deals with positions and velocities
(tangent bundle, or, better, jet bundle). Hamiltonian formalism deals
with positions and momenta (cotangent bundle). Metric sets a connection
between the two - but when metric is not fixed, or when it is
degenerate, then these are two different formalisms. ark

On Fri, 11 Jan 2002 03:54:19 GMT, Georgios Anagnostou
<ga@hep.ph.bham.ac.uk> wrote: > Is it true that in GR space-time are affecting each other while in the
>geometry of gauge theories in terms of fiber-bundles the base space is not
>affected by the existance of the internal space?
>
> Thanks
> G.Anagnostou
>
>[Moderator's note: For Yang-Mills-type gauge theories in and of
> themselves, this is true. Of course if the gauge theory exists in
> combination with general relativity, then since the gauge fields
> carry energy and momentum, they will have consequences for the
> geometry of the base space. -MM]

I agree with the moderator's note. But, as always, there are several
levels on which the question can be addressed. Gauge fields
often interact with "matter fields" - thought of as being represented by
sections of associated bundles. General relativity can be thought of
as such a theory, where the "matter field" is the "soldering form".
It is via this soldering form (which can be represented in different
ways in different versions of the theory) that "pure gauge theory"
of Lorentz (or Poincare, or SL(2C) or ...) intervenes in molding of the
geometry of space-time (the base manifold).

ark

From: Arkadiusz Jadczyk (ark@...)
Subject: Re: reasons for particle decay
Newsgroups: sci.physics.research
View: Complete Thread (5 articles) | Original Format
Date: 2002-01-18 12:40:03 PST
On 16 Jan 2002 15:24:10 -0000, "Bob Jones" <ulic_qel_droma@c4.com>
wrote: >I have some questions about the decay of elemtary particles.
>I have read many times that particles will spontaneously decay in about the
>amount of time that is their average lifetimes.
>What conjectures have been made as to the reasons for this decay?
>What I'm asking is, when everything seems to have some underlying cause, does
>decay lack cause? And if so, why?
>If anyone can help alleviate my curiosity, please do.

In order to answer this question other questions need to be addressed
first: 1) do truly random events exist in Nature?
2) if so - what is the definition and the operational meaning of a
"truly random event?"
3) if not - then do processes of complexity that is beyond human
comprehension, whatever it means" are thinkable, and can they
"exist" - whatever it means? It seems to me that your question about "causes" involves all
of the above. On the other hand, if you are satisfied with: "what is the algorithm
that Nature is using when generating events similar to radioactive
decay - a possible answer is "piecewise deterministic Markov process",
part of which is an inhomogeneous Poisson process. You can find refernces here: "EVENT ENHANCED QUANTUM THEORY AND PIECEWISE DETERMINISTIC DYNAMICS. " http://www.quantumfuture.net/quantum_future/jadpub.htm#blaja95a

ark

From: Arkadiusz Jadczyk (ark@...)
Subject: Re: Particle tracks
Newsgroups: sci.physics.research
View: Complete Thread (3 articles) | Original Format
Date: 2002-02-01 12:11:57 PST
On Fri, 1 Feb 2002 05:45:42 +0000 (UTC), Christopher Tyler <cwt@ski.org>
wrote: >My question is, what is the QM formulation for this highly
>predictable particle track in, say, 2 dimensions? I have asked many
>physicists but have yet to receive a straight answer.
>
>Many thanks,
>
>Christopher Tyler

PARTICLE TRACKS, EVENTS AND QUANTUM THEORY.
Progr.Theor.Phys. 93 (1995), 631-646 available also from http://www.quantumfuture.net/quantum_future/jadpub.htm#jad94b and also HOW EVENTS COME INTO BEING: EEQT, PARTICLE TRACKS, QUANTUM CHAOS, AND
TUNNELING TIME
in "Mysteries, Puzzles and Paradoxes in Quantum Mechanics",
Rodolfo Bonifacio, Ed., Woodbury, NY:
American Institute of Physics, 1999, [AIP Conference Proceedings,
no. 461], J. Mod. Opt. 47 (2000), 2247-2263, available from http://www.quantumfuture.net/quantum_future/jadpub.htm#jad94b#blajaru99 provides a mechanism for particle tracks within "Event Enhanced Quantum
Theory". The mechanisms works in any number of dimensions (see
also ON QUANTUM JUMPS, EVENTS AND SPONTANEOUS LOCALIZATION MODELS.
Found. Phys. 25(1995) 743-762 http://www.quantumfuture.net/quantum_future/jadpub.htm#jad94b#jad94c I have a computer simulation of the piecewise deterministic Markov
process ( a uniques single-system solution to the Liouville equation) -
and you can see with your own eyes, in real time, how a simulated
track is being formed. The Poisoon process for the track is
non-homogeneous, controlled by the quantum particle wave-function
and its relation to the "detectors" and their "state" (grains on the
photographic plate in our case) Even if this is only one of several possible approaches, yet it works,
so I hope it helps.

ark

From: Arkadiusz Jadczyk (ark@...)
Subject: Re: How to measure velocity in quantum?
Newsgroups: sci.physics.research
View: Complete Thread (25 articles) | Original Format
Date: 2002-02-01 18:35:12 PST
On Thu, 31 Jan 2002 16:35:45 GMT, "Norm Dresner"
<ndrez@worldnet.att.net> wrote: > Are there any good references to enable me to start to understand
>these checkerboard models?
>
>Thanks
> Norm

Hi, Check "The Feynman Propagator from a Single Path" Authors: G. N. Ord, J. A. Gualtieri http://xxx.lanl.gov/abs/quant-ph/0109092 and references therein. Write to Ord for more references.

ark

From: Arkadiusz Jadczyk (ark@...)
Search Result 7
Subject: Re: Hilbert spaces in quantum mechanics
Newsgroups: sci.physics.research
View: Complete Thread (2 articles) | Original Format
Date: 2002-02-09 15:09:35 PST
On Wed, 6 Feb 2002 22:56:06 +0000 (UTC), Anselmi_Fabio@hotmail.com
(fabio) wrote: >Hi!
>I'm an italian student in Physics.
>1) I know that there is an isomorphism between an the hilbert space of
>the quantum states (ket) and the space of linear functionals (bra)
>given by Riesz's lemma.
>2) I also know that there is an isomorphism (Jamiolkowski isomorphism)
>between the set of quantum operators and the set of superoperators
>(maps acting on operators).
>My question is : does exist any isomorphism (that respect the
>principles of quantum mechanics) between the sets that I have
>mentioned in 1) and those in 2)?

I do not know why you call it "Jamiolkowski theorem". It is known from the theory of vector spaces that L(V tensor W) = L(V) tensor L(W) and that X tensor Y = L (X*,Y) Thus L(V tensor W) = L(L(V)*,L(W)) For finite dimensional spaces L(V)* is isomorphic to L(V)
thus you have what you call "Jamiolkowski theorem" http://www.itp.uni-hannover.de/~kreutzm/data/qit_main.pdf Yes, the above have to do with Riesz's theorem - a similar
reasoning is needed.

ark

From: Arkadiusz Jadczyk (ark@...)
Search Result 6
Subject: Re: metric on the space of metrics
Newsgroups: sci.physics.research
View: Complete Thread (20 articles) | Original Format
Date: 2002-02-16 22:17:11 PST
On Thu, 14 Feb 2002 20:21:41 +0100, Urs Schreiber
<Urs.Schreiber@uni-essen.de> wrote: >So, will you now be looking for the curvature of the space of
>Riemann curvature tensors? I do not dare to imagine what
>meta-meta-idea you're after, but I'd be interested in the
>torsion of the space of torsion tensors... :-)

J.A. Wheeler, in "Superspace": "Not space, nor space-time, but
superspace is the dynamical arena of geometrodynamics, both classical
and quantum." Now, what IS superspace, is million dollar question. Usually is
is "space of geometrical structures of some kind" modulo some group
acting on this space. The devil, as always, is in the details. Space of metrics is one choice. Space of connections (or of gauge
fields) is another choice. Space of torsions would be, I think, an
awkward choice, as well as space of curvatures - becuse one would first
give and abstract definition of a torsion or of a curvature, independent
of the connection from which it comes from. The point is that it is possible to construct an action principle out of
metric alone, but also, which is less known, out of a connection alone.

ark

From: Arkadiusz Jadczyk (ark@...)
Search Result 2
Subject: Re: some problems about the two-slit experiment in quantum
Newsgroups: sci.physics.research
View: Complete Thread (17 articles) | Original Format
Date: 2002-03-06 19:34:02 PST
On Tue, 5 Mar 2002 20:18:57 +0000 (UTC), kevin@inky.its.caltech.edu
(Kevin A. Scaldeferri) wrote: >>Ahm... Well, I take the view of Leslie E. Ballentine's text book, "Quantum
>>Mechanics, A Modern Development", i.e. "the collapse of the wave function" is
>>also "imaginary". i.e. it don't exist. Its a complete nonsense concept that
>>results from a false interpretation of QM, i.e. an interpretation that
>>Ballentine clearly shows results in a contradiction with experiment.
>
>Hmmm... what is this contradiction? (Or, rather, disagreement. You
>can't have a contradiction with experiment.)

In fact, Ballentine is wrong. Makes an elementary misrake. See
the following papers available on the CASSIOPAEA web site PARTICLE TRACKS, EVENTS AND QUANTUM THEORY
http://quantumfuture.net/quantum_future/papers/9407157.pdf and especially TIME OF EVENTS IN QUANTUM THEORY.
http://www.quantumfuture.net/quantum_future/papers/time/time.html the last paper quotes Ballentine's paper. (Reference [4])

ark

From: Arkadiusz Jadczyk (ark@...)
Search Result 1
Subject: Re: Many Worlds, Copenhagen & Simultaneous Measurement Paradox
Newsgroups: sci.physics.research
View: Complete Thread (2 articles) | Original Format
Date: 2002-03-06 19:34:03 PST
On Tue, 5 Mar 2002 20:14:56 +0000 (UTC), whopkins@alpha2.csd.uwm.edu
(Mark) wrote: > Non-commuting operators cannot be applied simultaneously

Who says so and why? Check papers available on the Cassiopaea
web site: HOW EVENTS COME INTO BEING: EEQT, PARTICLE TRACKS, QUANTUM CHAOS, AND
TUNNELING TIME
http://www.quantumfuture.net/quantum_future/papers/garda.htm
COMPLETELY MIXING QUANTUM OPEN SYSTEMS AND QUANTUM FRACTALS
http://www.quantumfuture.net/quantum_future/chaos.htm
EEQT A WAY OUT OF THE QUANTUM TRAP
http://www.quantumfuture.net/quantum_future/papers/petruc/petruc.html
TOPICS IN QUANTUM DYNAMICS.
http://quantumfuture.net/quantum_future/papers/9506017.pdf
RELATIVISTIC QUANTUM EVENTS
http://quantumfuture.net/quantum_future/papers/9610028.pdf Very soon (a week or two from now) online simulations of chaos caused by
"simultaneous mesurement" of noncommuting quantities (in java) will be
available. I say "simulatenous" in quotation marks because the theory and
simulation deals with "cotinuous" measurement - that is extended
in time - as any real measurement is.

ark