From: Arkadiusz Jadczyk (ark@...)

Subject: Re: Probability theory & Quantum mechanics.
Newsgroups: sci.physics.research
View: Complete Thread (2 articles) | Original Format
Date: 2002-03-17 15:44:23 PST

On Tue, 12 Mar 2002 08:36:58 +0000, Charles Francis
<charles@clef.demon.co.uk> wrote:

>But in any case understanding quantum probability is not sufficient to
>constitute a full interpretation of quantum mechanics. To do that the
>Schrodinger equation must also be explained. It is a good step forward
>to separate off the probabilistic part of the model, which applies at
>any time, from the evolution of the model through time.

Is it really a good step forward? I am not convinced.
In fact, I doubt. It would take a long post to explain why,
so let me just give an example. In EEQT the aim is to derive the
probabilistic interpretation from the dynamics. That is we
have a Markov process ( a standard one, but on a
peculiar space), we have a pointer that shifts
accordingly, and we deduce that pointers
positions are related to the wavefunction that
approximately (exactly in some limit) reproduces
what we call "probabilistic interpretation".
But the point is that it works also in indefinite
metric Hilbert space, where normal probabilistic
interpretation would fail. The Markov process
is standard, its governed by positive transition
probabilities. So, on this example we see that
deriving the probability interpretation from some
deeper dynamical (or "binamical" - in this case)
principle may have some advantages.

This is like the factorial function. At first we
have it only for natural numbers. But once we
understand it deeper, once we know about
Gamma function, we can do more things.

Once we understand where the peculiar
probabilistic interpretation is coming from -
we can do more.

ark

From: Arkadiusz Jadczyk (ark@...)

Subject: Re: Lie Algebras / Operators
Newsgroups: sci.physics.research
View: Complete Thread (6 articles) | Original Format
Date: 2002-03-18 05:31:26 PST

On Fri, 15 Mar 2002 00:42:09 +0000 (UTC), baez@galaxy.ucr.edu (John
Baez) wrote:

>In physics, elements of your Lie group of symmetries act as unitary
>operators, while elements of the corresponding Lie algebra act as
>Hermitian operators. Unitary operators describe "processes" - things
>you can "do" to a system. Hermitian operators describe "observables" -
>things you can "measure" about a system.
>
>To get from the Lie algebra to the Lie group, or from the Hermitian
>operators to the unitary ones, you need to exponentiate.
>
>In particular, if J_k is the Hermitian operator for angular momentum
>about the kth axis,
>
>exp(i theta J_k)

To be precise: elements of the Lie algebra acts as anti-hermitian
rather than hermitian operators.

In a complex Hilbert space, but ONLY in this case, we have
at our disposal "i" which commutes with all coplex linear operators,
and which serves as a handy links between generators of symmetries
and observables. But in real or quaternionic Hilbert spaces we do
not have such a handy gadget. In these theories there is no
simple connection between symmetries and conserved quantities.

ark

Subject: Re: Ref for Lichnerowicz eqn
Newsgroups: sci.physics.research
View: Complete Thread (8 articles) | Original Format
Date: 2002-03-19 13:50:02 PST

On Tue, 19 Mar 2002 03:38:53 GMT, Urs.Schreiber@uni-essen.de (Urs
Schreiber) wrote:

>
>But what I do not know at all is: How does the Lichnerowitz
>formula help in calculating the variation of the Ricci tensor?

That was also my thought. You calculate variation of the Levi-Civita
connection, and from that you calculate variation of the curvarture
tensor and, by contraction, of the Ricci tensor.
When deriving field equations one has to be careful though:
in metric-affine theories connection and the metric are considered
to be apriori independent. Therefore Ricci tensor is a function of
the connection alone, it does not depend on the metric. Only scalar
curvature depends.

ark

Subject: Re: local gauge invariance
Newsgroups: sci.physics.research
View: Complete Thread (8 articles) | Original Format
Date: 2002-03-19 18:40:59 PST

On Mon, 18 Mar 2002 12:10:53 GMT, Daniel Doro Ferrante
<danieldf@het.brown.edu> wrote:

>For example, if I want to
>> construct a theory from first principles, based on the least amount of
>> assumptions, why would I necessarily include local gauge invariance?
>>
>I think there's a good motivation for this on Weinberg's book
>(QFT, vol 1, i think).

As Hans Ekstein wrote in 1979:

"All gauges are equal, but some are more equal than other."

Gauge invariance is a powerful principle - it allows us to deduce
charge conservation (or generalized "Higgs charge" for non-Abelian gauge
groups.). But are we sure that charge is conserved?
How sure? And what is charge anyway? Do charges exist?
Perhaps they are approximations to very complex topological
structures? Like kinks and/or knotted wormholes in fractal
spacetimes?

Now, gauge invariance principle is sometimes understood as
Gauging of a symmetry group." Thus, for instance, we "gauge Poincare
group." In geometrical terms we introduce an abstract principle bundle
with P as its structure group, and with a principal connection. The next
step is to "solder" this bundle, somehow, to the frame bundle, usually
by introducing soldering map as a dynamical filed and coupling it
to the connection. There are many ways in which such theories
can be produced. It all has to do with the general prgram of
"geometrization of physics".
It is also important to realize that we are at the beginning rather than
at the end of this program. There is no reason to restrict to first
or second order structures.

ark

Subject: Re: What If Ether Frame Existed? Galilean-Invariant Maxwell Eqs.
Newsgroups: sci.physics.research
View: Complete Thread (27 articles) | Original Format
Date: 2002-03-21 20:37:25 PST

On Wed, 6 Mar 2002 09:54:27 +0000 (UTC), Moataz Emam
<emam@physics.umass.edu> wrote:

>This is interesting. It reminds me of the famous Feynman derivation of
>Maxwell's homogenous equations. He starts with space-momentum
>commutation relations and F=ma. With an elaborate, yet straightforward
>calculation, he manages to derive the Maxwell equations, never using
>relativity at any point.

If you are really really careful, if you understand that momentum
operators are unbounded, with a dense domain where they are
self-adjoint, when you exponentiate their commutation relations, so as
to get finite quantities - then you get cocycle-like relations which
tell you that Maxwell equations _can_ be violated on a set of measure
zero - thus you allow for for discrete magnetic monopoles. From the
cocycle relation you derive at the same time quantization of the
magnetic charges.

ark

From: Arkadiusz Jadczyk (ark@...)

Subject: Re: Photons travelling fater than c?
Newsgroups: sci.physics.research
View: Complete Thread (9 articles) | Original Format
Date: 2002-03-22 23:19:11 PST

On Thu, 21 Mar 2002 04:06:20 +0000 (UTC), warpbauble@yahoo.com (Corey
Hart) wrote:

>Question: is it possible to construct a spacetime in which photons
>travel faster than c (3*10^8 m/s) if all particle world lines stay
>within the local lightcones of these photons?

Your question needs to be refined, as geoemtrical model of gravity does
not know what is "m/s" ;-)

So, my suggestion is to replace your question with a different one:

Given a 4-manifold with a conformal structure (= light cone structure)
is it always possible to deform the conformal structure in in such a way
that the old light cones are properly included in the new ones?

Locally the answer is yes. But are there possible topological
obstructions from doing it globally?

Of course my interpretation of your question may be wrong....

ark

Subject: Re: Solar System Atoms & Loretz Transformations (was: Dirac's "sea of electrons")
Newsgroups: sci.physics.research
View: Complete Thread (3 articles) | Original Format
Date: 2002-03-27 18:59:24 PST

On Fri, 22 Mar 2002 04:23:37 GMT, "Danny Ross Lunsford"
<antimatter33@worldnet.att.net> wrote:

>What you are saying is that the solar system and the uranium system have
>central potentials to a first approximation. After that, there isn't much in
>common between them.

There may be more than that, but we are not aware of it as yet.
There are quantization effects on the cosmic scale that lead
to speculations and theories going beyond the present paradigm:

[Barnothy 74] J.M. Barnothy, "Can the solar system be quantized?", in
Proceedings of the IAU Symposium 62 , 'The Stability of the Solar System
and of Small Stellar Systems', Y. Kozai (ed.), Reidel 1974
[Lehto 90] Ari Lehto, "Periodic Time and the Stationary Properties of
Matter", Chin. J. Phys. 28(1990), 215-236
[Lehto 98] Ari Lehto, "On the Invariant Properties of Matter",
Contribution to the 10th Anniversary Volume of The Finnish Society for
Natural Philosphy, pp.179-200
[Rubcic 98] Antun Rubcic and Jasna Rubcic, "The Quantization of the
Solar-like Gravitational Systems", Fizika B7 (1998), 1-13
[Tifft 96a] W.G. Tifft, "Evidence for Quantizad and Variable Redshifts
in the Cosmic Bacground Rest Frame", Astrophysics and Space Science 244
(1996) 29-56
[Tifft 96b] W.G. Tifft, "Three-dimensional Quantized Time in Cosmology",
Astrophysics and Space Science 244 (1996) 187-210
[Nottale 97] L. Nottale, G. Schumacher, and J. Gay, "Scale Relativity
and Quantization of the Solar System", Astronomy and Astrophysics 322
(1997) 1018
But check also
[Hayes 98] W. Hayes and S. Tremaine, "Fitting Selected Random Planetary
Systems to Titius-Bode Laws", Icarus 135 (1998), 549-557

ark

Subject: Re: Information and Physics [Was: Conservation of Information]
Newsgroups: sci.physics.research
View: Complete Thread (2 articles) | Original Format
Date: 2002-03-27 19:26:56 PST

On Tue, 19 Mar 2002 21:43:48 +0000 (UTC), Chris Hillman
<hillman@math.washington.edu> wrote:

>> I never encountered any "conservation of information" laws in
>> undergraduate physics; must be one of those graduate courses I missed
>> since I didn't go for a doctorate.
>
>No, you didn't hear about such a law because there -isn't- any such law!

In our semi-phenomenological "event enhanced quantum theory (or EEQT)"
as described in "EEQT A WAY OUT OF THE QUANTUM TRAP" we wrote:

"It is to be noted that the time evolution of statistical ensembles is
due to the presence of 's, non-automorphic. The system, as a whole, is
open. This is necessary, as we like to emphasize: information (in this
case: information gained by the classical part) must be paid for with
dissipation! The appropriate mathematical formalism for discussing the
ensemble level is that of completely positive semigroups, as discussed
by Kossakowski et al.[..]

http://www.quantumfuture.net/quantum_future/papers/petruc/petruc.html

That observation came from realization that every automorphism a C*
algebra maps center into center, therefore automorphic evolution of the
classical observables can not mirror in any way what happens to the
quantum part of the total system. There is no information transfer from
quantum to classical in an automorphic evolution. Thus: "information
must be paid with dissipation." In this case by "information" we mean
"information about the quantum state" transmitted to a classical (i.e.
Boolean logic+monitoring without perturbation) system. We tried to find
a quantitative law that would express this observation - but we did not
succeed. Still I hope that one day such a law will be found.
BTW the non-automorphic part of the evolution, the one responsible
for information transfer - we called it "binamics" in contrast to
"dynamics." While dynamics is due to exchange of forces (dyna), binamics
is due to exchange of "bits". But again, the precise formulation
of quantitative laws is still missing. What we have is a general
mathematical framework, some theorems and some examples.

ark

Subject: Re: Simple question related to basic quantum mechanics
Newsgroups: sci.physics.research
View: Complete Thread (16 articles) | Original Format
Date: 2002-04-01 09:20:57 PST

On Fri, 29 Mar 2002 02:08:07 GMT, "mark howe" <markhowe@tinet.ie> wrote:

>Can you prove the Schrodinger equation? Or more precisely, that the
>Hamiltonian operator is the energy operator? And if you can, does this
>proof only involve the commutator relations, or is some 'other' idea
>necessary?
>
>I would very much appreciate help with this.
>
>Sincerely,
>
>Mark Howe.

It all depends on assumptions and how did you get to the Schroedinger
equation. What is taken as an assumption in one book is being proven
in another book, and conversely.

Some books start with the quantization rules that associate operators
with classical functions of position and momentum. These rules
work to some extent. Some books start with irreducible unitary
representations of the Galilei group. There you get automatically the
correct form for time translation generator - you get the Laplace
operator, and you can also get the Pauli equation for particles
with spin. This works for free particles though. One can generalize
the method for homogeneous fields. From there on it becomes
somewhat fuzzy and no good method that I know know exeists,
except by "generalizing" and "geometrizing." Hans Ekstein tried
to extend this group theoretical method using the concept of
presymmetries, but he left this program unfinished. What
we have today is "gauging of symmetrties" - a very fuzzy and
incomplete set of ideas and skills.

But, as I said, there will be many other who will answer your question
in completely different ways. Youd did not make your assumptions
clear.

ark

Subject: Re: Covariant Derivative
Newsgroups: sci.physics.research
View: Complete Thread (4 articles) | Original Format
Date: 2002-04-08 13:00:13 PST

On Mon, 18 Mar 2002 23:12:47 +0000 (UTC), Terry Pilling
<terry@offshell.phys.ndsu.nodak.edu> wrote:

>The covariant derivative in gauge theories
>is covariant, but is it actually a derivation?

One has to be careful here as one needs to distinguish between
covariant derivative and covariant exterior derivative. Covariant
derivative (defined simply by parallel transport) is not a
derivation. It leads from p-forms with values in associated vector
bundle to forms with values in p-forms with values .... Covariant
exterior derivative on the other hand leads from "p-form with values"
to "p+1-form with values" and is a derivation provided exterior
product of forms with values in an associated vector is defined (see
Greub et al., , Connections, ... , Vol II, p.254 Proposition VIII).
In a particular case where the associated bundle corresponds to the
adjoint representation, the exterior product is defined through the
commutator (Greub et al. p. 246), and in this case the fact that the
covariant exterior derivative is a derivation involves Jacobi identity
for commutators. Covariant exterior derivative is always a derivation
with respect to taking exterior products of vector valued forms with
scalar valued forms.

ark

Subject: Quantum jumps and the Five Platonic Fractals
Newsgroups: sci.physics.research
View: (This is the only article in this thread) | Original Format
Date: 2002-04-12 13:23:21 PST

I promised some time ago to put online simulations of quantum jumps and
particle tracks. Although the project is still under construction, the
first paper and OpenSource Java files are already available:

http://quantumfuture.net/quantum_future/qfractals.htm
http://www.sourceforge.net/projects/eeqt
http://arXiv.org/abs/quant-ph/0204056

and the applets are running (although no help for a while - still 'under
construction')

ark

Subject: Re: principal fibre bundle
Newsgroups: sci.physics.research
View: Complete Thread (2 articles) | Original Format
Date: 2002-04-23 12:55:02 PST

On Sun, 21 Apr 2002 04:17:06 +0000 (UTC), baez@galaxy.ucr.edu (John
Baez) wrote:

>So, for example, if you want to visualize a principal U(1) bundle
>over the space M, you should just imagine a circle sitting over
>each point of M in a smoothly varying way. You should NOT
>imagine each circle having a distinguished point corresponding to
>the identity element of U(1) - if you do this, you're implicitly
>assuming the bundle is trivial! Instead, you should simply assume
>that you know how to rotate each circle by whatever angle you like.

I think it is also good some concrete, illustrative example in mind.
In the above case you can think of a 2-sphere S as the base manfold.
At each point of the p of the sphere imagine tangent plane P(p).
Imagine the field of these tangent planes as p moves all over S.
Now, on each of these planes P(p) draw a unit radius circle C(p) with
center at p. Remember now that these circles live on tangent
planes, and these are attached to the repective points, thus do not
pay attention to the fact that these planes and circles may intersect
in 3-space surrounding S. Even if two planecs or circles intersect in
this representation - it is an artefact of the representation.

You have now a principal bundle. You can say: "rotate by 45 degrees!"
and imagine all circles rotate by 45 degrees on your command. This
is the action of U(1) on the bundle.

Moroever, this bundle is nontrivial - it has no global section:

http://www.lns.cornell.edu/spr/2000-08/msg0027213.html

http://www.mimuw.edu.pl/popularyzacja/delta/delta7/czesanie/czesanie.htm

http://www.math.niu.edu/~rusin/known-math/95/hairy

ark

Subject: Re: Non-compact symmetry groups
Newsgroups: sci.physics.research
View: Complete Thread (8 articles) | Original Format
Date: 2002-04-27 22:38:52 PST

On Sun, 21 Apr 2002 21:43:12 +0000 (UTC), grubb@lola.math.niu.edu
(Daniel Grubb) wrote:

>I am just curious why non-compact internal symmetry groups are
>not usually discussed. For example, could there be 'translation
>symmetries' in iso-spin space? It seems that unitary representations
>would have to be infinite dimensional in general, but why is that
>a bad thing?

If you go to

http://www-library.desy.de/cgi-bin/spires.pl?

and type in the window:

find keyword noncompact

you will that there is quite a number of papers dealing with noncompact
symmetry groups. Compact are easier to deal with, they lead to finite
multiplets. Do we wanna deal with infinite multiplets? We don't, so
we hope that we will not be forced too. But better be prepared :-)
Noncompact groups can have indecomposable representations -
not a nice thing either. But there are papers dealing with these
subject too.

ark

Subject: Re: geometry of gauge fields
Newsgroups: sci.physics.research
View: Complete Thread (8 articles) | Original Format
Date: 2002-04-30 14:34:32 PST

On Sun, 28 Apr 2002 05:39:09 +0000 (UTC), Terry Pilling
<terry@offshell.phys.ndsu.nodak.edu> wrote:

>So we would need to use
>a more complicated action for GR. If we formed the free action
>in the usual way from gauge theory, namely from the commutator
>of covariant derivatives, we get an action quadratic in the
>A_\mu field strength Tr F /\ F just as in QCD but this gives a
>propagating A field and the metric becomes a background rather than
>a fundamental propagating field.

Check:

CONCEPT OF NONINTEGRABLE PHASE FACTORS AND GLOBAL FORMULATION OF GAUGE
FIELDS.
By Tai Tsun Wu (Harvard U.), Chen Ning Yang (SUNY, Stony Brook).
ITP-SB-75-31, 1975. (Received Sep 1975). 40pp.
Published in Phys.Rev.D12:3845-3857,1975

C.N. Yang was seriously looking in this direction - perhaps check his
"Selected Papers 1945-1980 With Commentary", Freeman and Company, 1983 .

Of course there are hundreds of papers on this and
related subjects, but is always a pleasure to read the "classics."

ark

Subject: Re: Mathematical treatment of quantum electrodynamics?
Newsgroups: sci.physics.research
View: Complete Thread (3 articles) | Original Format
Date: 2002-05-05 15:27:58 PST

On Fri, 3 May 2002 02:08:18 +0000 (UTC), axel@uni-paderborn.de (Axel
Boldt) wrote:

>Hi,
>
>I am looking for a mathematically rigorous (or at least as rigorous as
>currently possible) treatment of quantum electrodynamics or quantum
>field theory. I'm a mathematician by trade and am familiar with the
>formalism of quantum mechanics. The treatments of QM I like best are
>in G. Mackey's books. Is there anything comparable for QED?
>
>Thanks,
> Axel

I would suggest to start with the old one but a good one
(like G.W. Mackey !)

D. Kastler, D., Electrodynamique
quantique, Dunod, Paris, 1966

ark

From: Arkadiusz Jadczyk (ark@...)

Subject: Re: Why Non-Euclidean Space?
Newsgroups: sci.physics.research
View: Complete Thread (23 articles) | Original Format
Date: 2002-05-28 14:27:05 PST

On Sun, 26 May 2002 04:34:07 +0000 (UTC), vstenger@mindspring.com (Vic
Stenger) wrote:

>I have read many books on general relativity and many biographies of
>Einstein, and it is still not clear to me why he introduced
>non-Euclidean space into the theory. The principle of covariance is
>sufficient to tell you that you need to replace Poisson's equation. So
>you write
>
>G_munu = -8*pi*G*T_munu
>
>and you have a covariant equation. Then you have to figure out how to
>relate this to experiment. Still, it
>seems that it is an additonal assumption to say that G_munu is related
>to the curvature of spacetime. It's very elegant and works
>beautifully, but is it necesary?

The main observation is that equations of motion can be interpreted
as geodesics with respect to G_munu. So straight lines of the underlying
flat metric have no physical significance. So why to keep this metric
around if all the relevant information is contained in G_munu?
Of course Einstein's assumption goes a little bit too far, as there
is no sufficient reason for assuming that G_munu is non degenerate.
The only reason that I am aware of is that otherwise we are in trouble.
But that may not be a good reason for Nature as sometimes She seems
to put us in trouble deliberately - so that we can make progress
replacing our childish concepts with a more appropriate ones ;-)

Seriously, there are theories based on two metrics, and there are
theories with flat metric and G_munu field. Weinberg discusses
some of these issues in his monograph. Logunov and collaborators in
Russia developed a similar approach.

ark

Subject: Re: decoherence and the double slit experiment
Newsgroups: sci.physics.research
View: Complete Thread (10 articles) | Original Format
Date: 2002-06-03 11:32:26 PST

On Sun, 5 May 2002 22:27:22 +0000 (UTC), cal@cal.state.disneyland (Cal)
wrote:

>I am a casual layman, but am curious:
>
>In the "double slit" experiment, why does not the particle/wave decohere as
>soon as the photon leaves the photon gun and before it reaches one of the
>slits? I would think surely something must interact with with the photon
>before it reaches the slit. (thus causing it to decohere "choose" a slit and
>be a particle rather than ever going through as a wave).
>
>Bill

And what does it mean "decohere". I know the term is being often used.
I would propose to start with the following:

But can one define decoherence in precise and noncontradictory terms,
and can one prove that it can happen in finite time?

I've never seen it done. Like John Bell who never seen
a definition of "measurement", so that he had to write
his "Against Measurement" paper.

John Bell is not with us any more. Otherwise, I am speculating,
he would write "Against Decoherence".

But, of course, I could be wrong....

ark

Subject: more quantum fractals
Newsgroups: sci.physics.research
View: (This is the only article in this thread) | Original Format
Date: 2002-06-03 12:42:23 PST

More quantum fractals.

The EEQT algorithm work as well with indefinite metric producing quantum
jumps on the Poincare disk.

It is interesting that for reasons not yet understood it is possible to
unify the expressions for jump probabilities and for the resulting
states into one formula using Clifford algebra! Foe reasons not
yet understood the resulting maps happen to be Moebius
transformations, thus producing conformal maps of the
n-sphere (also with p,q signature). It seems that Clifford
algebra formalism allows for generalizations of quantum
mechanics (this has been suggested by others long ago).

http://www.quantumfuture.net/quantum_future/papers/qfract/images/index.htm

ark

Subject: Re: This guy says he's refuted Bell's Theorem. Is he nuts?
Newsgroups: sci.physics.research
View: Complete Thread (2 articles) | Original Format
Date: 2002-06-04 16:24:52 PST

On Tue, 4 Jun 2002 05:02:20 +0000 (UTC), "Rick Padua"
<menoma@hotmail.com> wrote:

>
>"A Refutation of Bell's Theorem" by Guillaume Adenier, Université Louis
>Pasteur/Université de Strasbourg; stated to have been delivered at the
>November 2000 International Conference on Probability and Physics held at
>Växjö; and available in full (8 pages, with a lot of mathematics) on PDF at:
>
>http://arxiv.org/pdf/quant-ph/0006014
>

General remark: Bell's theorem belongs to the family of "no-go"
theorems. Every no-go theorem can be refuted on the basis
that it relies on assumptions that can be questioned.
Therefore proving no-go theorems without giving a constructive
alternative is, as a ruler, futile.

>This is the Abstract in full:
>
>"Bell's theorem is based on a linear combination of spin correlation
>functions, each of these functions being characterized by a different couple
>of arguments.

Bell's theorem is based on "standard quantum mechanical probabilistic
interpretation" which is good for children (those little babies and also
those working on their PHDs). Bell himself wrote several papers
questioning the standard intepretation (in particular "Against
measurement"), but he did not live long enough to find a satisfactory
resolution of his life dilemma.

> The meaning of the simultaneous presence of these different
>couples of arguments in the same equation can be understood in two radically
>different ways: either as a strongly objective meaning, that is, all
>correlation functions are counterfactual properties of the same set of
>particle pairs, or as a weakly objective meaning, that is, each correlation
>function is measured on a different (and contextual) set of particle pairs.
>It is demonstrated that once this meaning is explicated, no discrepancy can
>appear between local realistic theories and quantum mechanics, and that the
>discrepancy exhibited by Bell's theorem is due to a meaningless comparison
>between the local realistic inequality written within strongly objective
>interpretation (thus relevant to a single set of particle pairs) and the
>quantum mechanical prediction written within weakly objective interpretation
>(thus relevant to several different sets of particle pairs)."

From my own research and my own experience I seriously doubt
whether indeed "no discrepancy can appear between local realistic
theories and quantum mechanics." All depends on the definition of
a "local realistic theory."

But I would have to study the paper in details, very carefully, in
order to "dsiprove" it.

So, to answer the question in the subject line: "Is he nuts?"
I don't think so, Thus another partial result that does not address
the real issue.

But, of course, as always, I can be wrong.

ark

P.S. I met John Bell at CERN and we discussed some of the problems
of the quantum theory. He was well aware of all the open problems
and possibilities. Always searching for something better. Rudolf
Haag, with whom I spent endless hours discussing the problems
of foundations of physics, have had more personal interaction
with John Bell. He deveolped his own "Theory of Events". He writes
[1] This indicates that the 'non-local aspects' do not concern causal
relations between events, but correlations in the propensity for the
joint appearance of events, as in the simple example, where spin
was replaced by the charge.

(Note that the very concept of event is undefined here. It is precisely
defined in EEQT).

The devil, as always, is in the details.

ark

[1] Rudolf Haag, "Objects, Events and Localization", in "Quantum
Future", Ph. Blanchard and A. Jadczyk (ed.), Springer LNP 517,
199

Subject: Re: Internal vs. external symmetries
Newsgroups: sci.physics.research
View: Complete Thread (3 articles) | Original Format
Date: 2002-06-04 21:14:40 PST

On Mon, 3 Jun 2002 07:07:30 +0000 (UTC), baez@galaxy.ucr.edu (John Baez)
wrote:

>Internal symmetries get gauged using the theory of fiber bundles,
>and there is a very precise theory of how this works. The idea
>of gauging an external symmetry is a bit less precise; physicists
>say that gauging the above external symmetries gives the diffeomorphism
>group, but it's not quite clear what general concept of "gauging"
>they are using here.

I would encourage her reading the following paper, which clarifies
at least some of the fuzziness in this area:

Krzysztof Pilch "Geometrical Meaning of the Poincare Group
Gauge Theory"
Lett.Math.phys. 4(1980), 49-51

Abstract: We find a condition (6) under which a gauge theory of the
Poincare group is equivalent to the Einstein-Cartan theory of
gravitation.

"If we perfor now a translational gauge transformation .... then ...
is a general coordinate transformation.
Also the statement that the 'translational part of the connection is a
nontrivial part of the 'vierbein' [2] becomes clear now.(...)"

ark

Subject: Re: does someone know for God's sake!!
Newsgroups: sci.physics.research
View: Complete Thread (4 articles) | Original Format
Date: 2002-06-04 21:14:42 PST

On Mon, 3 Jun 2002 01:20:04 +0000 (UTC), aslicetinel@hotmail.com (Asli
Cetinel) wrote:

> 1- I know that the peak of any wave packet moves with a constant
>classical "group velocity". What I need to know is whether an
>infinitely localized packet could also have a group velocity before it
>instantaneously spread to whole of space. If so, what would this group
>velocity be? In a delta function representing an infinitely precisely
>measured particle position, there is nothing otehr than a single
>"peak", so, could we say it could represent a constant classical
>velocity (coexisting with Heisenberg's absolute lack of any definite
>constant velocity!)?

Using delta function is a bad way of looking at a collapse.
A better, IMHO, mechanism is described in

http://www.quantumfuture.net/quantum_future/jadpub.htm#jad94b
http://www.quantumfuture.net/quantum_future/jadpub.htm#jad94c

> I know this would not seem to make sense to
>anyone who has not read my article, but nevertheless it does support
>my conclusions about the coexistence of opposites and complementarity
>principle . Would you please provide me with information about whether
>a coexisting constant velocity of an infinitely precise particle
>would be technically correct?

I doubt that the concept pf "infinitely precise particle" makes sense.

> 2- When the delta function instantly spreads to whole of space,

Delta function is a bad approximation to reality in this kind of
questions. Multiplication by a delta function is not allowed within
quantum mechanical formalism. Delta function is a useful concept for
discussing continuous spectrum "eigenstates" and also within
Gelfand triples and rigid Hilbert spaces, but should not be used
in interpretational discussions. It can lead to all kind of oaradoxes
that has little or nothing to do with reality.

>would the final shape of the waveform of absolute position uncertainty
>be exactly the same as that of a unique frequency sine wave of some
>pure momentum value (I do know the initial momentum distribution stays
>the same as wave packets propagate, I am only asking about shape of
>the final waveform)?
> Would someone please finally provide me with some information?

I am not sure if my comments deserve being quoted. My comments are based
on my experience and my own bias.

Anyhow, if you want to see real collapse model in action, go to

http://quantumfuture.net/quantum_future/qfractals.htm

download

"OpenSource Java Files"

and run EEQT lab with detectors. You will see the wave function
collapsing and yet keeping its velocity.

ark

Subject: Re: Bohm's Formulation of Quantum Theory
Newsgroups: sci.physics.research
View: Complete Thread (6 articles) | Original Format
Date: 2002-06-08 14:17:07 PST

On Fri, 7 Jun 2002 22:36:26 +0000 (UTC), whopkins@csd.uwm.edu (Alfred
Einstead) wrote:

>> "The development of a Bohmian replacement for
>> relativistic quantum field theory is still under
>> way [...]
>> What progress, if any, has been made in this
>> direction since then?
>
>There is a fundamental problem with any particle-based
>relativistic Quantum Theory. Particles come into and out
>of existence. So, how would you describe their worldlines?
>Particularly: what's the equation of motion of a particle
>at the ENDPOINT of its worldline?

You are assuming that the laws of physics are governed by differential
equations. This point of view is based on assumptions.
Another point of view is possible: algorithms are more general than
differential equations. Here is an example taken from quantum optics
(or quantum measurement theory, if you wish):

Real time events of an individual system are described by a piecewise
deterministic Markov process. Continuous (even differentiable) evolution
is interspersed with discontinuous "jumps" or "catastrophes". There are
laws for the continuous part (vector fields give these laws) and there
are laws for jumps (this is inhomogeneous Markov process where
probabilities depend on the actual state and change with time). Thus
there is random element involved. When you average over sample paths -
you get a nice differential equation for probability distributions. But
sample paths are only piecewise differentiable.

Thus, going only a little bit beyond the present day paradigm we CAN
accomodate finite length worldlines and particle creation/annihilation
processes in terms of space-time events.

Of course we (some of us, at least) fear randmoness at the fundamental
level. But isn't randomness just a convenient tool for studying complex
and/or non-computable levels of reality?

ark

P.S. Reference:
"How Events Come Into Being: EEQT, Particle Tracks, Quantum Chaos, and
Tunneling Time"
http://www.quantumfuture.net/quantum_future/papers/garda.htm

Subject: Re: the Lorentz force
Newsgroups: sci.physics.research
View: Complete Thread (6 articles) | Original Format
Date: 2002-06-11 11:17:19 PST

On Fri, 31 May 2002 04:34:55 +0000 (UTC), aether@narod.ru (Mechanist)
wrote:

>Can we derive the Lorentz force from Maxwell's equations?

One can derive Lorentz force from general coordinate invariance
and gauge invariance alone. Thus you do not need to know
Maxwell equations - you can change them if you wish. The
main thing is invariance. From invariance alone you can
derive energy-momentum and current conservations. Then assuming that
matter and charge are distributed on a 1-dimensional submanifold, and
assuming that we deal with a point particle (no internal degrees of
freedom) - you derive Lorentz force.
This is "Souriau's method." You can find it applied to charged strings
(and also to super symmetric particles), together with references to the
original papers by Souriau and Duval, in my "Conservation Laws and
Stringlike Matter Distributions", available online at

http://www.quantumfuture.net/quantum_future/jadpub.htm#jad83

Paper summary: Equations of motion for singular distributions of matter,
like point particles, strings, membranes and bags are derived by Souriau
method. Interactions with metric tensor, non-Abelian gauge fields and
G-structures are taken into account. Particles carrying spinorial
charges in super-gravity field are also examined.

ark
--

Subject: Re: Relativistic Liouville equation?
Newsgroups: sci.physics.research
View: Complete Thread (4 articles) | Original Format
Date: 2002-06-13 20:26:33 PST

On Mon, 10 Jun 2002 18:23:15 +0000 (UTC), "Urs Schreiber"
<Urs.Schreiber@uni-essen.de> wrote:

>"Arkadiusz Jadczyk" <ark@...> schrieb im Newsbeitrag
>news:f3f2gu0661fvh2pb6grf03hqh3jmgo88ne@4ax.com...
>> For non-relativistic Schrodinger equation for pure states one derives
>> Liouville equation for mixed states.
>
>So that's
>
> d/dt psi = H/ih psi
>=>
> d/dt rho = [H/ih , rho]
>
>> Is there a manifestly relativistic Liouville equation for, say, a Dirac
>> particle?
>
>I'd say it's
>
> 0 = D psi
>=>
> 0 = [ D , rho ] .

(Snip)

>What do you think?

I am aware of this possibility, but it goes beyond standard quantum
theory. First of all you have to go off-shell, second, you have
indefinite metric. Then standard quantum mechanical interpretation
does not apply (negative probabilities) and special care is needed.
In particular the very concept of a "density matrix" as a positive,
trace 1 operator is dubious (what kind of "positivity" is required?)
There is no problem with Dirac equation itself - we can take
the Hilbert space of solutions of the Dirac equation - with positive
definite scalar product that is invariant under (unitary) Poincare
transformations. Going off-shell (all spinor valued, "square integrable"
over space-time) with indefinite scalar product (Krein space) brings
interpretational problems.
When I was asking about manifestly relativistically covariant Liouville
equation, I was thinking of something that has no problems with
negative probabilities.
I was not very clear, perhaps.

ark
P.S. Another paper using off-shell
approach for Dirac particles in conjunction with Fock-Schwinger "proper
time":
http://xxx.lanl.gov/abs/quant-ph/9610028
In this paper a physical interpretation is proposed, but
I was not able to give a reasonable meaning to the
concept of a "mixed state" within this framework
--

Arkadiusz Jadczyk

Subject: Re: formulating a metric
Newsgroups: sci.physics.research
View: Complete Thread (2 articles) | Original Format
Date: 2002-06-16 12:33:44 PST

Siddharth Srivastava <ssrivast@esat.kuleuven.ac.be> wrote in message
news:<Pine.GSO.4.33.0206131153510.11186-100000@rubens>...

> My
> question to this newsgroup community is:
> given a metric M in R^3,
> and P in [0..1] the probability measure,
> is it possible to define a metric M': R^3 \times [0..1] -> R
> What are the mathematical tools i should be looking at to come around to a
> solution?

One can take sqrt(d_{e}^2+d_(p)^2), for example. Defining metric on
the product space, when metrics on both components are known is part
of the Kaluza-Klein scheme. There are many solutions to your
question. To select one particular solution one needs more information
about the desired properties of your metric.

ark

[Moderator's note: I don't understand ark's formula - perhaps
it's just the usual Euclidean metric on R^3 x [0,1]? - but he's
certainly right that there are zillions of ways to define a
metric in this context, and the problem is deciding what properties
it should have. -jb]

Subject: Re: Time Quanta & A Priori
Newsgroups: sci.physics.research
View: Complete Thread (2 articles) | Original Format
Date: 2002-06-16 12:33:58 PST

On Sat, 15 Jun 2002 00:27:08 +0000 (UTC), BaconChaser@yahoo.com (Stinky
Piggy) wrote:

>Quantum experiments seem to violate the
>"a priori" of cause and effect.

It is not clear what is a "quantum experiment" in contracts to
"non-quantum" experiment. It is not clear what "experiment" is, in
contrast to just "doing something" or "experiencing something."

(snip)

>The same as asking "Does a calculation take place,
>for a quanta to move from a present state to one of several
>future possible states?"

Here different people will have different opinions.
I think that the term "calculation" is appropriate here.
But physics is not yet at that level - except for some models
based on cellular automata type idea - like those of Noyes,
perhaps also Finkelstein and few others.

>Out of curiosity,
>Do quantum effects, experiments,
>such as the transactional handshake,
>have a time limit in which to make the
>decision or effect?

I do not know about "transactional handshake", but "quantum decisions"
seem to involve inherent randomness (Einstein and many others didn't
like that), which, at a deeper level, may come from complexity (this
term was probably not known to Einstein at that time).

ark

Subject: Re: How particle spin follows from relativity and quantum mechanics
Newsgroups: sci.physics.research
View: Complete Thread (10 articles) | Original Format
Date: 2002-06-18 20:25:41 PST

On Sat, 15 Jun 2002 04:47:21 GMT, timrobinson@paradise.net.nz (Dr Tim)
wrote:

>So far I have grasped the Schroedinger equation, general relativity,
>exterior differential forms, matrix algebra, Hamiltonian theory, and I
>can see how electromagnetism follows from adding an extra rolled up
>dimension to general relativity.

If you are interested in spin, a good thing to add to your list would be
group theory and unitary representations. The simples way to derive spin
is by studying unitaru group representations and quantu mechanics via
imprimitivity systems.

The book by Jauch may be of help, laso the two volumes by
Varadarajan's "Geometry of Quantum Theory" and references there.

Spin comes out automatically from projective unitary representations
of SU(2). You do not need to embed it into Lorentz group as in the Dirac
equation. Pauli's Hamiltonian for free particle with spin comes from
(somewhat extended) analysis (Mackey theorem) of imprimitivity system:
Euclidean group of RxR^3 plus covariant (generalized) spectral measure,
along the line described in

"Logics Generated by Causality Structures.
Covariant Representations of the Galilean Logic"

available online at

http://www.quantumfuture.net/quantum_future/jadpub.htm#ceja75

ark

Subject: Re: difference between pseudo-tensors and densities?
Newsgroups: sci.physics.research
View: Complete Thread (4 articles) | Original Format
Date: 2002-06-18 20:49:13 PST

On Sat, 15 Jun 2002 04:12:50 GMT, waterballon@hotmail.com (Hari Seldon)
wrote:

>Greetings,
>
>I have a short question. Is it correct that what Frankel calls a
>pseudo-form, Schutz calls a density ? So is density just another word
>for pseudoform ? If not, what is the difference between them ?
>
>Thanks in advance,
>
>H. Seldon

I would say "density" is a more general concept. There are tensor
densities of arbitrary "weight". In conformal theories they usually
relate to different scaling properties under dilations.

Pseudo-form is a rather particular case of these, I think. But I do not
have Schutz at hand, so I am not sure whether what he calls "density"
is the same as what, for instance, Schouten (and Einstein) calls "tensor
density."

ark

From: Arkadiusz Jadczyk (ark@...)

Subject: Re: Regional conservation of energy and momentum on a curved spacetime
Newsgroups: sci.physics.research
View: Complete Thread (7 articles) | Original Format
Date: 2002-06-25 14:25:41 PST

On Thu, 20 Jun 2002 19:25:34 +0000 (UTC), timrobinson@paradise.net.nz
(Dr Tim) wrote:

>But what about a curved space-time?
>
>I have heard it asserted that integrations over
>curved spaces can yield only scalar results
>- never vectors. Is this true?

My comment will not answer your question, nevertheless it will point out
another possible approach to the same problem.

There are reformulations of general theory relativity using teleparallel
connection, for a review (even though somewhat outdated) see for
instance:

Folkert Müller-Hoissen, "Teleparallelism - a viable theory of gravity ?"
(with J.Nitsch) Phys. Rev. D 28 (1983) 718-728.

Folkert Müller-Hoissen, "Teleparallelism - an alternative theory of
gravity ?"
(with J.Nitsch), in 10th International Conference on General Relativity
and Gravitation, Padova (Italy) 1983, Contributed Papers, eds.
B.Bertotti et al., pp. 594-596.

Folkert Müller-Hoissen, "On the tetrad theory of gravity"
(with J.Nitsch) Gen. Rel. Grav. 17 (1985) 747-760.

In teleparallel theories it is possible to integrate vactors and still
get vectors (curvature is zero and all the relevant information is
in the torsion). But one must be careful, because covariant derivatives
do not behave quite the same way as in theories with a symmetric
connection. Thus some of the difficulties with conservation laws can be
simply shifted to another place.

ark

Subject: Re: coordinate functions and vector valued 0-forms?
Newsgroups: sci.physics.research
View: Complete Thread (8 articles) | Original Format
Date: 2002-06-25 21:09:00 PST

On Sat, 22 Jun 2002 18:50:40 +0000 (UTC), baez@galaxy.ucr.edu (John
Baez) wrote:

>>A short question. In Frankel it is said that dx (the exterior
>>derivative of the coordinate functions) can be viewed as a vector
>>valued 1-form (field??).
>
>If you are talking about the list of all the 1-forms (dx^1, dx^2, ..., dx^n)
>given by taking exterior derivatives of coordinate functions x^i,
>then yes, this thing is an R^n-valued 1-form.

I would add to the above a warning for those who just start learning
this subject, for instance from Frenkel:

when speaking of "vector valued forms" - pay really close attention to
where these forms take values. This is especially important whent iot
comes to differentiation.

When Frenkel introduces the concept of vector valued forms,
in Ch. 9.3, he starts wit a mixed tensor, and then he says that
a mixed tensor (which is skew symmetric in its covariant indices) can be
also considered as a vector form. Here it is clear that what he means is
a form with values in a vector bundle. Not a form with values in a
vector space or in R^n.

Of course, a form with values in a vector space is a particular case
of a form with values in a vector bundle. But in 9.3 Frenkel discusses
forms with values in vector bundles. Unfortunately the example that he
takes is a in R^n in cartesian coordinates, and then any difference
between the two concepts disappears.

The concept of an exterior covariant derivative that Frenkel
discusses in 9.3d really applies to forms with values in vector
bundles.

Good and comprehensive references on this subject are:

1) Dieudonne, Treatise on Analysis, Vol. IV, Chapter 20 (and whatever
is needed in Vol 3 and previous chapters to understand completely this
chapter).

2) Greub, Halperin, Vanstone: "Connections, Curvature,
Cohomology" Vol I,II (you do not have to learn all, just selected
sections.)

and as an addition

Kolar, "Natural operations in differential geometry"

ark

From: Arkadiusz Jadczyk (ark@...)

Subject: Re: Calculus Lemma?
Newsgroups: sci.physics.research
View: Complete Thread (2 articles) | Original Format
Date: 2002-07-02 15:43:27 PST

On Thu, 27 Jun 2002 03:58:41 GMT, "Jim Goodman" <sawf@comcast.net>
wrote:

>Show d/dx = d/d(x+c), where c is a constant.
>
>Briefly |x+e - x| = |(x+c)+e - (x+c)|
>
>Did not see this in any of my Calculus texts. Anyone ever use it in Physics?
>--
>Jim Goodman
>sawf@comcast.net
>mywebpages.comcast.net/sawf/
>
>
>[Moderator's note: It's implicitly used whenever one talks of translation
> invariance-- ordinary derivatives are always assumed to be the same if you
> shift the coordinates a little. -MM]

Indeed, this is translation invariance. Translation group acts on
functions by

(U(a)f)(x)=f(x-a)

It has an infinitesimal generator, call it X:

X=dU(a)/da | a=0

and it happens to be nothing but -d/dx

(Xf)(x) = d/da (f(x-a))|a=0 = -df(x)/dx

Then, of course d/dx commutes with U(a) - and that is the statement:
d/dx = d/d(x+c),

ark

Subject: Re: Another Purported Refutation (This Time of Quantum Teleportation)
Newsgroups: sci.physics.research
View: Complete Thread (6 articles) | Original Format
Date: 2002-07-02 15:43:27 PST

On Thu, 27 Jun 2002 07:02:54 +0000 (UTC), "Rick Padua"
<menoma@hotmail.com> wrote:

>
>Assuming, soley for the sake of discussion, that the man is completely
>incorrect ... how is it possible that presumably reputable professionals
>appear to take him at all seriously? Is V‰xjˆ a hotbed of lunacy? How
>widespread is this sort of behavior in the scientific community? Isn't it
>arguably a threat to science itself?

That is nothing new. Conference proceedings publish papers of various
quality. To give an example, in a conference I was organizing, the
Editor from Springer Verlag requested rejected a paper - even if I was
in favor of publishing it. The Editor decided it was "too weird for
Springer." But other publishers have different criteria, and some
conference proceedings are so liberal that they publish all that
is sent to them.
Even respectable journals, once in a while, publish papers that
make no sense, and that is because the referee could not understand
what is in there, and, being busy, decided that it "sounds right," and
"has right references," so "let it goes."

Is it a threat to science? Well, cars are threat to human life. Yet
we use them.

Value of a paper has little to do with where the paper was
published. Statistically one expects better papers in "serious",
"established reputation" peer reviewed journals, while quality
of papers in conference proceedings is expected to vary.
But even "peer reviewed" journals, statistically, differ in quality.
That is why "impact index" for journals has been created.

But even knowing statistics is of little help when it comes to an
individual case. Each paper needs to be judged separately.

ark

From: Arkadiusz Jadczyk (ark@...)

Subject: Re: Bell's Theorem
Newsgroups: sci.physics.research
View: Complete Thread (12 articles) | Original Format
Date: 2002-07-05 23:26:27 PST

On Tue, 2 Jul 2002 19:38:27 +0000 (UTC), Ilja Schmelzer
<schmelzer@wias-berlin.de> wrote:

>> You can as well say that Heisenberg's uncertainty principle is a purely
>> mathematical result that has no dependence on quantum mechanics or any
>> other physical theory. And that will be even true - ina sense. It is a
>> theorem about scalar produscts and Hermitian operators, yes?
>> You can say that Einstein field equations have nothing to do with
>> general relativity.
>
>That's not the point. Bell's theorem is that Bell's inequality holds
>in all Einstein-causal realistic theories. It does not even mention
>the word "quantum", nor does it use operators and so on.

Bell's theorem is about probability distributions and joint probability
distributions. These, by themselves, have nothing whatsoever to do
with our world - where all the data we have are finite and repeataing
the same experiments is impossible - it is never *the same*.
The standard quantum theorem is believed to be probabilistic, and
it is also believed, by some, not by all, that the only statements of
quantum mechanics are about probabilities. This follows from the
formalism that was developed mainly by von Neumann. At that time
people were willing to buy into ANY interpretation that would justify
"great successes" of quantum theory in dealing with radiation.

Von Neumann offered a simple interpretation of scalar products,
spectral measure, eigenvalues, developed "quantum logic" -
it was soooo.... pretty!

Today perhaps we need to start thinking on our own again.
What if quantum theory - the next version of it - version 2.0, say,
is not gonna be probabilistic? What is the very concept of "experiment"
is gonna be defined within the theory, and what if Bell's theorem
simply will not apply, because Bell's theorem in a popular edition
(not Bell's original one) is based on oversimplified concepts that
have little to do with ANY reasonable physics whatsoever?

Do not forget that Bell wrote his paper in 1964 - it is about
"measurements" and "experiments". More than 20 years later
he wrote another paper "Against measurement" where he realized
and pointed it out to the rest of the physics community that these
concepts are not even defined! Few people really listened.

ark

Subject: Re: Physicality of div A
Newsgroups: sci.physics.research
View: Complete Thread (4 articles) | Original Format
Date: 2002-07-08 19:56:06 PST

On Fri, 5 Jul 2002 23:44:52 +0000 (UTC), David Rutherford
<drutherford@softcom.net> wrote:

>Conventionally, the 3-div A and 4-div A, where A is the vector
>potential, are considered to be unphysical. This is said to justify the
>freedom to set their values arbitrarily. However, if they are physical,
>this freedom vanishes. Therefore, there must have been attempts to
>determine their physicality.
>
>Does anyone have knowledge of these tests of the physicality of 3-div A
>or 4-div A that have been performed and their results? If so, could you
>please give references? If they haven't been performed, please explain
>the justification?

They ( 3-div A and 4-div A) can be physical, yet not very interesting.
For their physicality may consists of the fact that they vanish.

I do not have the reference at hand, but you may like to check
Physics Abstracts around 1979 - there should be a paper
by late H. Ekstein who at that time was researching this
problem. His idea was to tie gauge freedom of QM to the
gauge freedom of A, and the conclusion was, as far as I
remember, that physics (that is thinking of experimental
manipulation of EM field and particle states) leaves no
such freedom. I would appreciate if someone could
find Ekstein's paper - it was probably in Phys. Rev.

ark