Subject: Burkhard Heim's quantum theory
Date: Sat, 07 Jan 2006 15:41:12 +0200
From: Dimi Chakalov <dimi@chakalov.net>
To: Jochem Häuser <jh@hpcc-space.de>
CC: Markus Pössel <mpoessel@aei.mpg.de>,
Markus Pössel <kontakt@einstein-fenster.de>,
Jürgen Ehlers <Jurgen.Ehlers@aei.mpg.de>,
Thomas Thiemann <Thomas.Thiemann@aei.mpg.de>,
Pavlos Mikellides <Pavlos.Mikellides@asu.edu>,
Roger Lenard <rxlenar@sandia.gov>,
Craig Smith <casmith@sandia.gov>,
Gary Jones <gjjones@sandia.gov>,
Graham P Collins <gpc@nasw.org>,
Graham Nerlich <graham.nerlich@adelaide.edu.au>,
Chris Isham <c.isham@imperial.ac.uk>

Dear Professor Häuser,

I wish you and your colleagues best of luck with your project [Ref. 1].

Regarding Burkhard Heim's quantum theory and your recent STAIF 2005 paper [Ref. 2]: you suggested that the hypothetical graviphoton field would induce "a transition of a material body into some kind of parallel space".

I have to confess that the way you elaborated on this parallel space [Ref. 3], and particularly the additional four coordinates introduced to explain the "steering of probability amplitudes (information)" [Ref. 4, footnote 4], is not comprehensible to me.

The way I see it, the so-called parallel space could be an entirely different geometrical object (global mode of spacetime), which could, at least in principle, be used for accelerating a physical body along a modified geodesic that is "partly" in the 3-D space, and "partly" in your parallel space (global mode of spacetime). I am, however, very skeptical about using magnetic field, since the only "device" that might have access to the global mode of spacetime is the human brain. Qui vivra, verra.

Best regards,

Dimi Chakalov
--
http://www.God-does-not-play-dice.net
http://www.God-does-not-play-dice.net/download.html
 

References

[Ref. 1] Haiko Lietz, Take a leap into hyperspace, New Scientist, 5
January 2006
http://www.newscientist.com/channel/fundamentals/mg18925331.200.html
 

[Ref. 2] Dröscher, W., Häuser, J. Heim Quantum Theory for Space Propulsion Physics. STAIF 2005
http://www.hpcc-space.de/publications/documents/
heim_staif2005-letter.pdf
 

[Ref. 3] Häuser, J., Dröscher, W., Dai, W., Muylaert, Jean-Marie, Physical and Numerical Modeling for Advanced Propulsion Systems, Proceedings  published as: Recent Trends in Aerospace Design and Optimization, SAROD-2005, ed. B. Uthup, ISBN 0-07-060829-6, Tata Mc Graw-Hill, 2005.
http://www.hpcc-space.de/publications/documents/JHSarod2005.pdf

p. 5: "A quantized spacetime has recently been used in quantum gravity. Heim went beyond general relativity and asked the question: if the effects of the gravitational field can be described by a connection (Christoffel symbols) in spacetime that describes the relative orientation between local coordinate frames in spacetime, can all other forces of nature such as electromagnetism, the weak force, and the strong force be associated with respective connections or an equivalent metric tensor. Clearly, this must lead to a higher dimensional space, since in GR spacetime gives rise to only one interaction, which is gravity."

p. 9: "That is, spacetime is a quantized (discrete) field and not continuous. A lower value of G or a higher value of c clearly violate the concept of minimal surface. Therefore, in order to resolve this contradiction, the existence of a parallel space is postulated in which covariant laws of physics hold, but fundamental constants are different, see Eq. (11). The conditions for a transition in such a parallel space are given in Eq. (12)."
 

[Ref. 4] Dröscher, W., Häuser, J. Guidelines For a Space Propulsion Device Based on Heim's Quantum Theory. AIAA Paper 2004-3700.
http://www.hpcc-space.de/publications/documents/aiaa2004-3700-a4.pdf

p. 5, footnote 4: "To be more precise, Heim's theory was extended from 6 to 8-dimensions by the first author and Heim, [7], to obtain the unification of the four known interactions (forces). In this process, it was found that two additional gravitational like interactions should occur, termed the gravitophoton field (attractive and repulsive) and the vacuum field (repulsive, interpreted later on as quintessence) [1, 7]. The dimensional law derived by Heim requires a 12-dimensional space, but the additional four coordinates are needed only in the explanation of the steering of probability amplitudes (information).
...

"Though HQT is based on geometrical aspects in a 6, 8, or 12-dimensional
space, it is neither continuous nor smooth, but contains an elemental
surface area, the metron, equipped with a spin vector."

[See also p. 22]
--
 

Note: I've said a lot of "crazy" stuff above, so will provide [Ref. 5] without comments. Regarding the suggestion about some modified geodesic that is "partly" in the 3-D space, and "partly" in the global mode of spacetime, see [Ref. 6]. Just recall that we've been pampered and patronized by our beloved governments for decades. If you wish to talk seriously about UFO and gravity control, you could only get a friendly offer for post-traumatic counseling. If you want to do something real -- don't. During the last world war, one accomplished pendulum dowser so astonished the U.S. Military with his accuracy in locating every U.S. and Japanese submarine using only a map and pendulum that he was deemed a security risk and was refused a passport to leave the country. All you can do is "street magic".

As to the experts in quantum gravity, see Robert Millikan below. And don't levitate your body like Daniel Dunglas (D.D.) Home, because this too is considered impossible.
 

D.C.
January 7, 2005
Last update: February 5, 2006

--
There is no likelihood man can ever tap the power of the atom.
Robert Millikan, Nobel Prize in Physics (1923)

Where a calculator on the ENIAC is equipped with 18,000 vacuum tubes and weighs 30 tons, computers in the future may have only 1,000 tubes and perhaps only weigh 1 1/2 tons. (Popular Mechanics, March 1949)


 

[Ref. 5] UFOs hidden under electromagnetic flux invisible to human eyes but thousands of them are hovering all around us. India Daily, February 16, 2005,
http://www.indiadaily.com/editorial/1629.asp

Scientists in India finally understands how UFOs hover all around us without being visible. In Pune, India, some DRDO (Indian Defence Research & Development Organization) engineers are busy experimenting with a device that can see through the stealth effects of intense electromagnetic flux. According to some of these super smart brains of India, the final stealth effects come from creating an intense electromagnetic flux around any object. The Russians have been experimenting with similar stealth mechanisms. 

The electromagnetic flux can be created through very advanced applications of super conductors. There are paranormal means of creating this flux that make anything invisible in true sense. The electromagnetic flux can be created through spiritual concentration by any human being. When such an event takes place, strange phenomena happen. And people call it miracle, heavenly effects and so on.

The scientists are getting very early indications that electromagnetic flux is used to keep the UFOs invisible from human eyes. Some animals have sensors that can sense energy levels beyond the electromagnetic flux. Probably dogs or cats are seeing UFOs all the time. But they cannot express what they see.

According to these scientists, a device that can see through electromagnetic flux is able to see UFOs all the time. The reason why UFOs are visible only in very rare cases and for a short time is as follows: When a UFO enters the earth’s atmosphere and approaches an object or a destination in the earth, the UFO has to transform from ultrasonic speed (speed of light times n) and maneuvering techniques to sonic or supersonic levels and adjust to earth’s electromagnetic and gravitational effects. Right at that moment, to avoid electromagnetic interference, the artificial flux is withdrawn for a very short span of time. After reaching speed levels that the UFO can use in earth’s atmosphere, the electromagnetic flux or cloud is regenerated and put all around the UFO. That explains why in many countries the Air Force Pilots have chased an UFO only to have them disappear in front of their own eyes.

Based on this new discovery, there can be innumerable UFOs all around us. There are early indications that teleport mechanisms will also come from advanced research of electromagnetic flux.

Copyright © 2003-2005, Indiadaily.com. All Rights Reserved.
 
 

[Ref. 6] Eric W. Davis, Teleportation Physics Study, AFRL-PR-ED-TR-2003-0034, August 2004, pp. 60-61.
http://www.fas.org/sgp/eprint/teleport.pdf
(1,709,941 bytes)

See also: Rudy Rucker, Infinity and the Mind, Princeton University Press, Princeton, 2004; ISBN: 0-691-12127-3.
 

=========

Subject: Creating a pseudo geodesic
Date: Wed, 15 Mar 2006 13:41:30 +0200
From: Dimi Chakalov <dimi@chakalov.net>
To: Marc Millis <marc.g.millis@nasa.gov>
CC: Jochem Häuser <jh@hpcc-space.de>,
Markus Pössel <kontakt@einstein-fenster.de>,
Pavlos Mikellides <Pavlos.Mikellides@asu.edu>,
Graham Nerlich <graham.nerlich@adelaide.edu.au>,
Martin Tajmar <martin.tajmar@arcs.ac.at>,
Orfeu Bertolami <orfeu@cosmos.ist.utl.pt>,
Clovis Jacinto de Matos <Clovis.de.Matos@estec.esa.nl>,
Christophe Carreau <Christophe.Carreau@esa.int>,
Danielle Graham <livingsys@ywave.com>,
david.defelice@grc.nasa.gov,
Jean.M.Schuerger@grc.nasa.gov

Dear Marc,

Suppose on 16 December 1868, the mass of D.D. Home's body was 80 kg,

http://www.god-does-not-play-dice.net/Hauser.html#note

Can you or some of your colleagues calculate how much energy was needed to levitate his body by creating a pseudo geodesic [Ref. 1]?

Let me please remind you that six years ago I did offer you to consider PK as a viable source of levitation, and you replied with just one word:

"NO."

I suppose you know something about levitation that I don't know, so I will appreciate your detailed calculations.

Kindest regards,

Dimi
--
[Ref. 1] Marc G. Millis, Assessing Hypothetical Gravity Control Propulsion, physics/0603113 v1.
http://arxiv.org/abs/physics/0603113

p. 13, "the nullification of gravitational potential"
...
p. 14: "To explore these general relativity formalisms in the context of creating space drives introduces entirely different energy requirements than with the Newtonian versions explored in this paper. In the general relativity approach, one must supply enough energy to manipulate all of the surrounding spacetime so that your spacecraft naturally falls in the direction that you want it to go. This can be referred to as creating a pseudo geodesic -- reshaping spacetime to induce the preferred freefall trajectory. Although such approaches require considerably more energy than the simple Newtonian concepts, they are nonetheless instructive.
...
p. 15: "Using the perspective of geometric general relativity, calculate the energy required to create a local null geodesic at the surface of the Earth. By "local null geodesic" it is meant where the local freefall path is a stationary trajectory."
 

=========

Subject: Superluminal motion in (semi)classical relativity?
Date: Thu, 16 Mar 2006 14:27:41 +0200
From: Dimi Chakalov <dimi@chakalov.net>
To: Serguei Krasnikov <gennady.krasnikov@pobox.spbu.ru>
CC: Thomas A Roman <roman@ccsu.edu>,
     Christopher J Fewster <cjf3@york.ac.uk>,
     Larry Ford <ford@cosmos.phy.tufts.edu>,
     Adam Helfer <adam@math.missouri.edu>,
     Don N Page <don@phys.ualberta.ca>,
     William G Unruh <unruh@physics.ubc.ca>,
     Graham Nerlich <graham.nerlich@adelaide.edu.au>

Dear Serguei,

I agree with you that, contrary to what Ford & Roman might claim, Eq. 8 from your latest gr-qc/0603060 v1 (p. 8) is not realistic at all. However, FTL "shortcut" (laz, in Russian) of bodies, depicted in Fig. 3b (p. 12), may not require any "exotic" matter. Perhaps all we need is a well-trained brain, as we know since 16 December 1868,

http://www.god-does-not-play-dice.net/Hauser.html#Marc

In other words, I believe the concept of superluminal motion is a misnomer, since we need to construct a modified geodesic that is "partly" in the 3-D space, and "partly" in the global mode of spacetime.

In order to understand what I mean by 'global mode of spacetime', please see

http://www.god-does-not-play-dice.net/Weinstein.html#F1

I will appreciate your professional comments, as well as those from your colleagues.

Again, we don't need any "exotic" matter: see the text printed below, from a Russian web site, and recall Serafim Sarovsky (the archbishop of Novgorod and Pskov) and Josef Desa (canonized in 1667). Nowadays we don't need to pray in order to modify the inertial mass of macroscopic bodies, but to understand the dynamics of GR. Please see the link above.

Kindest regards,

Dimi
--
"An interesting experiment was carried out in one of Russian universities, at the psychological department. A person was told during a seance of hypnosis that he was inside an orbiting spaceship. A hypnotist told the person that he was about to find himself into a state of weightlessness. When devices showed the complete absence of weight, the scientists did not believe their eyes: the weight of the hypnotized individual vanished totally."

=========
 

Date: Thu, 16 Mar 2006 19:20:24 +0200
From: Dimi Chakalov <dimi@chakalov.net>
To: Serguei Krasnikov <Gennady.Krasnikov@pobox.spbu.ru>
Subject: Re: Superluminal motion in (semi)classical relativity?

Dear Serguei,

>> In other words, I believe the concept of superluminal motion is a
>> misnomer, since we need to construct a modified geodesic that is
>> "partly" in the 3-D space, and "partly" in the global mode of spacetime.

> No, I needn't.

You are indeed 100% Russian!

>> In order to understand what I mean by 'global mode of spacetime',
>> please see
>> http://www.god-does-not-play-dice.net/Weinstein.html#F1

> No, Dimi, it doesn't work. In my belief (I already told this to you once)
> you can increase the number of people understanding your ideas *only*
> by retelling them in a conventional way (i.e. as a mathematical model).

That was done by Karel Kuchar many years ago. I can only set the framework of the dynamics of GR in conceptual terms: see the necessary and sufficient conditions at the end of the link above. If you really need math to understand the idea, I can ask my Chinese colleagues to get in touch with you. Shall I?

Regards,

Dimi
---

Note: Anticipating the reply from Serguei Krasnikov, let me just say that there are certain things that cannot be derived from classical GR. The topology of space is one good example. There are also things that cannot be explained with classical GR alone, such as the effect of the Holon, producing the quazi-local interactions (Serguei Krasnikov wouldn't click on the underlined words 'quazi-local', but I hope you will). Another effect of the Holon is what I called 'the sufficient condition' for GR dynamics. It is excluded from GR textbooks from the outset, as explained here and here. If you read GR textbooks with a Marxist-Leninist brain, you can never acknowledge the "remnants" from the Holon, which cannot be explained nor derived from 'the grin of the cat without the cat' that you call 'geometry'. We introduce these "remnants" in GR by hand only. We cannot derive the elementary timelike displacement from the physics of the gravitational fields alone. Serguei Krasnikov can say that the pointer of his thermometer has dropped down because it is getting cold in Leningrad, but if he thinks in the same vein he cannot find any physical force that could produce the observed dynamics of GR. Why? Because the Aristotelian First Cause is excluded from GR textbooks from the outset, again. It is an effect of the Holon, and is completely "dark". Marx and Lenin would not agree, of course, and neither would Serguei Krasnikov.

If you want math, read Karel Kuchar. The rest is known since the time of Aristotle.
 

D. Chakalov
March 16, 2006

================

Date: Sun, 19 Mar 2006 04:44:31 +0200
From: Dimi Chakalov <dimi@chakalov.net>
To: Serguei Krasnikov <Gennady.Krasnikov@pobox.spbu.ru>
Subject: Poetry

Dear Serguei,

>> I can ask my Chinese colleagues to get 
>> in touch with you. Shall I?

> No, thank you. I'm, in fact, not much interested in the "problem of
> time" in quantum gravity.

I didn't talk about the problem of time in quantum gravity. See the link in my first email.

I looked at your email since 2002, and couldn't find any piece of new information that has not been in your papers. I will, from now on, behave like you. Please don't expect from me anything more than what I've posted on my web site.

The reason why I suggested my "poetry" was that I have absolutely no idea how you would make your "shortcut" in the real world. If you believe have provided a feasible theory, please explain the experiment that would produce the phenomenon depicted in Fig. 3b from your gr-qc/0603060 v1. If you cannot do that, I'm afraid your wild guess will remain (in my belief) closer to poetry than to science. If you succeed, I think you will prove Yakov Terletsky wrong on at least one account. Well, read my mind.

Kind regards,

Dimi

================

Date: Tue, 21 Mar 2006 15:27:24 +0200
From: Dimi Chakalov <dimi@chakalov.net>
To: Serguei Krasnikov <Gennady.Krasnikov@pobox.spbu.ru>
Subject: Re: Poetry

>> No, Serguei, they aren't. Sorry.


> I take it, you have found a mathematical error in a paper of mine?

Don't mix apples with oranges. Your errors are not mathematical. You 
work with a theory that is essentially incomplete, for reasons explained 
at the link from my first email from Thu, 16 Mar 2006 14:27:41 +0200,

http://www.god-does-not-play-dice.net/Weinstein.html#F1

For example, there are no math errors in those "bulk space" models either, and you can play with "branes" as much as you want. You've simply chosen another Barbie. That's fine with me.

If some day you feel the need to get serious, please elaborate on the *physical* experiment, depicted in your charming Fig. 3b in your latest gr-qc/0603060 v1.


I beg you, don't procrastinate - publish it.

Dimi
---

Note: To make the 'pocket' of Chris Van Den Broeck, you'd need roughly 1 g "exotic" matter. Perhaps all you have to do is to convert the "dark" energy into that exotic matter, and you're done. I hope Serguei Krasnikov will provide the detailed calculations. He is so good in math!

I'm not, and Serguei Krasnikov denounced my idea as "poetry". Indeed, how can a macroscopic body travel "partly" in the 3-D space and "partly" in the global mode of spacetime? The main problem here is to imagine some kind of modified geodesic that is being compiled partly by infinitesimal timelike displacement in 3-D space, and partly by non-local "shortcuts" through that same 3-D space. Think of such macroscopic body as an UFO or as an object being "teleported" by Chinese researches (reference above).

Now, if you're inclined to think of the 3-D space as a fixed hypersurface, then the idea is indeed poetry. But recall that physicists use double standards in treating time and space in GR, after Dirac and ADM. There are no well-defined dynamical degrees of freedom for GR, which apparently does not affect the 3-D hypersurface. Consequently, there is 'problem of time' in canonical quantum gravity, but no 'problem of 3-D space'. If some day we discover the nature of 3-D space, we would perhaps explain the infinitesimal spacetime displacement of macroscopic bodies, in which the effect from 'traveling in the global mode' is vanishing small, like in playing Frisbee. Then the task would be much simpler: design a quantum version of such geodesic, resembling Feynman's Path Integral approach to QFT, and levitate your body, just like D.D. Home did on 16 December 1868.

Don't tell me you knew nothing about my "poetry"!
 

D.C.
March 21, 2006
Last update: March 23, 2006

==================
 

Subject: The divergence problem: does the vacuum "energy" gravitate?
Date: Thu, 26 Jan 2006 15:00:28 +0200
From: Dimi Chakalov <dimi@chakalov.net>
To: Peter Leifer <leifer@bezeqint.net>
CC: Larry Horwitz <larry@post.tau.ac.il>,
     Andrei Khrennikov <Andrei.Khrennikov@vxu.se>,
     Andre Gsponer <Andre.Gsponer@cui.unige.ch>,
     Chris Isham <c.isham@imperial.ac.uk>,
     Christian Beck <c.beck@qmul.ac.uk>,
     Steve Adler <adler@ias.edu>

Dear Peter,

It is a pleasure to read your papers. In your latest physics/0601201 [Ref. 1, p. 17], you suggested that "in the infinite dimension case there is smooth manifold CP([inf]) and dynamical quantum state (tangent vector) creeps from one tangent Hilbert space to another."

It does creep over the "vacuum landscape", in a stealthily and furtively fashion,

http://www.God-does-not-play-dice.net/Rosinger.html

I believe Dirac was right by stating that "the Schrödinger vector in QED does not exist at all, because it does not lie in any separable Hilbert space" [Ref. 1, p. 3]. In order to develop a *separable* Hilbert space -- one-at-a-time and pointing to the "same direction" [Ref. 2] -- we may need to operate with two forms of reality: potential reality ('time of being') and the fleeting snapshots of physical reality ('time of becoming'). This is, of course, a very old idea, which can be traced back from Prigogin and Whitehead to Plato. More at

http://www.God-does-not-play-dice.net/Stachel.html#point

Given the "deception" from QM textbooks [Ref. 3], I wonder what is your opinion on the following issue: does the vacuum "energy" gravitate? Please see

http://www.God-does-not-play-dice.net/Rendall.html#Frampton

I will greatly appreciate the opinion of your colleagues as well. Will keep it private. Perhaps the issue isn't strictly academic, but may have huge practical applications,

http://www.God-does-not-play-dice.net/Hauser.html

Best regards,

Dimi
--

References

[Ref. 1] Peter Leifer, Geometry of the divergences problem in QFT,
physics/0601201 v1.
http://arxiv.org/abs/physics/0601201

p. 1: "The classical material points moving in space-time are main original objects of the constructive quantum mechanics (QM) and quantum field theory (QFT). This approach bring a lot of conceptual and technical problems. We may assume that all attempts to localize matter in space-time, i.e. increasing of resolution by higher energy of collision leads in fact to the delocalization by defreezing new internal degrees of freedom. On the other hand, mathematically, this locality leads to the singular functions (the most serious artifact of the local QFT).

"The modern nonlocal objects like strings and membranes arose due to attempts to avoid these difficulties. Since physical status these objects is not clear up to now and their logic leads far away from ordinary physical paradigm [2], it is worth while do find a different solution of the divergences problematic. I show here another method of introduction of nonlocal objects arising in dynamical space-time which is built as specific section in the tangent fibre bundle over the "vacuum landscape".
...

p. 3: "... Dirac came to the conclusion, that the Schrödinger vector in QED does not exist at all, because it does not lie in any separable Hilbert space [1].
...

pp. 5-6: "Energy will be associated with tangent vector field to CP(N-1) giving velocity of the action variation in respect with a "second time" [12] close to the notion of Newton-Stueckelberg-Horwitz-Piron (NSHP) time [13].
--
ref. [12]: I. Prigogin, From being to becoming, San Francisco,
W.H.Freeman and Company, 1980.

ref. [13]: hep-ph/9606330
Lawrence Horwitz, Time and the Evolution of States in Relativistic
Classical and Quantum Mechanics, hep-ph/9606330 v1.
http://arxiv.org/abs/hep-ph/9606330
--

"Dynamical space-time will be built at any vacuum (see below). Therefore Minkowskyan space-time is functionally local in CP(N-1) and the space-time motion dictated by the field equations connected with two infinitesimally close "vacua". The connection between these local space-times may be physically established by the measurement given in terms of geometry of the base manifold CP(N-1). It seems like the Everett’s idea about "parallel words", but has of course different physical sense. Now we are evidences of the Multiverse concept [2]. I think there is only one Universe but there exists continuum of dynamical space-times each of them related to one point of the "vacuum landscape" CP(N-1). The standard approach, identifying Universe with space-time, is too strong assumption from this point of view.
...

p. 17: "One can treat this behavior of the tangent state vector as a finite dimension non-linear model of the "beat out" of the state vector due to the ‘divergences problem’ [4] from one tangent Hilbert space to another (Dirac thought that it is "beating out" to nowhere). Then we can assume that the real divergences problem may be resolved in similar manner: in the infinite dimension case there is smooth manifold CP([inf]) and dynamical quantum state (tangent vector) creeps from one tangent Hilbert space to another."
 

[Ref. 2] Peter Leifer, Dynamical Spacetime and the Curvature of
Projective State Space, gr-qc/9711059 v1.
http://arxiv.org/abs/gr-qc/9711059

pp. 2-3: "Spacetime structure is a derivable entity. All paradoxical results like "fasten-than-light-telegraph" [15] or "Everett phone" of [16] are rooded in the nonadequacy of assumptions about relationships between nonlinear quantum dynamics itself and their spacetime presentation.
...

"I will try show that the root of difficulties in interpretation of both ordinary (linear) quantum mechanics and its nonlinear generalizatin [17] is the neglect of general properties of the comparison procedure of quantum dynamical variables. The problem of the comparison of quantum states is not trivial one. As a matter of fact this lies in the basis of the measuremet problem in quantum mechanics and closely connected with the EPR problem [18]. Let me use some passage from the article of Gisin [15]. ‘The experimental testing quantum mechanics against local hidden variables do not only violate the Bell inequality, but they also agree remarkably well with quantum mechanics. This supports the clime that if one spin of a singlet state pair is "found" to be in the up state, then the other spin is in the down state, for the *same direction*’ (it is my italization P.L.).

"The question is: what is ‘same direction’? This is the crucial point because this notion should have a physical meaning [18, 4, 5, 6]. The comparison of ‘z-direction’ at A and B is, as a matter of fact, the comparison of directions of physical fields. Since fields have indefinite numbers of degrees of freedom, a "parallel transport" has to be done in the projective Hilbert state [5, 6]. That is our credo in some "a priori spacetime geometry" must be subjected to verification and just result of such quantum measurement gives us a possibility to judge whether this is the "same direction" or not. Furthermore, we have not any a priori geometry of spacetime and should construct it basing on quantum setup [19]."
 

[Ref. 3] A. Ashtekar, T. A. Schilling, Geometrical Formulation of Quantum Mechanics, gr-qc/9706069 v1.
http://arxiv.org/abs/gr-qc/9706069

"The geometric formulation shows that the linear structure which is at the forefront in text-book treatments of quantum mechanics is, primarily, only a technical convenience and the essential ingredients -- the manifold of states, the symplectic structure and the Riemannian metric -- do not share this linearity."
 

Note: To make the Anzats above a bit more clear, let me try to respond to two questions.

Thomas Jordan (quant-ph/0508092 v4) reminds us of Wigner's proof that quantum dynamics must be linear, or else it will change the absolute values of inner products of state vectors [E. P. Wigner, Group Theory (Academic, New York, 1959), appendix to Chapter 20 and first section of Chapter 26; see also V. Bargmann, J. Math. Phys. 5, 862 (1964)]. His question is: "Is there a reason in principle that quantum dynamics is linear? If not, quantum dynamics could be a linear approximation of a nonlinear theory; then experiments might reveal small nonlinear effects."

Well, it's not that simple. No experiment has so far revealed any "small nonlinear effects", because QM cannot in principle probe the 'quantum reality out there'. Hence QM can and should stay linear, despite the fact that its proper geometrical formulation isn't.

The second question was posed by Frans Klinkhamer (hep-ph/0511030 v4): "Can CPT invariance be violated at all in a physical theory and, if so, is it in the real world? It is obvious that something "out of the ordinary" is required for this to be the case."

If the tacit presumption is that CPT invariance "violations" can be observed at the scale of tables and chairs, my answer to Frans Klinkhamer's question will be 'Jain'. Yes -- because CPT invariance can and should be "violated" in the global mode of spacetime. No -- because the observable effects from such "violation" cannot provide a track to something "out of the ordinary": the global mode of spacetime. It is a Holon state of the whole universe. It is the only 'truly isolated system'. Viewed from the local mode of spacetime, the global mode of the Holon is hidden "inside" the infinitesimal geometrical point, and "outside" the cosmological horizon. There is no direct track in the local mode, which could lead to the global mode. The simplest example is the clash of QM and STR here. The issue has been raised by Erwin Schrödinger in 1931.
 

D. Chakalov
January 27, 2006