Subject: Växjö Interpretation of Quantum Mechanics
Date: Wed, 20 Feb 2002 14:27:49 +0200
From: "Dimiter G. Chakalov" <>
To: Andrei Khrennikov <>
CC: Itamar Pitowsky <>,
     Johann Summhammer <>,
     Karl Svozil <>,
     Jeffrey Bub <>,
     Gebhard Gruebl <>,
     Chris Dewdney <>,
     Abner Shimony <>,
     Caslav Brukner <>,
     Ark Jadczyk <>, "Jeeva S. Anandan" <>,
     Shelly Goldstein <>,
     "R. Tumulka" <>,
     Matej Pavsic <>
BCC: [snip]

Dear Andrei,

I'm reading your contextual statistical realist interpretation of QM [Ref. 1] with great interest.

You wrote: "Such contextualism and complementarity do not contradict to the possibility of finer description of reality than given by quantum theory." [Ref. 1]

Please help me understand that "finer description of reality" by examining Gleason's theorem.

Please also see

You wrote: "Numerical does not mean 'real number'. It can be as well e.g. p-adic number, see [2]. So the possibility of HV-description does not imply continuous infinitely divisible representation of physical reality."

Are you suggesting some beables that are hidden because they should be "described" with p-adic numbers?

If we are to reject the continuous real number model of reality, how would you develop some QFT grounded on p-adic numbers? Specifically, how would you define the hidden intrinsic "time" of those hidden variables and map it to the time read with a physical clock? See, for example, the problems of Bohmian mechanics [Refs. 2 and 3].

It seems to me that these efforts are nothing more than another 'relational reality' interpretation of QM [Ref. 4]. But 'relational reality' is fully consistent with Gleason's and Kochen-Specker's theorems, so we are back in murky waters, aren't we?

I will appreciate your help for understanding your interpretation of QM, as well as the opinion of all physicists reading these lines.

Thank you very much in advance.


Dimiter G. Chakalov
(last update 19 February 2002)


[Ref. 1] Andrei Khrennikov. Växjö Interpretation of Quantum Mechanics.

"If we remember about contextuality discussing complementarity we see that complementarity of contexts in quantum physics does not imply complementarity of corresponding objective properties (of elementary particles) contributing into such observables. In particular, contextual complementarity does not imply that elementary particles do not have objective properties at all. In particular, there are no reasons to suppose that it is impossible to provide a kind of hidden variable, HV, description (ontic description, see e.g. [1]) for these objective properties.

"Numerical does not mean 'real number'. It can be as well e.g. p-adic number, see [2]. So the possibility of HV-description does not imply continuous infinitely divisible representation of physical reality.

"It was a rather common point view: in classical mechanics the position and momentum of an individual (!) system are described by real numbers, in quantum mechanics -- by matrices. W. Heisenberg rightly underlined that matrice-description could not be used for describing objective position and momentum of electron. There (as everywhere in XVIIIth -- XXth centuries physics) objective reality was, in fact, identified with the continuous (real number) mathematical model of physical reality. Impossibility to create a continuous real number model for motion of electron in Bohr's model of atom was considered by Heisenberg (and many others) as impossibility to assign objective properties to electrons.

"In fact, the only possible conscious interpretation of Heisenberg's uncertainty principle is the statistical contextual interpretation, see e.g. [12], [13]. It is impossible to prepare such an ensemble of elementary particles that dispersions of both position and momentum observables would be arbitrary small. Everybody would agree that only this statement can be verified experimentally. Contextualism has to be statistical contextualism and, consequently, complementarity has to be statistical contextual complementarity. Such contextualism and complementarity do not contradict to the possibility of finer description of reality than given by quantum theory.

"I would like to thank J. Bub, P. Lahti, W. De Baere, A. Plotnitsky and I. Pitowsky for extended discussions on the interpretation of quantum mechanics."

[Ref. 2] Gebhard Grübl. The quantum measurement problem enhanced.

"States and their properties vary continuously and deterministically with time. (...) If the Bohmian program could be extended to the realm of relativistic quantum fields, a quantum frame work with the potential for universal validity were found."

[Ref. 3] Chris Dewdney, George Horton. Relativistically invariant extension of the de Broglie-Bohm theory of quantum mechanics.

"Our approach yields a unique and relativistically invariant coordination of the points on the individual particle trajectories in space-time. The system's motion is determined once an "initial" point in the configuration space-time is specified and our use of the word "initial" merely indicates a starting point for the calculation. Just as in non-relativistic de Broglie-Bohm theory there is no wave-packet collapse in our relativistic extension. Measurements play no fundamental role, they are simply interactions between systems during which a correlation is introduced between their variables such that by observing one variable one can infer the value of the other.

"If, for example, the wave packets emerge simultaneously (Sic! - D.C.) in a given frame of reference, then this determines the ensemble of possible, physically realizable, initial configuration-space points for this particular experiment. Observers in frames of reference in relative motion will judge simultaneity differently, but this has nothing to do with the actual set of initial points in configuration space that are consistent with the experimental conditions or the way in which the points on the individual particle trajectories are in fact coordinated according to our lorentz invariant rule."

[Ref. 4] J. Anandan. Causality, Symmetries, and Quantum Mechanics.


Subject: Foundations of probability and physics - 2, Växjö, June 2-7
Date: Fri, 10 May 2002 21:28:33 +0300
From: "Dimiter G. Chakalov" <>
To: Andrei Khrennikov <>
CC: Christopher Fuchs <>,
     N David Mermin <>,
     Asher Peres <>

Hi Andrei,

You wrote:

> (the main idea was to provide financial support to the good team
> of invited speakers varying from year to year).

Did you ask your invited speakers to formulate falsifiable hypotheses only? See the list of conferences in C. Fuchs' quant-ph/0205039.

Are you going to reply to C. Fuchs' criticism in quant-ph/0204146, as well as to ?

My favorite "interpretation" of QM is 'shut up and calculate'. I believe QM does not provide, and can not provide any basis for a fruitful discussion on the role that PROBABILITY plays in foundations of physics.

The very fact that QM contains classical mechanics as a limiting case, yet at the same time requires this limiting case for its own formulation (Landau L. and Lifshitz E. (1974) Quantum Mechanics. Oxford: Pergamon Press), casts serious doubts on the very possibility for resolving the main issue of your forthcoming conference.

QM says nothing about the nature of quantum reality, hence people can play with it forever. It's like looking at a yellow flower through blue glasses, although you can never take off your glasses and have no idea what is 'yellow'.

Please correct me if I'm wrong.

I extend this request to your colleagues as well.


The hardest thing of all is to find a black cat in a dark room, especially if there is no cat.



Subject: Prequantum observables
Date: Tue, 03 Jun 2003 12:36:55 +0300
From: Dimi Chakalov <>
To: Andrei Khrennikov <>
CC: Robert Oeckl <>,,,,,,,,,,,,,,,,,,,,,,,

Dear Andrei,

I do hope my email of Fri, 10 May 2002 21:28:33 +0300äxjö

has been received.

Today you introduced a prespace context represented by a so-called hyperbolic quantum model [Ref. 5]. Given the genuine difficulties in the "measurement" of prequantum observables, I'm wondering if you could be so kind as to cast your ideas in the context of Schrödinger's cat [Ref. 6, Fig. 3 and pp. 8-9].

Please keep in mind that the projective space is a genuine non-linear manifold,

and please don't forget the so-called zero space where observable time stops,

Thank you very much in advance.

I will appreciate the opinion of your colleagues as well.

BTW I believe you can "measure" prequantum observables with your brain, only they are UNspeakable,ömer.html#2


Dead matter makes quantum jumps; the living-and-quantum matter is smarter.


[Ref. 5] Andrei Khrennikov (June 3, 2003), Contextual approach to quantum mechanics and the theory of the fundamental prespace.

Comments: Plenary talk at Conference "Quantum Theory: Reconsideration of Foundations-2", Vaxjo, 1-6 June, 2003

Sec. 9, "Classical and quantum spaces as rough images of fundamental prespace.

"We are not able (at least at the moment) to measure an arbitrary preobservable (...).

p. 32: "In general the operators (...) corresponding to functions (...) or (...) are not directly related to prequantum observables (...).

"Thus the quantum theory is not a fundamental theory. It does not provide the complete (even statistical) description of the prespace reality.

"Human beings have been creating their own (very special) classical space. Since light rays play the fundamental role in the creating of our classical space it can be called electromagnetic classical space. So the electromagnetic classical space is created on the basis on electromagnetic reduction of information. In principle there can exist systems which are able to perform some other reductions of information, e.g., gravitation reduction. They would create a gravitational classical space."

[Ref. 6] Robert Oeckl, Schroedinger's cat and the clock: Lessons for quantum gravity.

"How does the system "know" about the time  [delta] t  elapsed on my clock when I cannot assume any definite evolution of time inside the closed box?"


Subject: ...huge (may be even infinite)...
Date: Wed, 11 Jun 2003 15:09:31 +0300
From: Dimi Chakalov <>
To: Andrei Khrennikov <>
CC: Howard Barnum <>

Dear Andrei,

In your latest "Classical and quantum spaces as rough images of the fundamental prespace", quant-ph/030606 of June 11th, you wrote:

"The crucial point is that X_cl is created via the huge reduction of information in the process of transition from the prespace contexts to points of X_cl. Each classical point x --> X_cl is the image of a domain B_x of the prespace [omega], see [1], and this domain can contain huge (may be even infinite) number of prepoints [...]."

The Holon also contains huge (may be even infinite) number of possible explications. I hope you have tried it with your brain, as I suggested previously,

You also wrote: "I neither have physical arguments. But I have strong probabilistic arguments."

What if your prequantum observables are 'neither true nor false'? Maybe this is why they are UNspeakable and indenumerable: "huge (may be even infinite)".

How could you possibly make a SET of prequantum observables? The only way to think of them as a *set* is by their Holon representation. Am I wrong?

I regret that was not informed about your conference. We could have had a lot of fun!

Not that I didn't want to say what I didn't actually say ... or did I?


Dead matter makes quantum jumps; the living-and-quantum matter is smarter.


Subject: Dynamical systems in the non-Archimedean field of Ideas
Date: Thu, 22 Dec 2005 18:42:48 +0200
From: Dimi Chakalov <>
To: Andrei Khrennikov <>
CC: Victor Pavlovich Maslov <>

Andrei dorogoi,

It seems to me that there is a typo in your recent math.PR/0512427 v1, p. 3, third para from below: "teh physical level ...".

I noticed in your CV that you've been in Moscow State University,

I believe you've met Vassiliy Vassilevich Nalimov and have read his books, particularly "Realms of the Unconscious. The Enchanted Frontier" (ISI Press, Philadelphia, 1982) and "Veroyatnostnaya Model Yazika" (Nauka, Moskow, 1979),

Regarding the non-Archimedean field of Ideas, see

I believe the non-Archimedean field of Ideas [I call them potential point(s)] contains a very special object -- an empty set -- from which brand new things can *emerge* from 'the unknown unknown'. If so, the dynamics of the potential point(s) should be strictly non-unitary,

Can you tackle all this with your p-adic number system (math.PR/0512427 v1)?

Also, can you introduce Lebesgue measure on infinite-dimensional spaces?

I will highly appreciate the opinion of Prof. Maslov as well.

Since we talk about dynamical systems, see a brief note from anonymous author at

"(Special - ) Relativistic Arrow of time

"We (any inertial reference frame) always have non-zero complex speed vector in Minkowski space with constant norm c (speed of light in vacuum). The unit vector of that vector is our (that inertial reference frame's) Arrow of time.

"In other words, even if we don't notice that while apparently at rest, we are always moving along our world lines toward the future with maximal (and minimal..., in fact only possible one) speed  c .

"I am aware that this, of course, is a circular definition, but it perhaps sheds some more light (or casts some more shadow, whatever) on the notion. As much as there is no absolute time, there also isn't neither any absolute Arrow of time nor absolute rest."

We're always "moving" toward the future with "speed"  c  in the putative global mode of spacetime,

Merry Christmas to you and Viktoru Pavlovichu.


Note: Angela Thompson stressed that "Nalimov's ideas run parallel with those of the Polish scholar Alfred Korzybski (A. Korzybski, Science and Sanity: An introduction to non-Aristotelian systems and general semantics, Lakeville, CT: Colonial Press, 1973) who first published works on general semantics and meaning as early as 1935. Nalimov in Realms of the Unconscious (1984, p. 281) acknowledges Korzybski's critical work on the logic of general semantics and describes his criticism of Aristotelian logic as "strikingly shrewd" (Angela Thompson, Journal of Humanistic Psychology, 33(3), 1993, 82-98; link here).

All this sounds quite heavy, isn't it? Here's a simple explanation. If you are familiar with digital sound creation programs (e.g., Magix Music Maker), perhaps you have noticed that you can play a given melodic theme with different musical instruments, but the "meaning" of the theme will remain invariant. Even if you have an infinite number of instruments, they will produce infinite variations of "the same" melodic theme. Yet you can never play "the generic" theme, because it is in the form of Platonic Idea. Perhaps Feodor Tutchev has gone too far in insisting that "the verbalized thought is a lie", but the moral of the story is that "the generic meaning" cannot be exactly and fully reproduced with a finite number of propositions. We can only catch John's jackets from the ideal point(s).

That's all. The rest is math, but not necessarily p-adic "numbers". Notice that the potential point(s) always carry an "empty set" in it, but we can say nothing about it. It is simply the "entry point" of brand new events, which are still in the realm of 'the unknown unknown'. Hence we have a time arrow: the information content of the universe is increasing in every step of the universal time arrow. Thus, the current Holon of the universe is evolving as well. The source is well-known [John 1:1].

I'm an unabashed Origenist [Ref. 7], and regret that we lost by just one vote. But the future is open, and we cannot know what might spring out of the "empty set" by November of 2015. My position is much better than that of Origen: he had fifteen anathemas, I got so far just one.

D. Chakalov
December 22, 2005
A positive attitude may not solve all your problems, but it will annoy enough people to make it worth the effort

Herm Albright

[Ref. 7] Brad Steiger and Sherry Hansen Steiger, Gale encyclopedia of the unusual and unexplained, Thomson Gale, November 2003, p. 44.

"A prolific Christian writer and leader, Origen preached a relationship between faith and knowledge and explained the sinfulness of all men and women by the doctrine of the preexistence of all souls. In Contra Celsum he asked, "Is it not rational that souls should be introduced into bodies in accordance with their merits and previous deeds, and that those who have used their bodies in doing the utmost possible good should have a right to bodies endowed with qualities superior to the bodies of others?"

"In response to the query, Origen continues: "The soul, which is immaterial and invisible in its nature, exists in no material place without having a body suited to the nature of that place; accordingly, it at one time puts off one body, which is necessary before, but which is no longer adequate in its changed state, and it exchanges it for a second."

"At the Council of Nicaea in 325, Origenism was excluded from the doctrines of the Christian Church and 15 anathemas were proposed against Origen himself. The Origenists, those who favored including the ethics of karma and the doctrine of preexistence in the official Church teachings, had lost by only one vote."

[To the best of my knowledge, the condemnation of Origenism was executed at the Fifth Ecumenical Council (the Second Council of Constantinople), around 553 AD - D.C.]


Subject: Quantum Probability, Information and Control (Nottingham 10-21 July 2006)
Date: Fri, 23 Dec 2005 14:55:08 +0200
From: Dimi Chakalov <>
To: Viacheslav Belavkin <>
CC: John Gaugh <>,
     Joachim Zacharias <>,
     Alexei Grinbaum <>,
     Jerry Finkelstein <>,
     Victor P Maslov <>,
     Andrei Khrennikov <>,
     Chris Isham <>,
     Christian Beck <>,
     Jeffrey Bub <>

How wonderful we have met with a paradox, now we have some hope of
making progress - Niels Bohr

Dear Dr. Belavkin,

I will be more than happy to attend your Symposium in July next year [Ref. 1], hoping that you any/or any of your colleagues can suggest a tentative explanation of the following conundrum:

There should exist a Lorentz-invariant, reversible, bi-directional, and smooth transition from the hidden unobservable quantum reality to the normal world of tables and chairs, and back to the hidden unobservable quantum reality.

I looked at your recent quant-ph/0512187 v1 [Ref. 2, p. 3], and spotted
the following statement: "There is no nontrivial reversible classical-quantum mechanical interaction, but as we have seen, there is
a Hamiltonian irreversible interaction within the time asymmetric Eventum Mechanics."

To understand your asymmetric Eventum Mechanics, I searched your paper for the word "relativity", but couldn't find any. The way I see it, the problem stems from the well-known statement, which can be found in many non-relativistic QM textbooks, say, [Ref. 3]: immediately *prior* the collapse, the quantum system *was* (notice the preferred basis problem) in some "eigenstate". Please see

Should this *immediately prior the measurement* quantum state existed as an 'objective reality', we could traced its history, starting with its "entry point" in our Minkowski cone, and discover some "quantum time parameter", hence reconcile the time parameter in STR with the "time arrow in Quantum Event-Mechanics" which is just "kinematicly irreversible" [Ref. 1].

Alternatively, if this *immediately prior the measurement* quantum state
exists as 'potential point(s)', I believe the clash of QM and STR can be
resolved only by suggesting new physics,

If you cannot reconcile your ideas with STR, I would be very skeptical about the prospects of your forthcoming Symposium. I do hope you agree.

You can read this email also at


Dimi Chakalov


[Ref. 1] Quantum Probability, Information and Control (Nottingham 10-21 July 2006)

"Conceptually, it is based upon the new idea of quantum causality and
eventum mechanics based on the irreversible endomorphic dynamics and
nondemolition principle which divides the world into the classical past,
forming the consistent histories, and the quantum future, the state of
which is predictable for each such history."

Quantum Universe and Reality

"Quantum Reality, identified with a pure Quantum State, may not determine measurement events, but at least it determines quantum potentiality, i.e. propensity of all quantum properties, or propositions, as well as probabilities of all observable events. However these events, if they all were observed, completely determine this reality, otherwise the Universe would emerge in a mixed state. Any mixed state of the Universe is nothing but a unique mixture of the undertermined realities in the result of the loss of unobserved Quantum Information."

Quantum Hidden Variables

"The Eventum Mechanics, in contrast, explains the quantum phenomenology of the visible events by simple and honest declaration of the existance of two worlds: the visible part of the universe is macroscopic, or classical world, and the quantum, microscopic world, although indirectly observed, will always remain hidden. In this sense it is the only mathematically consistent theory with Copenhagen interpretation. The time arrow in Quantum Event-Mechanics is kinematicly irreversible, since quantum part of the Universe cannot be moved by any Heisenberg dynamics into the quantum which is opposit direction for Eventum Mechanics motion. What was visible is the past, composes classical reality, and what was hidden is the future, remains quantum potentiality in due course of this motion."

[Ref. 2] Viacheslav Belavkin, On the Dynamical Solution of Quantum
Measurement Problem, quant-ph/0512187 v1.

[Ref. 3] Daniel T. Gillespie, Quantum Mechanics Primer: An Elementary
Introduction to the Formal Theory of Non-Relativistic Quantum Mechanics,
New York: International Textbook Co., 1973, pp. 49-58.


Subject: One directional, half-Lorentz-invariant "scientific communism"
Date: Fri, 23 Dec 2005 22:32:06 +0200
From: Dimi Chakalov <>
To: Prof V P Belavkin <>

Slava dorodoi,

> The symposium will not be directly related to any of your questions

As I wrote before, if you cannot reconcile your ideas with STR, I would be very skeptical about the prospects of your forthcoming Symposium.

> Why?

Please use your Internet connection and click on the links in my preceding email.

Your "one directional half-Lorentz-invariant" ideas sound like "scientific communism" to me. Sorry.

I will come to your Symposium  iff  you place your cards on the table, and declare the conditions under which you will accept that your ideas are wrong. I will do the same. That's science IMHO.

Do you agree?

If you do not agree, I won't come, because I'm afraid your forthcoming Symposium will be deadly boring.



Note: Viacheslav Belavkin was born in the former Soviet Union. He was given the (miraculous?) opportunity to leave it six years before the coup d'état on August 19, 1991: "... and in the spring of 1985 I was allowed (to my great surprise) to visit Italy" (link here). Well, I never had such luck, but at least hope will be lucky to receive his professional reply by July 2006.

D. Chakalov
December 23, 2005


Subject: Re: QM and Quantum Gravity
Date: Thu, 12 Jan 2006 19:27:07 +0200
From: Dimi Chakalov <>
To: Andrei Khrennikov <>

Dear Andrei,

Thank you for your feedback and interest in my opinion.

> So it is impossible to unify them at all, but just consider as projections
> (incomplete representations) of a more fundamental theory?

I think it is indeed impossible to unify them, since we don't have a 'back bone' for QM and GR. RE this 'back bone', I'm of course biased,

Specific proposal at

Can you dress it in math?

Best regards,


P.S. Regarding von Neumann's no-go Ansatz, see E. Rosinger's quant-ph/0408191,

> I presented a model in that the role of hidden variables is played by
> vectors of complex Hilbert space (non-normalized vectors!).

Beautiful! They got to be non-normalizable. Please see

Good luck.



Subject: Re: QM and Quantum Gravity
Date: Fri, 13 Jan 2006 01:29:40 +0200
From: Dimi Chakalov <>
To: Andrei Khrennikov <>

> >
> Would you agree to consider just points of the Hilbert phase space as
> your \"potential points\"?

Yes, provided you stress the non-linear nature of the manifold of states, the symplectic structure, and the Riemannian metric; please see below.

Best - Dimi
A. Ashtekar, T.A. Schilling. Geometrical Formulation of Quantum Mechanics, 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."