Subject: Quarks in Fibonacci series?
Date: Thu, 14 Apr 2005 20:53:41 +0300
From: Dimi Chakalov <>
To: Kevin Brown <>

Dear Dr. Brown,

I greatly enjoyed your MathPages, and have quoted from them extensively at my web site.

I wonder if you can come up with some ideas about a Fibonacci sequence in quarks,

The task is to find the next step in the Fibonacci sequence of quarks,
which would include the electron,

We've learned from John Baez that the fermions are "antisocial" while bosons, by contrast, are "gregarious",

Can you think of some layer of the quantum world, in which all these guys will be "gregarious", in a compound eight-quark state maybe?

Any ideas from the combinatorial theory of the icosahedron?

Best regards,

Dimi Chakalov

Note 1: There is a very important research paper by Gunn Quznetsov, which is available in Russian only [Ref. 1]. I do hope the author will translate it into English, as soon as possible. See Sec. 4, Masses (p. 18), and Sec. 11, Interpretation of quantum event theory (p. 44).

In a nutshell, Gunn Quznetsov elaborates on the fundamental ideas of Sir Nevill Mott regarding the generation of observable paths in Wilson cloud chambers.

I believe the conclusion of the 46-page paper [Ref. 1] is of crucial importance for all people trying to chase the 'God particle' with LHC and the "next generation" Barbie: you cannot observe anything "between" the events of spacetime, as modeled with the red  Z  axis here. You will only get 'more of the same': leptons, gauge bosons, and an infinite chain of quarks, in a Fibonacci sequence. More from Roman Jackiw here.

The paper by Gunn Quznetsov is mostly math, the wording is very brisk and simple, and if you have basic knowledge in Russian -- read it [Ref. 1].

However, if you want to waste billions of dollars and euro -- taxpayers' money -- do not read anything, not not think, and do not reply. Just join the community of LIGO.

D. Chakalov
May 23, 2005
Last update: May 25, 2005

[Ref. 1] Gunn Alex Quznetsov, It is not Higgs, physics/0302013 v2, 20 May 2005. 46 pages, no pictures, in Russian.

Abstract: Every physics event is interpreted by particles which similar well-known elementary particles - leptons, quarks and gauge bosons. Therefore, if anybody will claim that he had found Higgs then not believe - this is not Higgs.



Subject: Re: Quarks in Fibonacci series?
Date: Mon, 23 May 2005 16:46:23 +0300
From: Dimi Chakalov <>
To: Gunn Quznetsov <>,

Dear Gunn,

I mentioned your fundamental paper at

Hope to read it in English ASAP.

Best regards,


Note 2: It might take some time to translate the "Siberian bear" in English. Meanwhile let's listen the story about the Fibonacci numbers, from "Joy of Thinking: The Beauty and Power of Classical Mathematical Ideas. Course No. 1423. Taught by Edward B. Burger and Michael Starbird. The Teaching Company, 2005,
SizingUptheFibonacciNumbers.mp3, 5,492,988 bytes.

All you need to win your Nobel Prize in on this web page. Just follow the links.

"Whether you believe you can do a thing or believe you can't, you are right", says Henry Ford.

D. Chakalov
May 24, 2005


Subject: What is the nature of the "space" between "points"?
Date: Tue, 09 Aug 2005 13:57:39 +0300
From: Dimi Chakalov <>
To: Gunn Quznetsov <>,
CC: Valeri Dvoeglazov <>,
     Leonid Grishchuk <>,
     Andrei Khrennikov <>,
     Pavel V Kurakin <>,
     Serguei Krasnikov <>,
     Alex <>

RE: physics/0508042 v1, Sec. 5.10, p. 110: "Sledovatel'no, fizicheskaya
chastiza dvizhetsia potomy, chto sootvetstvuyzhaya veroyatnost'
razprostraniaetsya v prostranstve mezhdu etimi tochkami." ('Thus, the
physical particle is able to propagate, because its corresponding
probability propagates in the space between these points' -- translation
mine, D.C.)

Dear Gunn,

We don't want to "explain" an old enigma with a new puzzle, right?

I wonder what is the nature of the "space" between "points", and what is the relation/link of this "space" to the normal physical 3-D space made exclusively (=nothing else) by the same "points".

To the best of my knowledge, the "latest" update on this very old enigma is from St. Augustine. What do you suggest?

I will be happy to learn the opinion of your colleagues as well.

My efforts can be read at




Subject: Re: Hierarchical theories

Date: Wed, 25 May 2005 23:32:05 +0300
From: Dimi Chakalov <>
To: Erasmo Recami <>

Dear Erasmo,

It is so nice to hear from you. No need to send snail mail, as in 1984. Time runs so damn fast, it's not fair!:-)

> In any case, I had overlooked Leonardo (if you mean Leonardo da Vinci).

I meant Leonardo of Pisa, a.k.a. Fibonacci,

BTW I've quoted extensively from your Chronon theory (quant-ph/9706059 and quant-ph/0206117) at my web site. In the second paper, with Ruy
Farias, you wrote:

"Second: the new discrete formalism allows not only the description of the stationary states, but also a (space-time) description of transient states."

My hunch about this new "discrete" formalism is to introduce a new degree of freedom of spacetime, with an axis which comes 'from inside' the infinitesimal of Leibnitz,

Best regards,



Subject: Re: Hierarchical theories /Post Scriptum
Date: Thu, 26 May 2005 01:58:23 +0300
From: Dimi Chakalov <>
To: Erasmo Recami <>
CC: Giovanni Salesi <>

Dear Erasmo,

Thank you very much for your immediate reply.

I think you are too ahead of time with your ideas about the Chronon. I mean, you have suggested a generalized quantum mechanics: we obtain the standard non-relativistic QM only in the limit of [tau] --> 0 (quant-ph/9706059). I guess people are scared, since they can apply the "projection postulate" only in that (highly uninteresting) limiting case, and nobody knows how to handle non-Hermitean "operators" in the generalized case of a finite  [tau] . It's a bit like trying to "see" a dark room with the torch  [tau] --> 0 ,

I seriously believe you have discovered a fundamental theory, which will flourish when the time comes for it. As with a good wine, it stays 'out there' and waits for matured people to appreciate it.

Please keep me in touch about your insights regarding Fibonacci's numbers in non-Abelian gauge fields. In addition to the link in my preceding email, please see Roman Jackiw at

> I'll send a copy of your mails also to my coworker prof.G.Salesi
> (, who is engaged too with similar questions.

Thank you very much. Regarding your 1997 Zitterbewegung paper, with Prof. Giovanni Salesi [Foundations of Physics Letters, 10 (6) 533-546 (1997)], may I draw your attention to an intriguing paper by Daniel Sepunaru, "On the problem of Zitterbewegung of the Dirac electron", in which he claims to have eliminated the Zitterbewegung,

Let me say good night, since tomorrow (well, this morning) will have to fix two old PCs and an ancient printer, which will be a tough job, and need some sleep now.

Best wishes,

As ever yours,

E sarà mia colpa se così è?
Niccolò Machiavelli


Subject: quant-ph/9706059 v3
Date: Wed, 25 Jul 2007 16:36:08 +0300
From: Dimi Chakalov <>
To: Erasmo Recami <>
Cc: Salvatore Esposito <>,
Giovanni Salesi <>

Dear Erasmo,

I spotted your quant-ph/9706059 v3, and thought you may wish to see a third way to make a discrete time at

Have a nice summer!

Best - Dimi

Ruy H. A. Farias and E. Recami, Introduction of a Quantum of Time ("chronon") and its Consequences for Quantum Mechanics, arXiv:quant-ph/9706059v3,

"It is important to stress that, in principle, time discretization can be
introduced in two distinct (and completely different) ways:

"(1) by attributing to time a discrete structure, i.e., by regarding time not
as a continuum, but as a one-dimensional "lattice";

"(2) by considering time as a continuum, in which events can take place
(discontinuously) only at discrete instants of time."




Subject: Infinite-dimensional representations of the Lorentz group
Date: Mon, 10 Apr 2006 03:40:44 +0300
From: Dimi Chakalov <>

Dear Professor Esposito,

I have an immodest request.

If possible, may I ask you to help me understand the physical meaning and implications from 'infinite-dimensional representations of the Lorentz group', as discovered my Majorana (physics/0604064 v1, p. 18).

Also, I've been deeply puzzled by the nature of the electron. As E.L. Koschmieder put it in physics/0503206 v2, p. 15: "There must be something else in the electron but electric charge. It is equally clear from the most advanced experimental work that the "something else" in the electron must be non-interacting."

I will be very grateful if you and your colleagues can shed some light on these puzzles. Will keep you feedback private.

Kindest regards,

Dimi Chakalov


Subject: physics/0604003 v2
Date: Thu, 13 Apr 2006 04:07:36 +0300
From: Dimi Chakalov <>

Dear Professor Pecina-Cruz,

I too believe that the mass itself does not have an independent physical
meaning, and if the neutrino is a tachyon with a measurable property --
the square of its mass -- I think it may easily "propagate" in the space,

Best regards,

Dimi Chakalov


Note: The mass itself does not, and cannot have an independent physical
meaning, because the would is interdependent and relational: "properly speaking, GR does not admit a description as a system evolving in terms of an observable time variable." [Ref. 1]

The effect of the global time, mentioned in my email to Prof. Pecina-Cruz, is like "inserting" the square mass of the neutrino into the "dark" gaps in the local time: typical holistic effect. In neuroscience, it makes chemical reactions bio-chemical. In solid state physics, it produced phonons. In the Standard Model, it creates another physical stuff: quarks in Fibonacci series.

The nature of this effect is to add new physical stuff from the Holon into the local time, and if you seek the mass of the neutrino exclusively in the local time mode, you won't find it. To use the forest metaphor, we can say that the "trees" in the local time have acquired a brand new property from "the forest": the neutrino.

Go and figure it out by looking at the trees alone! You'd need tachyons, but tachyons are an artifact from the absence of the global time in present-day physics. That is, the bi-directional talk in the global time casts its blueprint on the local time, and people start believing in tachyons. I did too, from 1984 up until May 22, 1988. Anyway.

Any time you think of the electron and its unification with the other, composite elementary particles, keep your mind fully open to surprises from Fibonacci.

Talking about surprises, look at the latest paper by Chris Isham's student Carlo Rovelli [Ref. 1]: do you see something fishy? GR does not admit a description as a system evolving in terms of an observable time variable, but does admit a description as a system evolving in some "observable" 3-D space. As if you could cut the spacetime into "time" and "space", as does another philosopher of quantum gravity, L. Smolin. How would have Hermann Minkowski reacted to this philosophy? Politely, I suppose. More in my note to S. Deser here.

There is another very interesting issue in Rovelli's paper [Ref. 1]: "in the quantum context a single solution of the dynamical equation is like a single "trajectory" of a quantum particle". Thus, we should be deeply puzzled why we don't encounter any observational contradictions from GR by picking some "spacetime" that should be initially inadequate for describing the world. It would be like making a spacetime from, say,  |live cat>  only.

In my view (which I don't want to impose to anyone), we don't hit any contradictions because all "cat states" are permissible by virtue of the general covariance: see C. Isham and J. Butterfield here. Hence we may, with impunity, abuse GR by claiming that it shows some "observable time variable". Carlo Rovelli is right by stressing this error: "properly speaking, GR does not admit a description as a system evolving in terms of an observable time variable."

The reason why Carlo Rovelli is right is in the following. Recall that we don't have the luxury of some bare "spacetime points", after Einstein's Hole Argument (cf. active diffeomorphisms), hence if we seek some 'observable time variable' in the bi-directional talk of matter and geometry of space, we'll hit the following conundrum.

Suppose the distribution of matter fields has fixed a 'spacetime', after the bi-directional talk (John Wheeler) has been completed. Could this bi-directional talk be referring to some 'observable time variable'? Obviously not. We are allowed to talk about a 'spacetime' only after the dialogue of matter and geometry of space has been completed. If we try to bridge the gap "between" any two successive "talks" of the two sides of Einstein's filed equation, we would have to instruct the right hand side (matter) to negotiate, with the left hand side, its geometry of space valid for the next step along the alleged 'observable time variable'. But the "duration" of this negotiation is spanned "between" the instances of 'already completed talk', hence it is unobservable: "there is no external time variable that can play the role of observable independent evolution variable" [Ref. 1].

Here some people say: "And, after all, general relativity does seem to work well as a theory, and yet I can certainly read the time on my wrist watch!"

But of course you can read the time on your wrist watch! It is the local time of Flatlanders (see again the flash movie here). What your poor wrist watch cannot read is the genuine dynamics of the gravitational field [Ref. 1] and the intrinsic dynamics of its "dark energy". No way.

The fun part of quantum gravity begins if you try to imagine some principle that could single out one permissible spacetime -- one-at-a-time -- stretched by the "dark" energy. See again the 'two hands' picture here. Can you see the "dark" energy of the reference fluid? Just please do not forget that prosaic electron!

Recently Thomas Thiemann acknowledged a "devastating conclusion" [Ref. 2]: "Either the mathematical formalism ... is inappropriate or we are missing some new physics." Why not both? If you're missing some new physics, it could very well be because the mathematical formalism is inappropriate. Just a thought.

D. Chakalov
April 13, 2006
Last update: August 4, 2006

[Ref. 1] Carlo Rovelli, Unfinished revolution, gr-qc/0604045 v2.

[Introductive chapter of a book on Quantum Gravity, edited by Daniele Oriti, to appear with Cambridge University Press]

"In general relativity, when we describe the dynamics of the gravitational field (not to be confused with the dynamics of matter in a given gravitational field), there is no external time variable that can play the role of observable independent evolution variable. The field equations are written in terms of an evolution parameter, which is the time coordinate x0, but this coordinate does not correspond to anything directly observable. The proper time [tau] along spacetime trajectories cannot be used as an independent variable either, as [tau] is a complicated non-local function of the gravitational field itself.

"Therefore, properly speaking, GR does not admit a description as a system evolving in terms of an observable time variable.

"This weakening of the notion of time in classical GR is rarely emphasized: After all, in classical GR we may disregard the full dynamical structure of the theory and consider only individual solutions of its equations of motion. A single solution of the GR equations of motion determines "a spacetime", where a notion of proper time is associated to each timelike worldline.

"But in the quantum context a single solution of the dynamical equation is like a single "trajectory" of a quantum particle: in quantum theory there are no physical individual trajectories: there are only transition probabilities between observable eigenvalues."

[Ref. 2] T. Thiemann, Solving the Problem of Time in General Relativity and Cosmology with Phantoms and k-Essence, astro-ph/0607380 v1.

"Why is it that the FRW equations describe the physical time evolution which is actually observed for instance through red shift experiments, of physical, that is observable, quantities such as the scale parameter?

"The puzzle here is that these observed quantities are mathematically described by functions on the phase space which do not Poisson commute with the constraints! Hence they are not gauge invariant and therefore should not be observable in obvious contradiction to reality.

"Moreover, the time evolution described by the FRW equations is obtained from the Hamiltonian equations of motion generated by the Hamiltonian constraint and not by an actual Hamiltonian. This is due to the fact that the "Hamiltonian" used to derive the FRW equations is actually constrained to vanish by one of the Einstein equations. The "evolution equations" generated by a constraint must therefore be interpreted as gauge transformations and those, by the very definition of gauge transformations, are also not observable, again in sharp contradiction to observation. Thus we arrive at the following devastating conclusion:

"Either the mathematical formalism, which has been tested experimentally so excellently in other gauge theories such as QED, is inappropriate or we are missing some new physics."

F. Darabi, arXiv:0809.1282v2 [hep-ph]: "The Friedmann equations describe the physical time evolution which is actually observed for instance through red shift experiments. The puzzle here is that these observed quantities as functions of the phase space do not commute with the constraints, so they are not gauge invariant and therefore should not be observable, in sharp contradiction to observation.

"Moreover, the Friedmann equations are generated by a vanishing Hamiltonian constraint and must be interpreted as gauge transformations rather than evolution equations. Therefore, the phase space dependent quantities in these equations should not be observable, again in sharp contradiction to reality. The conclusion is: Either the constraint formalism which has been exactly tested by experiments in other gauge theories is inappropriate or we are missing some new physics in gravitation theory [1]."
[1] T. Thiemann, Solving the Problem of Time in General Relativity and Cosmology with Phantoms and k - Essence, astro-ph/0607380.



Subject: An elementary atom of space
Date: Tue, 29 Aug 2006 17:56:55 +0300
From: Dimi Chakalov <>
To: Simone Speziale <>,

Dear Dr. Speziale,

May I offer a conceptual solution to your problem of defining the "coherent tetrahedron" [Ref. 1], hoping that you and/or some of your colleagues will comment on my proposal. I sincerely hope that you will examine the issue with scrupulous intellectual honesty, just like your co-author Carlo Rovelli,

To suggest an elementary atom of space, which you model as some "quantum tetrahedron", I believe the first off task is understanding "the sense in which wave packets or coherent states approximate classical
configurations in ordinary quantum theory" [Ref. 1, p. 1].

Which, in turns, leads to the task of reconciling QM with STR, as shown in the measurement problem,

We cannot use ANY "semi-classical approximations", "semi-classical states", and "semi-classical limit" to recover the classical geometry of the world of tables and chairs around us: "One of the biggest mysteries is that we live in a world in which it is possible to look around, and see as far as we like" (Lee Smolin, Three Roads to Quantum Gravity, p. 205). Should you have doubts, please see Chapter 10, "Quantum gravity and the interpretation of quantum theory", from C. Kiefer's "Quantum Gravity" (Oxford University Press, Oxford, 2004). I will be happy to elaborate.

Thus, we need *perfectly* classical (not "semi-classical") explications of 'the quantum state', which (i) fully comply with STR, and (ii) correspond to the notion of 'point' in classical geometry and 'observable' in classical physics, by converting to a point-like numerical value upon observation.

The conceptual solution to the task of reconciling QM with STR (cf. the link above) boils down to providing the dynamics of actualization of *perfectly* classical explications of 'the quantum state'. I can offer four such *perfectly* classical explications, and I'm sure your brain can grasp very well 'the quantum state' from which these four classical states originate.

The four classical states can be illustrated with four sayings:

1. All are not hunters that blow the horn.
2. La robe ne fait pas le médecin.
3. Es ist nicht jeder ein Koch, der ein lang Messer trägt.
4. Non sunt omnes venatores, qui cornu canunt.

Can you grasp 'the quantum state'? It isn't in the Hilbert space though.

If you look at the beautiful animation made by Dmitry Budker at  ,

you will "see" the genuine dynamics of 'the quantum state', depicted
with the dynamics of the surface, in three dimensions, representing the
probability distribution of the angular momentum [Ref. 2].


Please notice that the dynamics of 'the quantum state' ('the angular momentum') cannot be read by your wristwatch. All you can do is to try to count the number of possible classical explications of 'the angular momentum', and speculate that they can be normalized with respect to some instant of observation, as recorded by your wristwatch.

To sum up, the reason why 'the quantum state' does not live on the Hilbert space can be explained with the task of reconciling QM with STR (see the link above). The 'quantum state out there' is 'relational reality' [Ref. 3] outside the Hilbert space. You can keep it in your brain though, and it will never "collapse",

If you brain can do it, Mother Nature can do it as well (maybe even better).

Many years ago, your co-author C. Rovelli flouted at Kuchar's Perennials by talking about 'evolving constants' and 'partial observables', but recently he stressed that "properly speaking, GR does not admit a description as a system evolving in terms of an observable time variable."

In our case, the 'observable time variable' is that of the four perfect classical explications of 'the quantum state', hence all you have to do is to chain these classical explications into a perfect continuum of classical states, while leaving the quantum-gravitational state 'alive and well', like Kuchar's Perennials and Unmoved Mover,

I will be happy if you or some of your colleagues can find a conserved quantity of 'the quantum-gravitational state', resembling Noether's current [Ref. 4, Eq. 3.4]. You may need it for an ‘off-shell’ propagation of quantum gravity degrees of freedom.

More on the elementary atom of space at

Kindest regards,

Dimi Chakalov


[Ref. 1] Carlo Rovelli and Simone Speziale, A semiclassical tetrahedron,
gr-qc/0606074 v2,

"Consequently, in general there is no state in H that corresponds to a
given classical geometry of the tetrahedron. This fact raises immediately the problem of finding semiclassical quantum states in H that approximate a given classical geometry, in the sense in which wave packets or coherent states approximate classical configurations in ordinary quantum theory. This is the problem of defining the "coherent tetrahedron"."

[Ref. 2] S. M. Rochester and D. Budker, Atomic polarization visualized,
American Journal of Physics, 69(4) 450-454 (2001).

[Ref. 3] Jeeva Anandan, Causality, Symmetries, and Quantum Mechanics, physics/0112020 v6.
Foundations of Physics Letters, 15(5), 415-438 (2002)

"The notion of relational reality is introduced in order to give physical meaning to probabilities. This appears to give rise to a new interpretation of quantum mechanics."

[Ref. 4] Rubens M. Marinho Jr., Noether’s theorem in classical mechanics revisited, physics/0608264 v1.

"If the action of a given system is invariant under the infinitesimal
transformation that changes q to q + xq, then, corresponding to this
transformation there exist a law of conservation, and the conserved
quantity, J, can be obtained only from the Lagrangian and the
infinitesimal transformation."