Bioelectronics - Cosmic Code Arkadiusz Jadczyk

Towards the theory of matter, geometry and information

by

Arkadiusz Jadczyk

....

Some history:

The first year of my graduate studies had passed and I still had no idea of what my PhD was to be about. Lopuszanski was an expert in quantum field theory, the most advanced and the least understood branch of theoretical physics. My attempts to understand it, to " really" understand, had been unsuccessful. From long discussions with my advisor I got the impression that I am asking questions for which he has no answers. Perhaps no one can answer these questions ? I didn't know. I was getting desperate. Many years later I realized that my questions could not be answered within the standard paradigm of quantum theory, that the very foundations of quantum theory needed to be changed. I didn't know then that in the future, for my own work on the foundations of quantum theory I would get the Humboldt Award.

Not knowing what the future would bring, with time passing so fast and with my understanding of physics and mathematics progressing so slowly I was becoming seriously afraid that I would never be able to find a worthy, unsolved problem, and to solve it within the next three years. Fortunately help was underway.

Since 1965, usually in February or March, the Institute of Theoretical Physics of the University of Wroclaw was organizing, in the mountain resort of Karpacz, the International Winter School of Theoretical Physics, each year devoted to a different topic, with invited top expert lecturers from all over the world. It was a real heaven for the young PhD student in distress.

In 1968 Lopuszanski agreed to be the Director of the 5-th School, and he chose as the topic the "Axiomatic Approach to Quantum Field Theory and the Many Body Problem". It was just right for me !

The term " axiomatic" means in this context " mathematically rigorous, derived from first principles". The point was ( and is to this day ) that Quantum Field Theory, the theory was designed to completely explain the quantum world, the mysterious conversion of light into matter and matter into light, atomic spectra and nuclear reactions, etc. etc. - this theory that was supposed to predict the results of all experiments with elementary particles - this theory, when asked to obey the principles of Einstein's special theory of relativity - was producing mathematically meaningless results.

No one was able to succeed in constructing a mathematically reasonably behaving theory starting from assumptions that physicists considered reasonable. It is for these reasons that physicists borrowed the "axiomatic method" from mathematicians.

The idea was this : " If we are not able to construct a reasonable theory, let us assume that it has been constructed. And let us make a list of the most important properties that such a theory should have. These properties will be called " axioms", and we will try to derive as much as possible from these axioms by a rigorous process of mathematical deduction !"

Such an approach, even if it looks like a good and attractive idea, has its dangers. Imagine that somebody, having problems with constructing a car running on " free energy" decides to study such an invention " axiomatically". So, our axiomatic inventor lists the desired axioms :

1) It uses no fuel ;

2) It produces no pollution ;

3) The driver is always safe.

These axioms look good and one can start to derive consequences for the vehicle of the future. But what if the only " model" that satisfies all three axioms is the car that has no gas tank and that never moves !

The mathematician will, of course, be satisfied. He has a " model" for his axioms. But the physicist will say : " Your model is not really interesting to us. In fact, it is trivial." And exactly the same applies to axiomatic field theory : the only models that satisfy all axioms proved to be of no interest to the physicists. Either they do nothing, or do something but not in our world !

Even so, axiomatic field theory, and later its more abstract version " algebraic quantum field theory" allowed mathematical physicists and mathematicians in the last fifty years to develop many interesting and highly non- trivial concepts, to achieve deeper insight into the relations between these concepts, and to develop new powerful mathematical tools that have found applications in other areas of physics, mathematics and engineering.

One such area, that proved to be easier to tame than Quantum Field Theory was the so called " Many Body Problem". An outsider could think that we are discussing the problem of three, or four, or 100 planetary bodies interacting with each other, isn't 100 already " many" ? But an insider knows that when a theoretical physicist talks about "many bodies", he has in mind, in fact, infinitely many bodies.

How can that be, you may ask. Well, there are infinitely many integer numbers : .,- -4,-3,-2,-1,0,1,2,3,4 ,. and mathematics somehow manages to operate with these, so there is also a way to deal with infinitely many bodies, provided their interaction with each other is not too weird !

The mathematical formalism of quantum field theory and of the many body problem is very similar, almost identical. We have " Hilbert" space, we have " Fock vacuum", we have " creation" and " annihilation" " operators", but in the case of " many bodies" we do not assume that Einstein's relativity must be obeyed and we avoid " photons". Photons are forbidden here - they are replaced by more tamable " phonons" - quanta of vibrations of a crystalline lattice.

The School brought in to Karpacz experts in all these areas. While the German theoretical physicist, master mind of algebraic methods, Rudolph Haag was lecturing on solved and unsolved problems of quantum fields, the French mathematical physicist David Ruelle and the Danish theoretical physicist NM Hugenholtz were deriving from scratch the mathematical schemes of Quantum Statistical Mechanics - which was in fact a different term to denote the same concept : Many (that is infinitely many !) Body Problem.

In the evenings, over a glass of wine, I could listen to their private conversations in small groups and hunt for " open problems". Once in a while someone would say : " it would be nice if we knew this, or that", and I would note it. And then, after much hesitation, and with my body trembling, I would dare to ask " my own" question, and watch the face of the Master - will he laugh at me ? Will he call my question " trivial" ?

I was lucky. When I asked my own questions, in both areas, quantum field theory and statistical mechanics, I received the same answer : " We don't know. Why don't you try to find it out ?"

And so I knew what to do in the coming months. I was going to bring to Haag and Hugenholtz and to Ruelle the head of the Gorgone, to find answers to questions that they didn't know. I wanted to find out about the properties of the " vacuum" state in both statistical mechanics and quantum field theory.

The meaning of the " vacuum" is somewhat different in the two cases, but in both cases we believe that it is a state of the highest possible symmetry. Indeed, if there is " nothing" at all, then however we translate or rotate in space this " nothing" - it will be the same " nothing". And if we wait, however long, to see if something happens out of nothing, we will never see anything happening. These were the " natural" assumptions that were put as the axioms defining the vacuum state in both theories, in quantum field theory and in quantum statistical mechanics. Were these the right assumptions ?

Good enough to deduce interesting properties and, at the same time, not too restrictive ones?

And then comes the difference between the two cases : in quantum field theory, when thinking about the " vacuum", we think about the state with no " particles", with the lowest possible " energy". In quantum statistical mechanics we usually want to describe states of a given " temperature", that is not necessarily " absolute zero" or " zero Kelvin". Such a state, as uniform as possible, and yet " vibrating" so as to have a definite temperature, would usually have an infinite energy - because infinitely many " particles" (or, as physicists would say more precisely : infinitely many degrees of freedom) are vibrating. The very concept of " energy", in this case have to be re-thought and redefined.

The first thing to do was to learn all that there actually was to know about the subject. It took me nine months to write my first "paper". In October 1968 I sent it for publication in a prestigious journal specializing in my area of research : "Communications in Mathematical Physics". Rudolph Haag was the Editor in Chief. It took another year to reply to the referee's objections, make changes, to add new references. The title was "On the Spectrum of Internal Symmetries in the Algebraic Quantum Field Theory." Three months later I submitted to the Communications my second paper : " On Some Groups of Automorphisms of von Neumann Algebras with Cyclic and Separating Vector." And again almost a year passed before it appeared in print. My time was running out, my stipend would last only till September 1970. I had to pass through a series of exams, collect referee reports and finally defend my dissertation.

On March 4, 1970 my Ph.D advisor, Jan Lopuszanski wrote a letter to Daniel Kastler as follows :

Professor D. Kastler
Centre de Physique Theorique 31,
Chemin Joseph Aiguier 13
Marseille 9e
France

Dear Professor Kastler,

Excuse me that I trouble you once more with the problem of Dr. Jadczyk. I am glad to inform you - en passant - that few weeks ago Mr. Jadczyk got his ph.d. degree summa cum laude. It is already a pretty long time ago we got your kind and warm letter concerning the visit of Dr. Jadczyk at your Institute. It takes a very long time to arrange such things in Poland after one gets an official invitation from abroad. Therefore we are anxious to learn from you in what stage things are at present to make tentative plans for Dr. Jadczyk for the future. We would very much appreciate to hear from you at your convenience. Looking forward to hearing from you

Yours sincerely

Jan Lopuszanski

I spent in Marseille three months - October till December. I had my ph.d. title and I could choose my new avenue of research according to my own preferences. Starting October 1, I was officially an assistant professor, which gave me seven years for pursuing my own research, whatever direction I would chose, which, if all went well, would culminate in the next academic degree available : doctor habilitatus.

Being totally free to choose the subject, no pressure whatsoever, I chose a direction that I felt was neglected but important : " geometry of indefinite metric spaces". What I have chosen to research during my stay at CNRS was an introduction into the studies of geometry of spaces that have infinitely many dimensions, studies by using algebraic rather than analytic methods. This was an introduction to the area of research that was later on generalized even further and became, as we call it today, " non- commutative geometry."

And here I would like to jump into the future and sketch a vision that I have developed over the years. This vision has been formulated and published in 1987, in the proceeding of the VI-th Symposium on Bioelectronics at the Catholic University of Lublin, Poland. I began with describing the situation of the fundamental research today which goes, as I believe, along a road leading to a dead end:

Dead end

What causes that a physicist, specializing in mathematical methods of high energy physics, who attempts each year to spend a part of his time in Hamburg or Geneve - the two largest European high energy centers, comes now to Lublin for this Symposium?

There are several reasons. One of them, perhaps the most essential one, is recognizing the fact that high energy physics, physics of elementary particles, physics which up to this time was considered fundamental, came to a dead end. The last essentially new ideas were the special and general theories of relativity (Einstein 1905-1912) and the theory of quanta (Bohr, Schroedinger, Heisenberg, Dirac 1913- 1928). These theories, based on diametrically different concepts of reality and mathematical formalisms, are today as far from each other as they were sixty years ago. In spite of an enormous effort it has not been possible to build a coherent theory that would include relativity and quantum theories. Physicists that were actively participating in these efforts have been experiencing tides of hopes and disappointments - with a somewhat regular period of about 10 years. The last unfulfilled hope was in "multidimensional supergravity". Actually almost all the capital has been invested into "theory of superstrings".

Till the end of the ten years period there remains yet five years. What will be the next "hit"? Observing the development of events from a certain distance, what strikes the observer is the tragic of the situation. It is seen that we are not witnessing the building of a solid edifice of science. Rather we witness the glueing together of a giant snow ball.

Glueing the snow ball

Watching the most talented physicists of our time roll their giant snowball of a theory fills the present author with a sense of tragedy. They are pushing it forward, not always in concert or the same direction, observing with attention the gestures of coryphaeuses of science that are balancing with great difficulty on the continuously moving top of the ball - from where the goal appears to be seen.... But each successive"goal" proves to be once more an ordinary piece of landscape.

With time the glue ball, the ball-conglomerate, becomes so heavy that - rolling forward with growing difficulties - it starts to break into pieces under its own weight. First class professionals, in a hurry, are glueing back together the pieces that have fallen off and are sealing up the cracks in the ball. Theoretically the bigger the ball is, the better the view from its top gets. But, at the same time, the more difficult it becomes to get to its top and the more dangerous it becomes to fall down from it. And, at the same time, the bigger it gets, the more the ball itself blocks the view of the pushing crowd.

Thus there are fewer and fewer of those who know what they are doing. Furthermore such knowledge is of little use for the careers of young scientists. The governments of the richest countries are spending billions for this "game". The new giant accelerator is being built. Today superstrings are in vogue. Today there is money for superstrings. Thus one has to work on superstrings. They call it "fundamental research". Physics of high energies is thus building the foundation of foundations .... from the glued snow and the litter that attaches to it by chance along the way.

Then I went on to describe the new paths in physics - physics of complex and self-organizing systems :

New Physics

Before our eyes do doors open leading from physics to biology. New physics is being born - the physics of complex and organized systems. It is yet in its swaddling clothes. It has not yet worked out its own methods. The methods that are being borrowed from statistical physics and from physics of condensed phase have proven to be insufficient already in the beginning. And, is it still physics?

This mixture of methods is taking elements from physics, informatics, and applying them to systems imitating biological systems. Slowly, and with difficulty, new horizons do open.

Computer experiments indicate new, as yet unsuspected regularities. New concepts are being formed. A virgin terrain is waiting for trailblazers. Adventure casts its lure.

One of the main mathematical objects in the theory of strings are "Virasoro algebras". Today professor Virasoro is preoccupied with the theory of self organizing neural networks. Most of his time he spends with a computer. He is not an exception. Nevertheless the theory is only starting to crawl on all fours. It is in the stage of simple classical models.

At the same time the collective phenomena, and it is with such that we probably have to do in biological systems, expose to us completely new dimensions that accompany the quantum description. To what extent can we expect here that taking into account quantum laws will prove to be essential in explaining the riddle of life, if the physicists themselves are not that sure about the methodological status of quantum theory itself?

2.2 The Quantum Seam of Life

We are witnessing breaking out of the ruling paradigm in biology, a paradigm according to which life can and should be reduced to chemistry. Clearly describes the new direction of attack W. Sedlak [11, p. 13] When he writes: "Life can be thus described as a process of a quantum nature, expressing the coupling of chemical reactions with electronics phenomena in a protein-nuclein super conductive substratum." And further, presenting his prognosis of the physics of life [11, p.29]: "It must be a quantum physics (...). The description will be extremely difficult, as it has to take into account at the same time the two coupled quantum events - chemical and electronical ones. The description addresses the quantum seam of the two processes. It is here that life in its most basic instance is being played." It is clear that chemistry alone is not sufficient to explain the action of even the simplest electrical circuit consisting of a battery and a light bulb. For this we have to go beyond chemistry and use the part of physics dealing with radiation phenomena.

But can chemistry together with physics, even quantum physics, suffice for making essential progress in explaining biological phenomena, and in particular the phenomenon of life? The Author of this text does not completely share the optimism of W. Sedlak who seems to believe that even consciousness will be explained through collective states of complex systems. Essential life processes probably do take place at the "quantum seam". But is life only the sum total of life processes? Or it is something more, a new quality? And if so, then what kind of quality?

Quantum Mechanics

The one writing these words knows little, in fact next to nothing, about biology. He is only a physicist who has spent most of his time on studying the works of other physicists, trying to add his own little bricks to that which is already known. And the remaining time he has spent meditating on how little in fact we know and furthermore how uncertain even this little that seems to be known is. Therefore he does not claim to understand those things that are beyond the scope of his active research up to this time. [f1] Therefore if in spite of this he has the courage to speak about things that extend so far beyond the scope of his competence, it is only because it seems to him that he is perceiving something essentially new. Something that demands attention.

Werner Heisenberg, in a chapter "Conversations about the connection between biology, physics and chemistry" of his book "Part and the whole" [7], while reporting on his discussion with Niels Bohr, quotes him as follows:

"In natural sciences it is always good policy to stay as conservative as possible and to create new extensions only under the pressure of observations that cannot be explained in any other way." The speculations presented below (in Sec. 2 and 3) will be in an evident violation of this certainly healthy principle. When deciding to publish them in spite of the above the author has taken into account these words: "And Jesus beheld a man working on the Sabbath, and He said to him, `Man, if you know what you do, you are blessed, for you break not The Law in the spirit; but if you know not, you are accursed and a transgressor of The Law."[1]

Quantum Theory - today.

Quantum theory has been formed in the first quarter of this century as the result of a stubborn search for a new mathematical and conceptual apparatus that would be able to explain the intricate spectra radiated by excited atoms. Pretty soon thereafter the scope of applicability of quantum theory was significantly expanded and it started to be applied (with considerable success) to all the problems of the micro world. From the very beginning, however its successes in predicting results of subsequent experiments were accompanied by difficulties of a philosophical and methodological character. As time progressed these difficulties were alternatingly falling silent and then exploding to the surface again.

During the last dozen years the discussion has been gathering strength again, and this because of two reasons. First, when the problem of a possible marriage between quantum mechanics and Einstein's general relativity gained importance, the problem of interpretation of the "wave function of the universe" appeared (as there were no "external" observers).

Second, progress in experimental methods made it possible to experiment with single quantum objects. This kind of experiment, as is the case with the cosmological "experiment" with the unique Universe which we happen to inhabit, does not exactly fit into the rigid scheme of the conceptual apparatus of the standard quantum theory.[f2]

To characterize the present status of quantum mechanics let us begin with stressing out that, as long as we are not dealing with too strong forces and too high velocities, this theory "works", and it even works wonderfully well. There are so many physical phenomena that are so surprisingly well described by quantum mechanics that those phenomena that somehow escape the quantum description are classified as "curiosities" and are set aside "for later". These successes of quantum mechanics are, from the very beginning, accompanied by a kind of a "methodological shock" - a shock whose force is getting weaker and weaker with time like a continuous pain gets duller and duller as time passes.

This shock was caused by the realization of the fact that quantum mechanics, as it seems, is censoring our essential and logical questions. "Is electron a particle or a wave?" This question is described as "having no meaning". We could accept it. But also other questions: "What is an electron?" "Which slit is it going through when it is not being observed?" "What is it doing between two consecutive observations?" are also denied meaning. Finally, when we are being told "It does not have any meaning" when we ask "Why a given radioactive atom decays at this and not at some other moment?" and "What happens during the decay? How does it go?", then we start to suspect that the conceptual system of quantum mechanics, even if logically non-contradictory, is, perhaps, not as perfect and complete as it aspires to be.

In fact, after some closer analysis, we realize that only those questions for which quantum mechanics can provide answers are classified as "making sense" ! But there are, as it seems, lots of other questions that make sense, if only because Nature herself answers them every now and then. In this way, after the initial excitement, we are beginning to perceive defects in this "perfect theory".

At the same time the experts cannot agree: Some argue that the theory is ok, that what we are lacking is a "proper interpretation". On the other hand those who blame the theory itself differ, often drastically, " in their diagnoses and prescribed "cures". The Author tends to believe that the main shortcoming of quantum mechanics is that "it has nothing to say about individual events". At the same time the world seems to be woven precisely out of such events.

Another weakness of quantum mechanics is in the fact that it is not able to describe the very process of a measurement.[f3] Therefore quantum mechanics is not a complete theory. Niels Bohr, one of the major founders, inspirations, and interpreters of quantum mechanics dogmatically announced: "it is so, because it must be so." But we do not have to follow Niels Bohr. We can choose to follow another great physicist, E.P. Wigner, who, trying to find a solution to the aforementioned difficulties of quantum mechanics concluded [19]: "the postulate that the equations of motion of quantum mechanics cease to be linear, in fact that they are grossly non-linear if conscious beings enter the picture."

In a "safe middle" are the views of the Princeton physicist J.A. Wheeler. On one hand he accepts after Bohr and Heisenberg, and even enhances it, this part of the paradigm of the quantum mechanics in which the question "what happens between two observation acts?" is qualified as meaningless. He writes: "No elementary phenomenon is a phenomenon until it is a registered phenomenon." [16] But he also notices: "No element in the description of physics shows itself as closer to primordial than the elementary quantum phenomenon, that is, the elementary device-intermediated act of posing a yes/no question and eliciting an answer. Otherwise stated, every physical quantity, every it, derives its ultimate significance from bits." [17 It from bit]

Quantum mechanics - tomorrow

We are living at the threshold of the century. From the sign of Pisces we are entering into the sign of Aquarius. From the age of Steam and Electricity into the age of Computers and Information. We have conquered, if only partially, Light, and today the time comes for the Word.

At the same time, it must be stressed, we have no other alternative than the well established and tested scientific way and scientific method. But, with even greater emphasis, we must realize that that the new tasks ahead of us require true boldness in thinking and abandoning all prejudices. The thoughts that follow are speculative. The predictions may come true or not. The idea may prove to be right or wrong. The future will show whether the weight have been correctly chosen, whether the impetus has been exerted at the right moment and in the right direction, whether the program that is sketched here will get, even if only in part, realized.

But first of all, here are the goals : we would like to know what the life processes and the processes of the mind consist of, and also what life itself is and, in a further perspective, what consciousness is.

The main thesis of the author of these speculations is this: for researching and explaining almost all basic life processes it is necessary and sufficient to use mathematics, physics, chemistry and biology, as they are developed today, that is without the necessity of going beyond the present day paradigm. The role of quantum physics will be here of a particular importance. But if we will have to make the next step and to answer the question : what is life itself and what is consciousness ? - then a real breakthrough will be needed in two domains : we will need to rebuild ab initio the quantum theory of complex systems and, on the basis of quantum mechanics, to build a new theory unifying the processes of exchanging of energy and information.

In the first domain the progress is rather fast, on the border of mathematics, physics, informatics, cybernetics, electronics and biology. In the second one, where a real paradigm break is needed, there is a long lasting stagnation. The few attempts at constructing a non-linear quantum mechanics [2,6,10] did not gather many followers. But, as this author believes, a theory that is able to describe irreversible events, a theory that is able to provide its own interpretation, must have a nonlinear character. Einstein's general theory of relativity can well serve as an example and as a template, as it is owing to the nonlinear character of this theory that equations of motion for test particles follow automatically from field equations, and need to be postulated ad hoc. We are still waiting for the demystification of the " reduction of the wave packet" - postulated in quantum theory as a discontinuous change of the state of the system as a result of the act of observation-measurement. Non linearity of the theory seems to be here, as proposed by Wigner, indeed necessary. But will it be also sufficient ?

The author of these speculations believes that more is necessary. That what is needed is a coupling between energy and information. [f4]

But is it not so that any exchange of information can be, after all, described in terms of exchange of energy ?

In a sense " yes", but in another sense, which is here more important, " no".

Again let us take the general theory of relativity as an analogy and example. There we have, from the very beginning, a division between matter and geometry. The gravitational field represents geometry. Other fields, taken together, represent matter.[f5] Can one reduce matter to geometry, or geometry to matter ?

Until now all attempts at such a " forced unification" have been, if one does not count side effects, unfruitful. analoguously, the dualism of energy and matter may have a primitive character.

Continuing the analogy : in the same way as a gravitational field curves space-time [f6], the information field may curve the state space. May change the geometry of the space of quantum states. May enable the flow of information and of energy through new channels. Now quantum matter gets a worthy partner, just as the gravitational field was a worthy partner to classical matter. The same way as gravitational field is local[f7] in space-time, the information field is local in Hilbert space where " near" means " similar". The geometry of the information field must be, as we have said, a nonlinear geometry. Only in this way can we explain the stability of structures, such as the structure of life. With the phenomenon of life we can in this way, associate a topological invariant (a kind of a vortex) in the nonlinear field of information. Physical and chemical life processes would be then controlled by a quantum feedback between information and matter. And, when we speak about geometry, it must be noted that it must be more than a classical geometry such as is sufficient for the Einstein theory of gravitation. What is needed here is a kind of quantum geometry. Such a geometry is today only in statu nascendi. [5,20]

Light.

Niels Bohr repeatedly stressed the paradoxical aspect of the quantum theory :

"On one hand we are formulating laws that differ from the classical ones, while on the other hand, in the domain of measurement and observation we are using the classical concepts without any doubt whatsoever. We have to proceed this way, because we have to use language when we want to communicate our results to others. A measuring device serves its purpose only when by observing it we can univocally draw conclusions about the observed phenomenon, when there is a clear causal connection. But when we observe an atomic phenomenon, we have to put a cut between the phenomenon and the observer or his apparatus. Even if the placement of this cut is to a large extent arbitrary, on the side of the observer we have to use the language of classical physics, because we have no other way to communicate our results."[7].

Quantum mechanics of the future, a nonlinear quantum mechanics coupling together matter and information that we are speculating about, has the aim of unifying the two aspects, the classical and the quantum one, including the " cut" between them, into a single formalism. In this the paradox that Bohr is talking about will cease to be paradoxical and will become a fact that has its counterpart in the theory.

Such a theory, with its main idea sketched as above, must include in its framework two completely different worlds : the quantum world and the classical world or, making the cut in a different direction, the world of flesh (matter) and the world of word (information). The differences between these two worlds are so enormous that unifying them seems impossible without a catalyzer. A probable candidate for such a catalyzer is light.

Why light and not something else ?[f8]

It is not easy to answer this question without going deep into rather difficult formalism of quantum field theory. But, if only to give a taste of the problems involved, let us begin with remarking that quantum electrodynamics, that is the theory of interaction between light (i.e. electromagnetic field of photons) with (electrically charged) matter, is struggling with difficulties such as how to get finite values out of quantities that appear to be infinite.

One can say that the theory would be almost " perfect", were it not for two " catastrophes" : The ultraviolet and infrared catastrophies.

The ultraviolet catastrophe is not of interest for us right now, as it has to do with extremely large energies, extremely small distances, and extremely high temperatures. The infrared catastrophe, which appears at the other end of the energetic scale, is related to the fact that every real physical process involving electrically charged matter is accompanied by a " photon cloud" consisting of very many photons of very small energy. The total energy of such a cloud, when measured by an energy gauge scaled so that the energy of the vacuum is zero, is infinite. Thus the term " catastrophe".

The most important fact for us is that the " shape" of this cloud can encode classical information. (Using the language of quantum field theory we may say that " coherent infrared states lead to continuous super selection rule¯, or that " the algebra of observables of the photon field has a non-trivial center, whose elements parameterize infrared representations"). For the sake of completeness one must notice that the " infrared cloud" consists of photons of very small energy, and therefore of very large, macroscopic (even cosmic) wave length.

Such photons are, on one hand, undesirable, because of the energetic " infinities" but, on the other hand, they seem to be absolutely indispensable for the description of the information transfer during a quantum measurement process. But also here the theory is only taking its first steps. [3,14]

Footnotes:

1 These words are a paraphrase of a paragraph of the introduction to the book by A. Carel ,Man unknown" [4]. This book has played an important role in shaping the interests and the views of the author of this text.
2 Unfortunately we can not devote to these problems, which are at the heart of the modern picture of the nature, more place than it is just strictly necessary for understanding this particular lecture.
3 This is, in a sense, the same problem as the previous one. Because one deals again with an " event", the event of the " registration" of the result of the measurement.
4 There are reports that living organisms emit, at the moment of their death, energy in the form of some kind of radiation. It would be interesting to find whether at the same time we have also emission of information.
5 By the way, this division is not rigid. In generalizations of the theory of relativity, different versions of a " unified field theory", electromagnetic field and other gauge fields belong to geometry. But the duality matter versus geometry (when gravitation always belongs to geometry) remains.
6 Such an information field could have certain functions that are ascribed by R. Sheldrake to a morphogenetic field. [13]
7 Locality means that disturbances propagate through the direct influence of the field in neighboring points.
8 W. Sedlak points out the special role of light in life processes in his book " At the beginning, after all, there was light.

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Woronowicz S.L.: Twisted SU(2) Group, An example of Non-Commutative Differential Calculus, RIMS (Publ of the Res. Inst. Math. Sci. Kyoto Univ., 23), 1987, 171-181

Looking back

(Preliminary version)

Each time I read the text above, I am puzzled by its its prophecy. The Bioelectronics Symposium took place in November 1987. In June 1990, in Florence, I sketched a plan of research for the coming years. Philippe Blanchard of the University of Bielefeld supported this plan and, a year later, in June 1991 in Bielefeld we started implementing a part of this plan. One year later we sent for publication our first joint paper. "Event Enhanced Quantum Theory", in short EEQT, was born. We brought together, in this theory, the two worlds: the quantum one and the classical one. But the theory was still linear. Our equations were describing only statistical ensembles and were unable to understand how does Nature work, how She decides at which moment a given radioactive atom will decay, at which moment a photon gets emitted or absorbed. Our equations, as it seemed to us, were correct, and yet we did not know how to get from them more, how to get from them a description of individual quantum systems.

The breakthrough came next year, in June 1993, in fact by a pure accident (or, perhaps, it was not so accidental ....). I remember this event distinctly. I was randomly searching in the library of the university of Bielefeld, checking one book after another, from different library sestions, and finally I took in my hand a shabby little booklet with lectures by M. H. Davis on "stochastic control and nonlinear filtering", published in 1984 by the Tata Institute in Bombay. A little yellow booklet, published evidently with a small and cheap poligraphy methods.... I opened it on a random page .... and decide to borrow it, so as to examine what it is about.

I started reading. At first I could not understand much, yet I was getting an impression that there may be some connection between EEQT (the term "EEQT" did not exist yet, at that time) and one of the chapters of Davis' monogrph. The monograph was dealing with processes in economics, such as stock market crashes. Following the stock market data closely we notice that stock prices fluctuate, grow up and fall down, and for long period of times vary, on average, in a continuous way. And then, abruptly, there comes a CRASH. A distinct and discontinuous change. After which we observe another period of a continuous evolution. One way to study these phenomena is via the catastroph theory.

But Davis, in one of the chapters, described a class of random processes that were fitting to this class of evolutions. I did not get motivated enough to study the whole monograph, but this particular chapter I begin to study with paper and pencil in my hand. I was trying to understand the definitions and the theorem - as there was a single theorem in this chapter. And I was getting the feeling that this theorem is exactly what we need....

It took me several days to reallly understand what was going on. Davis considered a piecewise deterministic random process, with a continuous evolution interrupted by occasional jumps, and he provided a form of its infinitesimal generator. This generator had a "differential" part, but it also had an "integral" part - it is this latter part was responsible for "jumps".

It occured to me, after having a better look at the formula, that the integral part was similar to the extra term that we were adding to the Hamiltonian evolution of a quantum system in our work on EEQT! But to see whether the idea was correct, I had to replace the flat space used by Davis by a unit ball in a Hilbert space - as it was needed in quantum theory. There was also an additional difficulty: in quantum theory expectation values of all observables are always being expressed in terms of a scalar product. These expectation values are therefore, in quantum theory, always bilinear in the wave function.

But to apply the Davis theorem we would have to have at our disposal all possible functionals of the wave function. That is the particularity of quantum theory that distinguishes it from a classical theory: in quantum theory the class of observables is rather poor! As the result of this particular feature of quantum theory, we could apply the Davis' theorem only one way: we could show that the random process described by Davis reproduced our equations (so called "Master equation"), but we could not deduce, as Davis did, that this is the only random process that could do that. And this was a serious drawback, because the process algorithm described the behaviour of an individual quantum system. And this was what we were looking for, as this was exactly the part of the description that was lacking in the standard quantum theory.

As at that time I was working in Bielefeld, with Philippe Blanchard, on the "Quantum Zeno Effect" (“a watched pot cannot boil”), we applied the Davis' algorithm to this particular case. We submitted the paper for publication in Physics Letters A. But we were not boasting there about the non-uniqueness of the process algorithm. Insetad we described the process as "natural" and "minimal", and it did not catch the attention of the refrees. In fact this was my intution at that time: that the process is minimal and natural. But, frankly speaking, if someone would attack our work asking for the precise reasons why we think this process is minimal and natural - we would have had a hard time finding a convincing answer. At least not yet. Another year, and another stimulus were needed for us to put the dot over that "i"....

Last modified on: June 27, 2005.