COULD WE MANAGE WITHOUT MICRO-UFOs ? (*)

A.K.Kwaśniewski - the Dissident - relegated by University of Bialystok authorities from

the Institute of Informatics founded by Prof. A. Krzysztof Kwaniewski to Faculty of Physics, Białystok University (**) ul. Lipowa 41, 15 424 Białystok, Poland e-mail: kwandr@gmail.com

November 12, 2007

(*) Physics Essays; (An International Journal Dedicated to Fundamental Questions in Physics) Ottawa; Vol.9 no 2 (June 1996) : 274-281 (**) former Warsaw University Division

Abstract

One unfolds the conviction that elementary particles are not names of flying objects subjected to wave-particle dilemma. The adequate reasoning based on elementary derivation of Bell inequalities is provided. We propose, as J. A. Wheeler puts it [1], ”to view every thing physical” as ”It from Bit” (1*); this being also confronted with the analysis of the above challenge as presented by R. Haag in [2]. The second part is mostly of pedagogical character. Its task is to introduce the quantum process kinematics without even mentioning the name of Micro-UFO and at the very elementary level.

1 On micro unidentified flying objects

I. In this essay we pursuit the goal of avoiding the usage of MUFO notion in the course of colloquial depicting the basic content of quantum mechanics. MUFO stands here for a particle-like, cloudy-like, wavy-like and etc. (1*), (2*) micro unidentified flying object. This attempt is inspired and prompted by Schrdingers criticism of the particle notion used in talking about quantum phenomena. Thorough discussion of inappropriateness of such MUFO-s for depicting quantum processes is also to be find in W. Heisenberg‘s ”Der Teil und das Ganze”. The awkward properties of quantum MUFO-s and their ”explanatory” destination resembles very much the role of ether in the 19-th century picture of electromagnetism. While used to run the electromagnetic business without the ether notion, many people think that we cannot deal with problems of quantum processes without the admittance of existence of some MUFO-s. We propose to deal without MUFO-s, similarly as we resign from the ether notion. One of several immediate consequences of such an attitude is the disappearance of ”problems” with particles‘ identity ”their nature” and so on.

II. Atoms are not things, atoms are states of matter” (”stationare Zustande aus Materie” p. 191 in Der Teil und das Ganze); this is what one may learn from Heisenberg. Another founder of quantum theory, E. Schrdinger also feels very uncomfortable with the notion of a particle-like MUFO, which is supposed to be a flying thing stroboscopically visualized by tracks on films or in cloud chambers and of wavy behaviour while passing through crystals. At the same time these things lack individuality or ”sameness” (see E. Schrdinger in [3]). Anyhow, let us momentarily admit that bosons or fermions are objects. What does this mean then: ”two undistinguishable objects”? - Are there two objects or not? (- ”Two perfect billiard balls are objects and are undistinguishable” - this is an authentic response to this question that I have got from One Person) (2*). The meaning of words is being established by an agreed upon correspondence between notions and rules of the theory (”language”) on one side and the measurable properties of events on the other side (3*). The relevant theory (language) is quantum mechanics with state notion and superposition principle as a background. So what is the correspondence establishing a meaning of this basic notion?

The designate of the state notion is a kind of MUFO ? States of matter superpose. Then MUFO-s do superpose too? Indivisible objects superpose? (4*), (2*).

We experience in every day life a lot of interferences. Motions and relations superpose; for example translations or waves. Impressions also superpose; for example colours or ... feelings. Potentialities superpose; for example chances or potential fields (4*).

Space-time events and states of classical phase spaces and corresponding objects - do they interfere ? Vaguely speaking - properties of situations may interfere while space-time events (”ultimate points”) - not. Note here the accuracy of ”SITUATION” notion (Beobachtungssituation - in Heisenberg‘s words; p. 127 ”Der Teil und das Ganze”). It is more general than the notion of an object or a property - separately. A relation between objects and properties, a decomposition [egzo/endo] of any kind (see (5*)), are examples of situations. An object in motion is a very special kind of situation. A decomposition [egzo/endo] with a characteristic property of tendencies for some special kind of space-time events (accompanied by quantum numbers) is another type of situation. We are then eager to designate to state notion rather a kind of property of events, than a flying MUFO; we would designate to the quantum state of matter notion rather a PROPERTY of SITUATION than a substantial micro-piece of wood or iron. This property is by no means of INFORMATIONAL character. ”It is made of Information” in a sense. The quantum states of matter are characterized by potentiality of space time events and the certainty of good quantum numbers. - What shall be then designated to the notion of, say, ”two free fermions’ state”? - A potentiality for doubled events and certainty of appropriately summed quantum numbers. Note however that these two events are never stochastically independent. While dealing with ”two free fermion states” we are not dealing with two separate quantum Markov processes.

We are dealing with ONE stochastic process (6*). And discovering - what is being called ”new particles”, we create and/or discover new kinds of EVENTS; we experience new properties of matter. We never see MUFO flying by - except for ”in our minds‘ eyes” as Shakespeare would put it probably. So what about tracks on films, clicks in detectors and so on? They seem though to be the result of MUFO just arriving or passing by or flying through.

Perhaps Newton‘s ”si esset” used by Him in his ”Principia ...” is validated to be used while organizing our impressions, especially that we are almost always eager to make unconscious assumptions.

We propose to resign from the MUFO Hypothesis.

Naturally the identity ”problem” then disappears automatically. No MUFOs - no problem. Though of course there is indistinguishability involved. But this does not concern two objects.

THIS CONCERNS TWO WAYS.

Two eventual ways of evoking a doubled event. If it could be learned that one event is a realization of the ⟨A| state potentiality, while the other event originates from the ⟨B| state potentiality, and these are two different kinds of events - say; an electron and proton type events - then there is no superposition of ⟨A| ⊗ ⟨B| and ⟨B| ⊗ ⟨A| states for proton-electron type event.

However, if these are events characterized by the same mass, charge, spin, strangeness etc. then nothing has chance to distinguish between two ways ⟨A| ⊗ ⟨B| and ⟨B| ⊗ ⟨A| (of assigning states ⟨A| or ⟨B| to events, which we would like to originate from a definite single-event state ⟨A| or ⟨B| ) . As both possibilities, as both ways are undistinguishable via space-time events, we end up with their superposition; (naturally with + or − sign, what results in existence of two kinds of informational states of matter i.e. boson and fermion ones). Which potentiality is being then realized by a doubled event: ⟨A| ⊗ ⟨B| or ⟨B| ⊗ ⟨A| ?

We answer. - It is an informational property, it is the potentiality that they CONSTITUTE ALTOGETHER; it is their superposition that is being realized (6*). This is how it might look like. However may be this is wrong; may be MUFO-s with their awkward properties do exist... Isn’t that the collection of interacting micro-pieces that constitute a macro-piece of wood or something?

From state point of view, a macro-piece of iron or wood is such a huge accumulation of potentialities for events that tremendous amount of them must certainly occur (”be verified”) forming an information aggregate which we describe as macro-phenomenon. Experiencing more or less average properties of this Cosmos of events, we call It a piece of wood or iron or a cloud.

- Really?

HYPOTHESIS

In order to make a choice between the two pictures reasonable, let us AS-SUME that the two-boson state i.e. the superposition of describes two MUFO-s, two flying microsystems. Their nature and interaction does not matter. As for the events evoked in detectors, we shall consider them to be the evidence of the corresponding MUFO arriving to cause a ”click”. Naturally we shall ASSUME that there is no energy exchange between any two space-like separated events.

These two assumptions is enough to prove Bell inequalities.

For that to see, consider a system with two detector devices: L (left) and R (right) and a source of radiation field S. The source S is right in the middle, in between R and L and is of special kind. Namely, all events evoked in R and L appear in strictly anti-correlated pairs. Precisely; both R and L could be set on to measure any of the three dichotomous observables A, B and C (for example ”spin 1/2 projections” on three directions a, b and c). We shall denote values of these observables by + and - . Denote now the probability of an event (+,-) with L settled on A and R settled on B, by P (A, B; +, −) and so on, so that for example P (B, B; −, +) denotes the probability of an event for L and R both settled on to measure values of B. Correlation functions of the outcomes for these measurements are then defined as follows:

DEFINITION

K(X, Y) = P (X, Y |+, +) + P (X, Y |−, −) − P (X, Y |+, −) − P (X, Y |−, +)

where X, Y = A, B, C.

In terms of correlation function K the source S of radiation states of matter is characterized by the property

K(B, B) = −1. (S)

Now, if one assumes that the events (x, y) are caused by pairs of microobjects arriving at L and R correspondingly (no matter what is their nature and interactions) then another condition is to be satisfied by the outcomes of measurements which are being carried out (just decision) in two SPACE-LIKE SEPARATED regions L and R. This implies that in the very moment of measuring, say, B in R the measurement of any of the observables A,B,C for the object just arriving at L, cannot be influenced by the instantaneous decision on which one of the three observables the device L is being settled on. For the results of measurements this would mean what follows.

Denote the outcomes for X in L and for Y in R by (x_{i}, (y_{i})) . Then, because of decision freedom in space-like separated regions R and L one has

(x_{i}, (y_{i}))) = (x_{i}, (z_{i})) (ST R)

where X, Y, Z = A, B, C.. The above notation - resembling the constancy of x function: means:

”neither y_{i} nor z_{i} decides which value x_{i} happens to show up with”.

Due to the requirement of (STR) (Special Theory of Relativity) one may introduce a shorter notation; namely.

NOTATION

x_{i}^{l} = (x_{i}, (y_{l})), x_{l}^{r} = (y_{r}, (x_{l}))

for any value y of an observable Y = A, B, C. As the observables are dichotomous, the expressions for correlation functions read as follows:

K(A, C) = \frac{1}{N} ∑_{i=1}^{N} a_{i}^{l}c_{i}^{r} K(A, B) = \frac{1}{N} ∑_{i=1}^{N} a_{i}^{l}b_{i}^{r}

and

K(B, C) = \frac{1}{N} ∑_{i=1}^{N} b_{i}^{l}c_{i}^{r} = −\frac{1}{N} ∑_{i=1}^{N} b_{i}^{r}c_{i}^{r}

From the above one immediately arrives at a condition that the correlation functions should satisfy [4] (just check it)

|K(A, B) − K(A, C)| ≤ 1 + K(B, C) . (Bell)

Both quantum mechanical description of states of matter and Nature in the corresponding experiments do not respect this Bell inequality. So either assumption of MUFO-s‘ existence must be postponed or the main principle of STR must be resigned from.

We propose to relieve of cumbersome Micro-UFO notion and stay with the reliable notion of informational states of matter. (As a matter of fact, this would render us with a lot of comfort and relaxation being not forced to consider and reconsider ”problems” of cats [10], moons [11], or ”identity problems” for individuals void of sameness [3], and so on).

Quantum states might be perceived as special - and perhaps basic properties of matter; properties of informational character. They are in a sense ”made of” bits of information (7*). From such a point of view, the known ”quantum Zenon effect” confirmed recently (see Wineland et all [5]) appears to be not a surprise. One might imagine such an effect already on the grounds. of interpretation given to the state notion. First - the confirmation of the unstable information is not continuous, is intermittent. However the confirmation of an ”unstable information” in proper i.e. Zenon time, re-establishes and/or confirms this information, thus making it last or survive longer. Concluding - we think that belief in flying micro-pieces of somethingness in nothingness is cumbersome in a way resembling troubles with ether. We prefer to believe, that what we experience and organize within mathematical structures, this is information (these are impressions in a sense). This information, for peculiar situations (”classical”) is quite well describable by space-time differentiable manifolds, which anyhow can be considered as imbedded into infinite dimensional phase space manifold of quantum states [6]. This occurs for situations for which both macro-scale and micro-scale examination of physical processes is admitted and/or important or even indispensable.

NAMING

Summing up we want to say that electrons, protons and other ”etc.-rons” - these are - colloquially speaking -names of informational, global properties of [egzo/endo] divisions (Finkelstein), or of M and S distinctions (Haag) (5*), or names of informational global properties of various families of ”filters” (Mielnik).

The precise naming is of course possible only within the appropriate mathematical models of physical situations. We are not going here to make a review of all mathematical concepts at hand indispensable or useful to describe quantum phenomena. Let us however mention just few of them, for the sake of illustration. And so Wigner’s attitude to the role of symmetry in organizing our knowledge on physical processes would perhaps stimulate giving names such as electrons, protons and other ”etc.-rons” to appropriately assigned representations of symmetry groups. This attitude could be incorporated - projective geometry of phase spaces included -into the theory of fiber bundles as exhibited by the geometrical quantization approach or as fruitfully applied by Sudarshan and Others [8] to derive the effect of the Berry phase. The theory of electrons, protons and other ”etc.-rons” viewed on as the representation theory within the Hilbert space formalism is known to be equivalent (under standard circumstances) to the quantum logic approach started by Birkhoff and von Neumann. One can thus transfer naming from on theory to another. Consequently electrons, protons and so on - these would be the names for various sorts of propositions. As it is well known, these ”various sorts of such propositions” are being rigged with the structure of an ortomodular poset [12] or ortholattice (not necessarily modular) [13] or as convincingly advocated by Mielnik [9] the structure of states (statements, propositions) is ”just” the convex set structure with geometrical interpretation of probability (information!). Within Mielnik‘s scheme of analysing physical phenomena then - electrons, protons, etc.- these would be the names for various kinds of geometries describing Haag‘s patterns or Finkelstein [endo/egzo] divisions.

SPECTRA AND NUMBERS

Depending on circumstances (quantum phenomena under modelling are in) - various ”working” identifications of them with mathematical objects are elucidative. For example, as pointed out by Reiter and Thirring [16] ”electrons in crystal can be confined arbitrarily closely to the atoms and yet their momenta stay arbitrarily near the reciprocal lattice. Thus, modulo periodicity, x and p can be simultaneously localized”. In such circumstances then, electrons are names of common eigenfunctions of nontrivial projectors of x and p - spectra. All this is manifestation of the specific properties of Fourier transformed distributions subjected to a support arrangement leading to Fourier transform that appears to be a discrete set of spots.

Alike electrons in atoms, electrons in crystals or quasi-crystals are recognized (”labeled”) via X-ray diffraction patterns of events. ”An x-ray diffraction pattern is essentially a Fourier transform that determines magnitudes of Fourier coefficients but loses all phase information” [17] . Following Lagarias further, we arrive ”at a harmonic analysis problem of studying all functions of a given type, whose Fourier transforms are of a given type”. - (One feels like returning back to the very source. It was Fourier expansion that had lead Heisenberg to the matrix mechanics‘ discovery.) One way of studying it is to simulate it. One can simulate ”an environment” for electron diffraction patterns of events - vide quasi-crystals - using computer techniques [18,19].

” The environment” is of number theoretic character. Electrons are then to be identified - according to Einsteins’ paraphrased (4*) pronouncement - with ”convenient abbreviation for the way an information ... can be assembled”?

One feels like returning back to the very source. It was fascination with numbers and pithagorian philosophy that had stimulated J. J. Balmers’ discovery of the magic formula (1885).

λ = b\frac{k^{2}}{k^{2}−4} , k = 3, 4, 5, 6

which had started and startled the new epoch of spectra.

THE CLASSICAL ASPECT

The classical aspect of quantum phenomena is already inherited in the very structure of all more or less general descriptions just mentioned. The classical frames of references in Takeuti sense [14], i.e. systems of classical propositions (states) - form an integral part of the whole quantum description (see the main theorem in [12]). In Gelfand triple description of a situation called a quantum system, classical frames of reference might be defined via for instance Boolean lattices of position or momentum operators spectrum and/or generalized coherent states. The last choice is also very suitable for that purpose in the fiber bundle approach [6]. So the classical description is obviously fragmentary - the system of ideas included. The quantum description is inevitably wholistic and coherent [13] - the system of ideas included.

CONCLUSION

One may see then that electrons, protons and other ”etc.-rons” need not to be the names of flying things. Even more. They are forbidden to be the names of unidentified flying objects.

2 Quantum Kinematics For Pedestrians

This part of the paper is mostly of pedagogical character. Its task is to introduce the quantum processes kinematics without even mentioning Micro-UFOs and at the very elementary level. Namely, from the assumption that there exist more than one ”filtering Beobachtungssituation” for quantum Markov processes, one derives here the representability of their transition amplitudes by means of a scalar product of appropriate vectors from Hilbert space. For that to do, one consequently takes the standpoint - close to that of Heisenberg-according to whom quantum states of matter are properties of situations, called by Him (see ”Der Teil and das Ganze”) - Boebachtungssituationen. As discussed in part one, quantum states are properties of apparently informational character and the stochastic processes, that we are dealing with, in sequences of quantum events, are of special kind; namely these are quantum Markov processes. We mean by that the following:

I. The probability P(x) of an event ”x” of a given kind is represented by the modulus squared of a certain complex number called a transition amplitude between states of sitation before and right after an event ”x” II. If an event ”x” could be evoked in two excluding each other ways, then the transition amplitude corresponding to the ”x” is a linear combination of amplitudes for the two would-be, eventual ways to achtieve ”x”. III. If a possible, ”potential” event ”x” (denoted since now on by [x¿) in the situation ”s” characterized by its informational status [s¿], might take place via preceding it some other potential event [i¿], than the amplitude for such a would-be process . is equal to the product of amplitudes for process . The first principle is formulated in accordance with the quantum interpretation of monochromatic, polarized electromagnetic waves, for which the polarization plane is interpreted as Gaussian plane, while the imaginary unit ”i” stands for */2 rotation between magnetic and electric vectors. The second principie reflects the interference phenomenon typical for properties of potential character, while the third one states the Markov property of processes consisting of sequences of separated micro-events. With the ingenious notation of Dirac, all this could be expressed with help of a well known formula: *=N,* (s) (Naturally P(x)= ). This is what we mean by a Markov quantum process. Any situation, with possibilities for micro-events labeled by , will be called in the sequel ”a filtering Beobachtunssituation” under the condition, that these intermediate possibities exclude each other by definition. Traditionaly one also assumes *=* i.e. the following: IV. There exist more them one ”filtering Beobachtungssituation”, such that the set of intermediary, potential events is egquipotent to the set of natural numbers. The very four principles of description of quantum Markov processes are enough to prove the representability of their transition amplitudes by means of a scalar product of appropriate vectors from infinte dimensional Hilbert space. For that to do, let us recall, that denotes the scope of relevant potentialities of a somehow estabilished situation * - relevant to a kind of events we are confined to or interested in. With all that in mind, the following is true: OBSERVATION 1 Proof: hence,

and then OBSERVATION 2

Proof:

Hence, due to (S) OBSERVATION 3 Proof: Obvious. Use observations 1 and 2. It is to be noted here, that due to the axiom II, the observation 3 is valid for any states, i.e. we have . The above three observations enable one to interpret (S) as an expression for scalar product in a separable Hilbert space. The unit radius sphere in this space of normalized states is then, what is called - a phase space for Markov quantum processes. The another choice of *=dimCH , **N leads to very interesting kinematical stage of the so called Finite Quantum Mechanics already considered by Herman Weyl. There, ie. for dimCH=n one may use generalized Clifford algebra setting for the realisation of Weyl’s program in the case of Galois fields. A class of problems then appears - characteristic to coding theory [20]. FOOTNOTES (1*) ”It from bit”.In this phrase John Archibald Wheeler epitomizes experience of human’s mind relation to the ”participatory universe” . ”...all things physical are infor- mation-theoretic in origin” - he writes - ”and this is a participatory universe” [1]. We find it quite interesting to conform these views with convictions of Rudolf Haag. In [2] Rudolf Haag reminds us ” Kant’s warning that all we know concerns ”things as appearances” not things ”as such”. A phenomenon is an ”appearance”.” He also says: ”With the increasing body of experimental information about phenomena and their interrelation it becomes less and less easy to device a model of real things which is in harmony with the observation. Indeed the problem faced in the development of quantum theory has not been the ambiguity inherent in the attempt to infer properties of real things from the phenomena but the inability of devicing any coherent realistic picture conforming with the observed phenomena.” Then his analysis leads him to the intuitive notion of ”a pattern” of events and interrelations between them (see p.248 in [2] ). In the following we try to make clear a conviction that electrons, protons, molecules, ... and perhaps every Wheeler’s ”It” ... that these all are names of Haag’s ”patterns” or may be these are names of properties of these patterns. Properties of apparently informational character. And this is only on macroscopic eventmultitudeness level that the feeling of thing-like firmness arises. Seeking of thing-like firmness at the background of quantum processes or say elementary patterns of events is by no means natural, but not indispensable. The firmness we would like to look for does not need to be thing-like firmness. In the presented note we investigate the consequences of the conjecture that ”Haag’s patterns” are caused by some flying micro-things. (1!* ) - What does that mean ”two undistinguishable objects”? - Are there then two objects or not? -”Two perfect billiard balls are objects and are undistinguishable” - this is an authentic response.- By whom or by what? - I ask. If there are two ”perfect balls” then does not that mean that somewhere and somehow it must be coded - denoted, that there are two? - If we were in Platon’s cave,believing in an outside perfect world with perfect balls then, of course seeing only shadows WE, we would not be able to make a choice...and say - this shadow belongs to a perfect ball while that shadow is caused by ... a perfect ball. The ways of prescribing the shadows - (an information!) to the hypothetical balls would be then undistinguishable, the ways, not the shadows nor the hypothetical balls. But do we need to assign any balls to an information (”shadows” ? ) forming quantum processes. In this paper we argue that WE perchaps ARE FORBIDEN TO DO THIS. The classical image of Cosmos appears to be narrower then its quantum description .The classical image is a limit picture admitting only such information forming processes for which the Plank constant is negligible. If we are then in a Platon’s cave then these are rather perfect balls that we see on the epistemological screen. It is the ”outside-cave” quantum description of ”It”. This is simpler and more fundamental image of our relation in Cosmos . ”It from bit” (1*). And note. Even ”perfect balls” would not interfere. Because they are distinguishable. Undistinguishable might be PROPERTIES.For example the property: ”one kilogram” is undistinguishable from the property ”one kilogram”. For example the property of a stochastic process (in Platon’s cave): the red color of a shadow (of would be S7 sphere) is undistinguishable from the property: the red color of a shadow (of would be S 15 sphere). So if here is no device to check the origin of shadows (via for example constructing the corresponding spheres) a redness is undistinguishable from the redness - a would be ”the”. And so, a whiteness interferes with redness, but red ball and white ball do not interfere. Similarily; heaviness interferes with lightness, but heavy ball and light ball do not interfere. (2*) electron,proton etc. these are names for measurable properties of the corresponding genus or sort of events - and note - elementary events * unsplitable bits of information. (3*) Electron,proton etc. these are ”no more than a convenient abbreviation for the way an information on the corresponding type of events can be assembled” - paraphrasing Einsten’s (!) pronouncement concerning the space in ”Meaning of Relativity”. -...So? - So ways of assembling an information - these may interfere, superpose ... but objects? Objects - no? (4*) This has been put into words in an unsurpassed manner by David Finkelstein in [7]. The distinction [M/and/S] introduced by R.Haag in [2] is quite close to Finkelstein’s [egzo/endo] division. According to views developed in the presented paper electrons, protons, ”etc.-rons” - these are - colloquially speaking - names of informational properties of [egzo/endo] divisions of Finkelstein or [M/and/S] distinctions of Haag. (5*) While dealing with two-quanta state we are dealing with ONE stochastic process . For that to see let us consider what follows. Let x denotes an elementary i.e. unsplitable event of a given kind (electron, proton, etc.-ron type event) in the vicinity of x*R , labeled by one-quantum state good quantum numbers. The same for y correspondingly. Let be a pair of orthonormal one-quantum states i.e. Then the two-quanta state describing the superposition of these two excluding each other possibilities has the form ( i * j ) :

where * =*1 depending on whether boson or fermion states of matter are considered. If , and this is why some people say, that we are dealing with two noninteracting particles. Meanwhile, the two-quanta state is the name for ONE stochastic process ,unsplitable into two independent stochastic processes. This is apparently seen from the formula

+ where we choose such functions ; that * i*j. Then for the event (x,y) such that we have prob (x,y) = 1/2 prob ( x ) prob ( y ) . We conclude then that such a two-quanta event (x,y) is the evidence of the ONE stochastic process . It is not the result of two stochastically independent processes . Which potentiality is being then realized by a doubled event (x,y): ? - It is the potentiality that they CONSTITUTE ALTOGETHER; It is their superposition that is being realized. (6*) Electrons, protons, etc. -rons are made of bits of information in the way numbers, laws, fractals, images and other mathematical concepts are made of information; ”Bit of It” (see (1*)). Finally: The Information ? - It seems to be the omnipresent Cosmic Stuff perceptible ,created and/or recreated by unsuppressed Universal Consciousness or Tendency manifesting itself via immeasurable kaleidoscopic appearances. With this respect we find quite suitable to make following quotation from Schlaeger’s unusual paper [15]: ”The apparently paradoxical idea that matter is not something substantial at the level of elementary particle but the pure form of motion, offers considerable advantages.” Then he proposes to extend the notion of substance or as we would say - the notion of reality. Paraphrasing his words we would say: that matter is something ”informational” at the level of elementary particles. Hence, Cognition and Information; - this is what our concept of Reality should perhaps also include, i.e. this ”nonsubstancial elusive material”. The Information should perhaps also be treaded as the very basic category not only of physics but of gnoseology and ontology, too. Acknowledgements The author expresses deep grattitude to Prof. Eftichios Bitsakis for his kind interest to this work.

References

[1] J.A.Wheeler Proc.3-rd Int. Symp. Foundations of Quantum Mechanics, Tokyo,1989, pp.354-368.

[2] R.Haag Commun.Math.Phys.132,245-251 (1990)

[3] E.Schrodinger Endavour, 9, 109 (1950);

[4] G.Tarozzi Mecanica Razionale E Fisica Matematica Universita di Bologna; p. 311-315 (1981);

[5] Piyush Ojha New Scientist; 10 March 1990

[6] A.Odzijewicz Commun. Math. Phys.114, 577-597, (1988)

[7] D.Finkelstein ”The Universal Quantum” Conference:”The World View of Contemporary Physics” Colorado State University,September 1986, revised December 31 1986.

[8] E.C.G.Sudarshan T.C.Govindarajan DOE-ER 40200-178 (1989) L.J.Boya E.C.G.Sudarshan DOE-ER 40200-225 (1990) R.Simon, H.J. Kimble, E.C.G.Sudarshan Phys.Rev.Lett.61, No 1, pp. 19-22 and references therein.

[9] B.Mielnik Commun. Math. Phys. 9, 55 (1968) B.Mielnik Commun. Math. Phys. 15, 1 (1969)

[10] B.Mielnik ”Schrodinger’s Cat and the First Impossibility” a talk given at the 4-th International Workshop in Analysis and its Applications; Dubrovnik, Yugoslavia, June 1990.

[11] N.D.Mermin Physics Today 4, 1985

[12] P.D.Finch The Journal of Symbolic Logic, 34, No 2, June 1969

[13] H.Dishkant Studia Logica Vol.XXX-1972

[14] G.Takeuti Proc. Int.Symp.Foundations of Quantum Mechanics,Tokyo, 1983, pp.256-260

[15] F.H.M. Schlaeger ”Is there a physical elementary constant 42,85” private paper (1984) Rheinallee/Pttzg. 6 D-5465 Erpel bei Bonn.

[16] H. Reiter, W.Thirring ”Are x and p Incompatible Observables?” UW Th-Ph 1983-3

[17] J.C.Lagarias ”Number Theory and Dynamical Systems”, Proceedings of Symposia in Applied Mathematics vol. 46 (1992) p.35-72 [18] Manfred R. Schroeder J. Audio Eng. Soc. vol. 37 No 10 (1989) p. 795-808

[19] V. Elser, C.L.Henley Phys. Rev. Lett. 55

[20] A. K. Kwaniewski Advances in Applied Clifford Algebras, 2 (1) (1992) pp.107-144

I Note added in proof: In the above essay we developped growing up conviction that elementary quantum Markov processes (vide: electrons, protons and other etc-rons) are ”made of” bits of information in the way numbers are built of. This conviction has been deepen after reading of Y.F.Orlov’s article [21]. Number theoretic character of quantum states of matter (... of quantum informational states ...) - is there starting point for basic constructions. Stochastic character of quantum processes in [21] is related to stochastic properties of irrational number’s binary representations ( - for the latter see [22]).

[21] Orlov, Y. M. (1993) The logical Origins of Quantum Mechanics, CLNS 93/1208; Cornell University;Ithaca, New York 4853 USA Annals of Physics vol.234 No 2 1994

[22] M. Kac ”Statistical Independence in Probability Analysis and Number Theory”, The Carus Mathematical Monographs, The Mathematical Association of America 1959

II Note added in proof While talking about ”naming” (pp. 8/9) we have not mentioned Feynman path integral formulation. This seems to be particularly ”particle-liking” way of calculation and way of commenting quantum processes in terms of ”particle-like” language (... tracks on films or in cloud chambers...). As it is well known (see for example [23]) rigged Hilbert space formulation of Q.M. migth serve to derive Feynman path technique. - So what are these ”trajectories” or ”histories” that we perform integration on? - These are virtual events’ patterns; one ”simply” counts all events’ possibilities via potentially classical trajectories’ patterns. And one needs not to restrict one’s mind to Micro-UFO’s. On the contrary. The need of freedom to talk about histories of structures (... paterns, images ...) instead of micro-UFO’s is spectacularly present in papers of C.J.Isham and others [24]. There one considers transition probability amplitudes for going from a metric g1 on a manifold to a metric g2 on a manifold . This ”going” is treated as composed of interfering possibilities (histories). Then the sum over all such possible histories in the form of functional integral gives the amplitude of quantum process. - ”The process of Micro-UFO’s flying?” ... - No! - The process of pattern structures’ changings.

[23] A.K.Kwaniewski; ”Description of Quantum Phenomenae. An Introduction” Wrocaw Unversity Press; Wrocaw 1990 (in polish)

[24] C.J.Isham Class. Quantum Grav. 6 (1989) 1509-1534 C.J.Isham, Y.Kubyshin, P.Renteln ibid. 7 (1990) 1053-1074