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Sommaire
As early as my very first contact with quantum mechanics, as a student, I felt strongly interested by the foundations of this theory, by the singularity of its mathematical formalism, by the cryptic significances that can be guessed to be incorporated in this formalism, and by the problems of interpretation which the quantum theory raises ever since it came into being.
My PhD thesis has been elaborated under the direction of Louis de Broglie. It is titled Étude du caractère complet de la mécanique quantique. This thesis – published in 1964 by Gauthier-Villars in the collection Les grands problèmes des sciences (1) [1], with a preface by Louis de Broglie, contains the first (and until now the most elaborated) invalidation of the proof of von Neumann's theorem [2] asserting that a theory of microstates more "complete" than quantum mechanics and compatible with it, is definitively impossible. This theorem was widely considered to be the institutionalization of the "impossibility of hidden parameters".
I point out that the analyses from my PhD thesis – the main character of which is of logical nature – already contained epistemological considerations that related the mathematical formalism of a theory of a domain of physical facts, with the human processes of conceptualization involved in this mathematical formalism.
After the publication of my thesis my research continued at the University of Reims, France, where, as a professor of theoretical physics, I founded in 1971 the Laboratoire de Mécanique Quantique et Structures de l'Information which I headed until 1997. I first concentrated upon questions raised by the quantum theory of measurement. How is it possible at all to "measure" quantities assigned to microscopic entities – states of microscopic systems (microstates) – which nobody can perceive and which moreover are essentially unstable accordingly to the very definition of a microstate [3] ? How, by the help of what organization of concepts-apparatuses-operations-coding can one succeed to construct concerning microstates, a knowledge able to lead to predictions of a precision as unthinkable as that one offered by the quantum theory?
These questions led me naturally toward the theory of probabilities and toward Shannon's theory of communication of information. In this way strong>[(quantum mechanics)+(the theory of probabilities)+(the theory of communication of information)] came to form in my mind one single whole inside which I was trying to explicate an epistemological-and-logical coherence.
Among the first works published after my thesis I mention only two ((2), (3)) which establish a second important invalidation, that of Wigner's theorem[4] asserting the impossibility of a joint probability of position and momentum that be compatible with the quantum mechanical formalism. Again, these works (especially the first one) contain explicit analyses of the connections between the quantum mechanical mathematical formalism and the operational-conceptual epistemological processes that are involved.
Notwithstanding this second invalidation, the period that followed my PhD thesis appears to me retroactively as very slow and laborious, as tinted by a shade of impotence. I kept failing to explicate the cognitive strategy which is necessarily incorporated in the quantum mechanical formalism, since this formalism is efficient (I postulated this). Correlatively, even though I was constantly teaching quantum mechanics and I had come to know it thoroughly, I still was failing to reach a feeling of genuine understanding of the conceptual status of this theory: in what a sense, exactly, does this theory yield "descriptions" of microstates? I did not even know clearly what I was looking for, what, if known, would have permitted me to claim that finally I had understood this theory. This question, when it arose in my mind, only called forth there as an answer an obscure place vaguely animated by blurred and fleeting contours.
This opaque period came to an end in June 1979. This happened suddenly, in the following way. The celebration of a centenary since Einstein's birth gave opportunity for a short Colloquium on Bell's well-known theorem of non-locality. I had been invited to expose my view on this problem. Only 20 minutes were assigned to each lecture. Three days before the meeting I wrote down all the 14 pages of my lecture(4), in only a couple of hours.
And it turned out that in this short text I had outlined a program of personal research which since then I never ceased to develop: while writing this text the questionings that had formed themselves during the 15 years which had passed since my thesis, had undergone a quasi instantaneous precipitation into a clearly formulated structure of problems and refusals. I showed there how, in the particular case of this problem of locality which at that time was shaking the whole community of theoretical physicists, the significances of the utilized words were loose, so that the expressed assertions involved much confusion which hindered a clear agreement with the conclusion of Bell's proof, even though the mathematical organization of the proof seemed not to by contestable. And I claimed the necessity – which already seemed pressing to me – to reach down into the very deep buried zone where the roots of logic and those of probabilities must merge into still unknown but fundamental epistemological features which might implicitly govern the organization of the primordial stratum of human knowledge; so also, in particular, the sort of knowledge contained in the quantum mechanical formalism.
Starting from 1979 the substrate of my works acquires a quite definite epistemological character. What principles, assumptions, rules, do command the forms of knowledge expressed by the fundamental quantum theory, the theory of probabilities and the theory of communication of information? Could these principles and rules be explicated and subjected to norms?
Of course, the mathematical structures which I had come to know continued to play a central role of reference and orientation, and they even became an object of tentative innovation. But the major goal was progressively becoming epistemological; epistemological and constructive-normative-unifying
I had ceased being interested by the invalidation of this or that particular proof. The nature and extension of my goal had undergone a mutation. Via the treatment of particular problems I was now trying to structure constructively an explicit and general manner of conceptualizing able to exclude a priori the emergence of forms of reasoning which later would allow invalidations or would indefinitely lose themselves in a conceptual labyrinth closed by dead-ends.
I was researching a system of norms for conceptualizing freely but in a protected way. I was trying to erect a modality of conceptualizing endowed by a transparency so perfect that it would permit to perceive explicitly how – at every step from a process of conceptualization – germs of ambiguity might get inserted, and how the installation of such germs can be avoided methodologically so as to banish by construction any possibility of fallacious developments that might induce false problems and paradoxes.
I furthermore wanted these openly exposed methodological preventive norms to be such as to permit re-construction of any already accomplished conceptual structure which, when analyzed accordingly to the mentioned norms, would turn out to be vitiated by an implicit insertion of some germ of possibility of fallacious development.
Of course, this complex goal was only progressively constituting itself, while effectively dealing with definite particular problems.
The most important stages of this process were accomplished while: (a)constructing "the functional of opacity of a statistical distribution with respect to the acting probability law"; (b) explicating the "probability tree of a microstate"; (c) bringing into evidence the logical structure involved in quantum mechanics; (d) representing the formalism of quantum mechanics as a mathematical calculus with the semantic contents of descriptions of microstates.
Between 1979 and 1982 I solved the following question: establish a mathematical relation between Boltzmann's concept of statistical entropy defined inside physics, and Shannon's "informational" entropy of a probability law. Indeed it seemed to me unthinkable that the quasi perfect formal similitude between two concepts involving so different semantic contents, be mere coincidence.
The desired definition has been constructed with full rigor and detail in (6). It has been summarized in (5). Finally it has also been reconstructed (in collaboration) in a much simplified way (but which is also much less innovating from a methodological point of view and much less explicative (7)).
Indeed the first approach quoted above – extremely mathematical – exhibits an apparently still quite classical character. But in fact this approach introduced a quite methodological feature, namely an explicit stratification of the process of construction of the researched mathematical expression. Precisely this methodological feature is what permitted to overcome difficulties which had stubbornly blocked the access to a constructed relation between a statistical entropy in Boltzmann's sense and Shannon's "informational" entropy of a probability law.
In 1984 was published the very first expression ((8)) of what I now call the method of relativized conceptualization (MRC). This initial presentation was still conceived in intimate connection with the specific probabilistic organization of the quantum mechanical formalism where I was identifying – for the first time – a non classical probabilistic structure which I called the probability tree of a microstate. This probabilistic structure is different from that of a Kolmogorov probability and, in a still nebulous way, it appeared already that though this new probabilistic structure was irrupting into thought as a non classical characteristic of the description of a microstate, it quite likely was in fact a particular instance of a universal feature of human conceptualization.
Later – and up to this very day – I kept clarifying the source of this new sort of probabilistic structure encrypted in the quantum mechanical formalism as well as the consequences entailed by it for, specifically, the particular case of descriptions of microstates (9). I also related this probabilistic structure with epistemological features (10,11) on and on the other hand with the classical theory of probabilities and with Shannon's theory of communication of information a href="travaux_fr.html">(13).
But at the same time the universal presence of a probability tree for any entity-to-be-described kept growing more and more obvious and significant.
When one examines the logical characteristics of the entire set of the quantum mechanical "propositions" (the quantum mechanical assertions that can come out to be true or false), it is difficult to escape the conclusion that the algebraic structure of this set is intimately tied with the tree-like probabilistic structure of the description of a microstate.
Furthermore it is obvious that this structure is not a lattice as it is currently asserted, for it is (1) stratified, and (2) it does not admit a factually significant logical conjunction between any two propositions from the set (12)
The characteristic (2) is probably the most profound specificity of what is called "quantum logic". One can guess in it a particular instance of a deep unity between probabilistic-and-logical conceptualization, of which the manifestation might become clearly perceptible only in the primordial – absolute – foundations of the general processes of construction of human knowledge [5] [6].
Thus the work (12) contains the very first indication of an essential unity between the probabilistic conceptualization and the logical conceptualization, well defined and entirely constructed but only for the particular case of descriptions of microstates. Before, inside the classical thinking, the separation between logic and probabilities had never been vanquished (for instance, think of the attempt of Reichenbach [7] or the analyses of Jean-Blaize Grize) [8].
The elucidation (accordingly to my own standards) of the probabilistic and the logical structure involved in the quantum mechanical formalism and the relation of these structures with epistemological features that seemed to be quite general, permitted in 1993 to represent the quantum theory as a mathematical calculus with the semantic contents of the descriptions of microstates, realized with the help of Hilbert vectors ((11)
.This was the first clear and rather compulsory indication of the possibility of a general and formalized epistemology – even formalized in mathematical terms – directly rooted in the physical reality and expressed in harmony with the nowadays microphysics.
Starting from 1993 this indication induced into my research a clear bifurcation.
On the one hand I continued to gather the elements that would finally permit to decode the structure of the epistemological-probabilistic-logical organization that underlies the quantum mechanical formalism.
But on the other hand I also resolutely undertook to elaborate – independently of quantum mechanics – a general and self-sufficient method of conceptualization, directly rooted in the physical reality and founded on a descriptional type that generalizes the formal essence of the descriptions of microstates. This descriptional type was now clearly recognized to be universal and basic
It now appeared with increasing obviousness that the quantum mechanical descriptions of microstates possess the following two major specificities.
Once this has been remarked, a deepened analysis brings forth that any natural description involves the three mentioned relativities – but more or less radically (sometimes in an evanescent way, or entirely occulted by a genetically cabled neurobiological organization) – and that any descriptional chain, if it is followed down to its very first beginnings, reveals there a direct rooting into a-conceptual physical reality.
So I developed the method of relativized conceptualization by founding it on an explicit requirement of the characters mentioned above.
This induces into the volume of the conceptualized a global structure possessing the character of a network of chains of increasingly complex relativized descriptions. Here and there two or more such chains meet in a descriptional knot. And each chain is rooted into a-conceptual physical reality via descriptions of the general type that synthesizes the essence of the quantum mechanical descriptions. The descriptions of this general type I called basic "transferred" descriptions (transferred on the registering devices of apparatuses).
The descriptions of the basic transferred type are entirely ignored by the current thinking and languages, and even by classical logic, classical probabilities and by the classical sciences. In particular they are ignored by the whole macroscopic classical physics [10]
The classical disciplines are exposed as if the construction of the descriptions contained in them were achieved by making use mainly of language ; language conceived as a sort of mirror that would form verbal images of things and facts that pre-exist (cf. the very important bibliographic indication from the note 5, of a famous work by Wittgenstein). Classical grammar and logic tend to occult the physical operations which in certain basic cases have to act quite radically for the construction of a description of a physical entity; even in current life; whereas in certain natural sciences – in particular in fundamental microphysics – physical operations often play a quite central role in the construction of descriptions.
But MCR, by the primordial stratum of conceptualization consisting of basic transferred descriptions, mpenetrates beneath language and it implants the roots of conceptualization into the a-conceptual physical reality. Indeed, every basic transferred description involves by construction a physical operation that acts inside the unknown physical reality and creates there an entity-to-be-described which did not pre-exist and which emerges strictly unknown, never qualified before. This still entirely unknown entity is then hoisted upon the floor of the volume of the conceptualized, by physical operations of "measurement interaction" that accomplish for it a very first, a primordial qualification. I say "on the floor" because such measurement interactions produce just a heap of marks observable of registering devices of apparatuses, devoid of any conceptual organization, devoid even of any organization in space or it time. MRC explicates entirely how such a heap of marks can be obtained, how it is possible to associate with it a "primordial" probabilistic organization that is equally devoid of any spatial and temporal structure, and how afterward, out of this primordial probabilistic organization, it is possible to construct indefinite chains of more and more complex pieces of "sense", so of descriptions, that can meet and combine and be organized in systems of conceptualization, logic, probabilities, theories, etc.
Inside MRC the processes of conceptualization are fully represented and subjected to norms, from their birth on and up to their metaphysical limit.
In consequence of the fact that any descriptional chain is explicitly rooted into the a-conceptual physical factuality via basic transferred descriptions, the MRC way of structuring the processes of conceptualization induces two effects which had not been required beforehand and had not even been anticipated.
Let us now mention some global characters of MRC
This means that a computer – by itself – cannot conceptualize accordingly to MRC because along a descriptional chain it will not "know" how to pass from one achieved descriptional cell, to the next one.
But a computer endowed with an MRC-program for achieving any isolated descriptional cell, if it were guided by a man who would enter in it – in the language of the MRC-program – his own descriptional aims such as these are suggested by his own cognitive curiosity, would work for that man exactly as required by the method.
This might be of some interest for computer scientists, especially if they are involved in the attempts to construct human-like robots. More generally, this might be of some interest for all those who are involved in "modelization of complex systems".
This is the major aim of MRC, structurally insured by it.
But it is not the unique aim that can be lodged inside the framework of this method.
Indeed MRC permits to develop inside its framework processes of conceptualization that are optimized
with respect to any chosen descriptional aim different from the major one, under the sole condition
that this aim be well defined and well expressed in MRC terms, and carried out accordingly to the
MRC norms. For the freedom, for the observer-conceptor, to choose as he wants, inside a descriptional
chain, the succession of pairs of an entity-to-be-described and a grid for qualifying this entity,
permits to orient the local descriptional aims in a way such that the chained descriptions shall
progressively realize any desired global descriptional aim.
This entails that MRC is structurally open to the insertion of processes of technical or artistic invention.
Finally, I mention the following results obtained up to now by the use of MRC.
During the same time in which the method of relativized conceptualization was being developed, the structure of its roots, hidden under the mathematical formalism of fundamental quantum mechanics or encrypted in it, kept becoming more and more clear, via to-and-fro elucidations. This process finally constituted an explicit and achieved separate representation of the whole cognitive strategy encrypted in the quantum theory, as well as of the corresponding descriptional result. This representation is intimately linked to, both, my researches on fundamental quantum mechanics, probability and information, and to my epistemological investigations.
Infra-quantum mechanics is a strictly qualitative description of microstates. It is constructed by making tabula rasa of the mathematical formalism of quantum mechanics and by then advancing, starting fro zero, exclusively under the constraints to which a human being who wants to generate knowledge concerning what is called microstates, is subjected by the cognitive situation where he finds himself and, on the other hand, by the requirements imposed upon him by the general human ways of conceptualizing.
Those who know the mathematical formalism of quantum mechanics can clearly recognize its essence in the descriptional form that arises inside infra-[quantum mechanics]. But they will equally identify there aspects which inside the mathematical formalism remain hidden and of which the fundamental importance is obvious.
In these conditions it seems likely that a face-à-face between infra-[quantum mechanics] and the quantum mechanical formalism will permit a simultaneous coherent elucidation of the whole set of interpretation problems which afflict quantum mechanics since a century already [13].
So for now the two distinct lines of my research that which since 1993 had separated from one another (even though they kept interacting), one devoted to the foundations of quantum mechanics and the other one to general epistemology, are joining again. This junction induces a new project, namely to accomplish a mathematical formalization of MRC in terms of Hilbert vectors, by a convenient weakening of the constraints from the Hilbert-Dirac formalism of quantum mechanics which on the level of generality of MRC are too restrictive and by confining this formalism inside the domain of finiteness, so of discreteness, thereby rendering it strictly effective [14].
This project, if it were realized, would offer a general mathematical epistemological method for conceptualizing in a way protected by construction from the insertion of germs of false problems or paradoxes. This method would include in particular a modified version of quantum mechanics, freed of interpretation problems and possessing the epistemological status of a calculus with the semantic contents of the particular quantum mechanical descriptions of microstates.
In 1994, several years before retiring from the University, I founded the Centre pour la Synthèse d’une Epistémologie Formalisée (CeSEF). The goal of this centre has been formulated in a manifest published by Gallimard in the review Débats (21).
The collective book Quantum Mechanics, Mathematics, Cognition and Action: Proposals for a Formalized Epistemology (22) published in 2002 expresses results and perspectives in the form which they possessed at that time.
In 2009 has been founded the Association pour le développement de MCR (adMCR). One of the goals of this new association is to develop explicitly inside the framework of MRC a Relativized Systems Engineering, thus producing an MRC-representation of the processes of invention (conception) and of technical realization of artefacts [16].
Correlatively would probably emerge also the main lines of a Relativized Systems Theory.
I take the liberty to express the hope that, sooner or later, MRC will be able to elaborate a deep and coherently worked out connection with the approaches practised nowadays in the domains of psychology, neurobiology, cognitive sciences, and computer sciences. This, if it happened, would be a big jump of our knowledge of the processes by which we generate knowledge, in the direction of a unification of human thought.
This last assertion leads me, as a closure, to a declaration of faith.
I am convinced that a unification of the whole rational human thought – the vast domain of physics included – is possible. But I am also convinced that it can only be achieved in a purely methodological sense. A common methodology of conceptualization unanimously applied, able to distinguish between the various epistemological levels that are involved, able to confront any cognitive situation, to associate to it a specifically corresponding descriptional type, and able to assign to each representation its own descriptional location as well as its relations with representations of other sorts, appears to me as the unique conceivable way of unifying the rational human thought.
In particular, I believe that any attempt at mixing representations that have initially been achieved as a specific answer to some particular given cognitive situation, with representations that correspond to different cognitive situations, is doomed to fail.
I am equally convinced that any methodologically blind attempt at achieving a unification of some non negligible scope is inexorably doomed to fail.
I think that in the present state of complexity of the human representations of domains of reality, physical, social, psychological, the dance of the involved physical or abstract operations, points of view, cognitive situations, has got so diverse and wild that it finally has become clear that the unique conceivable sort of universal organization and of correlative "unification" can only be methodological. I think that when unlimited smallness and unlimited largeness of space-time dimensions and any degree of abstraction or of material precision, are equally addressed and when technical realizations merge so intimately and immediately with the theoretical constructions wherefrom they stem, it finally becomes blindingly obvious that unification by mere considerations of this or that particular aspect – quantity (for instance the number of involved microsystems for defining the "passage" from quantum representations to classical ones), or mathematical tools and treatments (like in the theories of chords) or the nature of the involved entities (organic or inorganic, etc.) – cannot even suffice for local unifications, if one wants these not to be superficial.
Only a general method of conceptualization, commonly applied, can aim at acting as a universal modality of organizing human thought so as to insure a universal and deep sort of unification.
[1] A number inserted in the current text, between parentheses, sends to the work with the same number from the list of works published on this site.
[2] [2] Neumann, J., von, Mathematical foundations of quantum mechanics, Princeton University Press, 1955.
[3] Dirac has defined the “mechanical state quantities” assigned to a microsystem, as those characters which evolve (in contradistinction to those which are constant and characterize the considered type of a microsystem).
[4] Wigner, E. P., in Perspectives in Quantum Theory, W. Yourgrau and A. van der Merwe, eds., MIT Press, 1971.
[5] Wittgenstein, Remarks on Logical Form, lecture for the Aristotelian Society, 1929 (text of an undelivered lecture).
[6] Reichenbach, H, Introduction à la logistique, Herman 1939.
[7] This question of the non-generality of a logical conjunction between two quantum mechanical propositions is very fundamental indeed (cf. an explicit and detailed treatment in (16) pp. 226-229 and (17) pp. 172-176 et 259-262). This treatment, in both quoted works, includes a key-quotation from the above cited lecture by Wittgenstein, wherefrom one can understand that for those who did not thoroughly practice the foundations of quantum mechanics there was a quasi null chance to reach the absolutely primordial stratum of human conceptualization where it becomes possible to perceive the genetic unity between the probabilistic and the logical conceptualizations, as well as the way in which this unity is achieved.
[8] Grize, J-B, in Logique et connaissance scientifique, Encyclopédie de la Pléiade, pp. 135-288, Gallimard 1967.
[9] The method of relativized conceptualization has been publicly expressed in all its successive forms. Here we quote only the last ones which are the most complete and thoroughly elaborated.
[10] Notwithstanding this ignorance of the descriptional type qualified by me as "basic and transferred", descriptions of this type are rather currently achieved (more or less "perfectly") at all the levels of conceptualization, macroscopic and even cosmic, not only at the microscopic level where the quantum mechanical descriptions of microstates are located : they characterize any strictly first gathering of data concerning a fragment of reality (of physical or psychic nature) which has never before been qualified by the help of the considered grid for qualification.
[11] Erroneously called also "information theory", which led to an endless sequence of confusions.
[12] "Infra" has to be understood as "beneath the formalism and partially encrypted in it"
[13] This face-à-face is now being elaborated (20). It seems to lead to a reformulation of the quantum mechanical formalism where the formal modifications – as such – are minuscule, but the changes introduced by them in the semantic associated with the formalism, are radical and clarifying.
[14] Another mathematical formalization has been already achieved, in the terms of the theory of categories (cf. in (16), and seems to be enlightening from a conceptual point of view. But for practical applications of MRC it certainly is much less useful that a Hilbert-vectors formulation might be.
[15] In English : Center for the Synthesis of a Formalized Epistemology and association for the development of MRC.
[16] Henri Boulouet, systems-engineer with Peugeot-Citroën (PSA) is developing a thesis with this goal inside the laboratory CEDRIC from the CNAM (Centre National des Arts et Métiers), Paris.