> [ 4bjbj4ΐΐ\+8TD2I$:PPP???iHkHkHkHkHkHkH$JM.H]?????HPPH111?XPPiH1?iH11)+P ٣y*UHI02I*MM(+M+1???HH1???2I????M?????????:Fundamentals of complex physics
Presentation
Marc Halvy
October 2009
HYPERLINK "mailto:marc@noetique.eu" marc@noetique.eu
The following pages give an introduction to our original and complete work edited under the same title. Such a resume, by a definition, is incomplete and simplified. Its only purpose is to present, on a more pedagogical mode, a global overview of the concepts and of the reasoning which have inspired this research.
(Version originale franaise de l'autre ct)
Assessment
Classical physics under this term, we include all theories of Newtonian, relativistic and quantum physics, and all their derivatives - lead today to two standard models : the so-called cosmological standard model derived from the general theory of relativity, and the so-called elementary particles standard model derived from the quantum theory.
Beside these theories, thermodynamics and theories of statistical physics are presented as "side-products" with one exception : the concept of entropy which is not reducible to the space-time-energy complex but, thanks to Boltzmann, points to the concept of configuration.
Today, the assessment is triple :
Each of the two standard models contains internal contradictions which lead, in order to save the model, to conceptual and mathematical conjuring tricks far from Occam's parsimony principle. But first and foremost, these tricks extend the gap between theory and reality and make Popper's principle of falsification inapplicable. Can we then still talk about science ?
These two models are incompatible with each other ; their unification - the great dream of the past decades - is still failing despite so many mathematical artifices without any physical meanings. If the universe is "one", may science not be "two" ?
Last but not least, none of the two standard models is able to give the embryo of an approach to complex phenomenon like self-organization or autoposes. The reason is that our two models are analytical and reductionist : both are based on the principle that the universe is a huge assembly of elementary structures, forces and laws given a-priori - by who ? - at the very beginning of its history.
If we follow Kuhn's concept of paradigmatic mutations in science, it does not seem too difficult to predict a soon-coming radical and deep bifurcation in physics. Our ambition, in this work, is to suggest some hypothesis about new fundamentals for physics, not against but beyond the classical ones.
We are aware that our ambition is enormous : it is as enormous as the theoretical and conceptual confusion known by today's physics. Moreover, we strongly believe that time is come to deliver physics from mathematics which are an excellent servant but a delirious mistress. Physics must come back as a science of reality instead of being a mathematical branch.
Methodological consistency
The research in physical sciences is a long-term complex process born some 3,000 years ago. As we will see it later on, to understand a complex process consists in defining its intention, its territory, its structure and its dynamics. In order to be consistent with this approach, the paradigmatic bifurcation of physics must be described according to these four dimensions.
Bifurcation of intention : the purpose is not necessarily to build up a mathematical model of the universe, to predict or to foresee (except in some elementary cases or rudimentary configurations). Indeterminism is one of the fundamentals of a complex universe. Emergence of holistic properties is unpredictable and unforeseeable. As Ren Thom suggested, the problem is not any more to explain from outside but to understand from inside. The aim is to describe an auto-referential processing logic, constrained but not determined by all its former states.
Bifurcation of territory : in the past, because they are not reducible to their components, complex phenomenon were always considered as "accidents", "exceptions" and "later-to-be-explained" quirks. Here, on the contrary, we will assume that the mechanistic systems are the exceptions and that complexity is the first and irreducible property of the universe : elementariness does not exist and the universe, taken as a whole, is organic and holistic.
Bifurcation of structure : The question is not any more to formulate the invariable and platonic laws of the universe. These laws are always idealizations. To say it on a more philosophical mode, time is come to leave Parmenides and to rediscover Heraclites. The universe is not an assembly of pieces according to laws ; the universe is a global, consistent and self-referential logic and all structures that mankind believes to distinguish as particles, fields and laws are just contingent emergences.
Bifurcation of dynamics : formalizing the invariance of the Being under the form of idealized mathematical laws is not the point any longer. The point is to express the consistency of the Becoming under the form of a logic of accomplishment of the cosmic process in which the present universe is nothing but an instantaneous appearance.
We urge not to consider the universe as an object any more but well as a process. Our approach is drastically evolutionist in the more radical sense of this word. Everything evolutes, everything transforms, everything complexifies.
The following of this article will be structured as the climbing of a staircase with a succession of stairs and jumps, each jump linking two successive stairs.
As said above, complexity is the basic and fundamental property of the universe. Let us start by understanding what complexity is.
Stair 1 : Complexity
We will recognize a complex phenomenon as soon as it shows emerging properties which are properties that belong to the whole without belonging to any of its parts. So, these properties are not linked with the components of the whole, but well with the interactions between these components.
For instance, the taste or the white color of salt do not belong nether to the sodium nor to the chlorine. Similarly, transparency and hardness of diamond do not belong to the atoms of carbon. Similarly, life or thought do not belong, respectively, to the molecules of the cell, or to the neurons of the brain ; they emerge from them but are not reducible to them.
The sudden appearance of such emerging properties is not foreseeable : it would be impossible to predict the taste of salt before having produced it for the first time. These emerging properties is a "more" that enriches the reality of the system ; this explains why, in complex physics, the whole is "more" than the sum of its parts.
Lastly, because emerging properties define and fund the concept of complexity and because they express complex interactions between the components of a system, we must conclude that analytical and reductionist methods are inadequate because, by separating the parts as by dismantling a mechanical assembly, they break their interactions and, as a consequence, they destroy the emerging properties and, thus, the complexity of the system itself.
Jump 1 : Auto-reference
The first principle that we applied in our research, is to refuse any kind of "given" from outside the universe. This leads to say, very simply, that all what exists into the universe is an emerging property from the universe itself. Nothing is "given" neither from "outside" nor from "before" the universe. We make the hypothesis that there is nothing "given" a-priori : neither space, nor time, nor energy, nor matter, nor physical laws, nor universal constants. All these concepts characterize products of the cosmic process a but not its (pre)conditions.
Stair 2 : Cumulative logic
Why do there exist structures in the universe, more or less stable forms, more or less regular movements, more or less recurrent rules ? Why, after all, is there a cosmic organization, an universal consistency, a harmony in reality ?
The answer lies in one single word : accretion. The cosmic process applies a cumulative logic : what follows is the - constrained but not determined - result of all what preceded. To say it another way : time does not pass, it piles up. To say it another way again : the fundamental of auto-reference is accretion of memory : from the initial chaos and from the first random accretions of the beginning, the universe climbed up the scale of complexity by accretion of cumulative emerging properties.
The cosmic process is a fractal process : as soon as a new pattern pops up, it will develop on it a phylum of cumulative innovations till the extinction of all its potentials.
At that very moment, each phylum has ended up its logic in producing new stable "objects" which, by their combination, will give up new germs, on an upper level, which, at their turn, will give rise to new phylum, ad libitum.
So the phylum "elementary particles" leads up to electron, proton and neutron which, combined, give atoms developing themselves in crystals, materials, chemicals, fluids of higher complexity.
Let us understand clearly this : the universe builds up itself by accretion as a tree builds up itself at its periphery (in the cambium), by accretion of rings accumulated one upon each other. On the same way, the universe is a fractal tree that builds up itself trough its peripheral layer that we call the present. It builds up itself by leaning on all the previous layers that are now inactive but that entirely and definitely remain in it.
Our human consciousness belongs entirely to this active peripheral layer called "present" and this explain why its is generally impossible, for us, to be aware of the tremendous amount of layers that sustain us. These layers are the cosmic memory. It self only makes possible the auto-referential development of the universe : the only reference possible to do now something consistent is the sum of all what have been done before. This accumulation of memory contains all the germs of all the possibilities for the future, some in continuity, others by arousing original sprouts or new patterns.
Jump 2 : Intention
The principle of auto-reference means that the universe is to be considered as a global autopoietical process, that is to say as a process which engenders in itself, for itself, by itself, all elements needed for its own accomplishment. Space and time, energy and matter, laws and constants are products, consequences, results inferred by accretion processes, by quests for optimizations, by states of homeostatic equilibrium corresponding to this optimum : they are not "given" but constructed.
For instance, laws and constants of physics seem universal and immutable simply because they reflect a progressive sedimentation upon which all the rest, afterwards, was made of.
But where comes this accumulation from ? What is the "engine" that pushes the universe to accomplish itself ? What is this "will" that nourishes the cumulative and phylogenetic logic ?
To remain true to our auto-reference principle, we reject any trial to find this "engine" outside the universe itself : so, any theist temptation is dispelled. The only remaining way is immanence : this "will" is to be intrinsic to the universe self. Therefore, we introduce the concept of intrinsic immanent intention : the universe is animated by one and only one fundamental intention which is to become all what it can, all what is possible, all what it potentially already is.
This immanent intention is, if I may say so, the cosmic anima in the Latin sense of this word : "what animates". It precedes all emergences including space and time, energy and matter, laws and constants qui, all together, are only its products.
By the way, the concept of immanent intention allows an answer to the question to understand why emergence of very complex and sophisticated forms as life or thought has happened much more quickly than as if they just rose random : one finds faster as one searches than as one counts on chance only to find.
Stair 3 : Integral quantities
How to characterize a complex process ? Because space and time are products of its own accomplishment, because the process creates by itself its own space and time, it looks necessary to define another "space" of representation than the classical time-space.
This space of representation will be an abstract space called "space of states" which may have a big number - even infinite - of dimensions. The accomplishment of the process will there be represented by a simple curve like a trajectory.
The crucial question is : knowing that there are no extrinsic parameters (like were space or time for Newton, Einstein or Schrdinger), we must consider only intrinsic parameters that characterize the state of the process in itself. And because this process is global, non reducible to any local part or property, these intrinsic parameters must be integral quantities which mean quantities calculated by integrals on the whole of the process and of its history.
Finally, because nether extrinsic frame of reference can exist and thus nor measurement unities, our integral quantities, as intrinsic parameters, must be quantities without dimension, that is to say ratios between the variation of an integral quantity and this quantity itself.
Let X be an integral quantity, then we define the "propensity" according to X as dX/X (that is to say : dln X) which is well an quantity without dimension whatever X could be.
One can notice that, doing so, we enter into the domain of the exponential functions (or, of their inverse, the logarithmic functions) which are the only functions that are auto-referential and autopoietical because the primitive and the derivative of an exponential is this exponential self.
Jump 3 : Propensities
Any complex process is animated by its immanent intention to fully accomplish itself. This accomplishment is realized trough its proper logic. This logic is one as a fundamental but plural in its modes. To engender complexity, it must include a ternary structure (any binary system necessarily evolutes towards an equilibrium state that prevents any creative evolution). We make the hypothesis that any complex process - and, mainly, the whole universe itself - is driven by three propensities.
If we look at Newton's equation of movement, we find three terms :
an acceleration which expresses the kinematics of the object,
a force which expresses - according to the general relativity - the geometry of the local territory where the object evolutes,
a mass (or gravitational charge) which is a a "form" parameter of the object (as would its electromagnetic, its hadronic or its leptonic charges).
Schrdinger's equation is base on the same ternary :
a wave function which carries all kinematic properties,
the mass, again,
and a potential from which forces are stemmed.
We generalize and postulate the existence of three universal propensities of which all combinations give rise to all global or particular process logics :
a "territory" propensity (volumic propensity) that engenders space-time and gives to it a geometry, a metric, that is to say a metric tensor equivalent to a force tensor (cfr. Relativity) ;
a "form" propensity (eidetic or morphic propensity) that engenders progressive structures and/or organizational architectures in which the classical concepts of entropy and neguentropy take root ;
a "movement" propensity (dynamic propensity) that engenders evolutions, transformations and moves.
To understand better what lies under these definitions, let us take a musical metaphor. The complex process of composing a symphony necessitates three sets of parameters before to begin :
a structured sound territory characterized by the chosen sound scale, by the ranges and timbres of all the implied instruments (this is the volumic domain) ;
a musical organization characterized by melodic lines and harmonic modes and structures (this is the eidetic domain) ;
and an activator characterized by a rhythmic tempo which will give life to the musical movements (this is the dynamic domain).
To go a bit further with this metaphor, let us notice that our symphony would stop if there was no musical logic : each chord calls the next one and so on for a simple euphonic reasons. This a good example of what we called intrinsic intention : all what has been composed pushes the symphony further, by itself, for itself just because the sounds and chords call for other sounds and chords to succeed them.
More generally, the ternary propensities apply to ant real process. And so do for human activities that develops itself according to three main axis :
a space-time axis which develops the consistency and coherence of the territory : the political functions (this is the volumic domain),
a paradigmatic axis which develops values and beliefs structures : the noetical functions (this is the eidetic domain) ;
a productive axis which develops a set of activities and modalities : the economical functions (this is the dynamic domain).
But, moreover, a human society necessitates a strong collective intention to build up a sustainable and long-living mankind. Is not this the main problem in these days ?
Stair 4 : Optimization
Any complex process develops itself through the three universal propensities at the service of its immanent intention of self-accomplishment.
These three propensities combine, interfere, fight and mix with each other.
From all this comes out an infinity of possible scenarios, enriched by an infinity of possible emerging properties.
What could be the criterion which will elect this combination instead of that one, this scenario instead oh that one ? We propose two criteria which will be synthesized in one single word hereunder.
The first criterion is the maximum of simplicity (which is not the maximum of easiness) : effective simplicity is never easy and necessitates intelligence and efforts, subtlety and frugality. Under this criterion of simplicity, we find back the Occam's parsimony or the mechanical principle of energy minimization (Maupertuis, Lagrange, Hamilton).
The second criterion is the maximum of complexity (which is not the maximum of complication) : complexity implies a perpetual enrichment of the possible scenarios, an inexhaustible fecundity. Complexity, in opposite of complication, is not incompatible with simplicity, on the contrary.
Alliance between these two criteria leads to the concept of elegance which implies, on the same time, the search for a maximum of simplicity AND for the maximum of complexity.
So can we propose the optimization principle which determines the development and accomplishment of any complex process - the universe as a whole included : the principle of the maximum of elegance.
Jump 4 : Equations
Our original and complete work shows clearly the detailed expression of the reasoning that lead to these equations.
In synthesis :
we define three integral quantities V,E and D that measure respectively the volumic, eidetic and dynamic dimensions of the process ;
we define K = V.E.D as a measure of the global complexity of this process ;
we put the idea of an auto-referential optimization of this complexity by the equation (dln)mK=0 where dln is the propensity factor and where the exponent indicates on what level of the complexity scale the process is (we have shown in our work that the whole classical physics lies on complexity level =1 and that, then, the equation becomes dV/V + dE/E + dD/D = 0, where the sum of the three propensities is equal to 0 corresponding to the stationary states and the equilibrium situations that classical physics study).
The fundamental equation (dln)mK=0 allows two types of developments.
First development : this equation allows to understand how processes interfere with each other. Therefore, we must consider that any process is a part of a bigger process that contains it (this bigger process is called its environment) and is the envelop of all the sub-processes that constitutes it (these sub-processes are called its fibers).
So appear a three levels structure that organizes the accomplishment of any process : there is the process self, there is its environment and there is its fibers. Each level applies for itself the principles of intrinsic intention, of self-accomplishment and and of elegance, and this often leads to conflicts. The sprouting of emerging properties is the answer to these conflicting situations between the three levels.
Second development : the fundamental equation allows to attempt a connection between our theory and the physical classical theories. To do this, an important remark must be understood : classical physics studies the universe on a phenomenological level because it studies the successive states of the systems and objects that it observes. But these systems and objects are only superficial manifestations of the processes that express them.
Complex physics, on its side, works on a ontological level because it studies the intrinsic logics of the processes selves without looking at the systems that express them.
Transcription from classical theories to complex theory implies a bridge between phenomenology and ontology. This bridge implies to translate integral equations into differential equations, which is only possible in some simplified and particular cases.
Stair 5 : Triangle.
If, in order to schematize, we put the three process dimensions/propensities on the apexes of a equilateral triangle, one can easily understand that the theories of the classical physics concern the sides of the triangle and that complex physics cover the whole triangle and sits in its center.
Let us look at the triangle side between volumic propensity (the metric one which engenders space-time and forces) and dynamic propensity (the kinetic one that engenders moves) : it corresponds to classical mechanics that links forces and movements without taking in account the internal forms and organizations of the studied objects.
Let us look now at the triangle side between volumic propensity (the metric one which engenders space-time and forces) and eidetic propensity (the morphic one that engenders structures and forms) : it corresponds to classical thermodynamics that links energy (the work of the forces) and entropy (or neguentropy or forms or information) without taking in account the external moves of the studied objects.
Let us look finally at the triangle side between eidetic propensity (the morphic one that engenders structures and forms) and dynamic propensity (the kinetic one that engenders moves) : it corresponds to classical cybernetics (or systemic) that studies regulations that is to say the link between organizations (i.e. neguentropic structures) and moves without taking in account the external forces applied to studied objects.
These remarks allow a path to connect complex physics and classical physics : mechanics, thermodynamics and cybernetics. Therefore, one takes the simplest form (=1) of the fundamental equation and one translates it on a phenomenological way. Then, for each of the three classical branches of physics, one simplifies the simplified equation by neglecting the effects of the opposite apex of the triangle (this leads to binary situations
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