Universal Concept of Complexity by the Dynamic Redundance Paradigm: Causal Randomness, Complete Wave Mechanics, and the Ultimate Unification of Knowledge
The fundamental impasses and ruptures in various domains of the canonical, unitary science, or the 'end of science', become the more and more evident. The natural unity of being is recovered within a universal nonperturbative method leading to the dynamic redundance paradigm. It is shown that the unreduced behaviour of any nontrivial (isolated) system includes many equally real, but incompatible dynamic regimes, each of them being roughly equivalent to an ordinary 'complete' solution of the unitary science. Therefore the regimes should 'spontaneously' and randomly replace one another, which provides a universal, purely dynamic origin of randomness. The discovered dynamic redundance leads to the universal, reality-based concept of dynamic complexity and its permanently developing hierarchical structure, alias the world. Its lowest levels give the causally complete mechanics of dynamically quantized elementary fields, extending the double solution found by Louis de Broglie. One obtains a physically complete solution for the 'mysteries' of quantum mechanics, unifyng it with the extended, causal versions of relativity (emergent space and time), quantum and classical gravity (dynamical mass), field theory (electric charge and spin), particle physics, and cosmology. The same key features of the unreduced dynamic complexity determine behaviour of any system at higher levels of complexity described by a case of the single, universal equation in its two related versions, the extended Lagrange-Hamilton (trajectorial) and Schroedinger (distributional) equations. The end of the unitary science opens the renaissance of the ultimately complete and universal understanding initiated by Rene Descartes (but then mechanistically falsified), which is confirmed by many sound, practically important results.
The fundamental impasses and ruptures in various domains of the canonical, unitary science, or the 'end of science', become the more and more evident. The natural unity of being is recovered within a universal nonperturbative method leading to the dynamic redundance paradigm. It is shown that the unreduced behaviour of any nontrivial (isolated) system includes many equally real, but incompatible dynamic regimes, each of them being roughly equivalent to an ordinary 'complete' solution of the unitary science. Therefore the regimes should 'spontaneously' and randomly replace one another, which provides a universal, purely dynamic origin of randomness. The discovered dynamic redundance leads to the universal, reality-based concept of dynamic complexity and its permanently developing hierarchical structure, alias the world. Its lowest levels give the causally complete mechanics of dynamically quantized elementary fields, extending the double solution found by Louis de Broglie. One obtains a physically complete solution for the 'mysteries' of quantum mechanics, unifyng it with the extended, causal versions of relativity (emergent space and time), quantum and classical gravity (dynamical mass), field theory (electric charge and spin), particle physics, and cosmology. The same key features of the unreduced dynamic complexity determine behaviour of any system at higher levels of complexity described by a case of the single, universal equation in its two related versions, the extended Lagrange-Hamilton (trajectorial) and Schroedinger (distributional) equations. The end of the unitary science opens the renaissance of the ultimately complete and universal understanding initiated by Rene Descartes (but then mechanistically falsified), which is confirmed by many sound, practically important results.
The qualitatively new concept of dynamic complexity in quantum mechanics is based on a new paradigm appearing within a nonperturbational analysis of the Schroedinger equation for a generic Hamiltonian system. The unreduced analysis explicitly provides the complete, consistent solution as a set of many incompatible components ('realisations') which should permanently and probabilistically replace one another, since each of them is 'complete' in the ordinary sense. This discovery leads to the universally applicable concept of dynamic complexity and self-consistent, realistic resolution of the stagnating problems of quantum chaos, quantum measurement, indeterminacy and wave reduction. The peculiar, 'mysterious' character of quantum behaviour itself is seen now as a result of a dynamically complex, intrinsically multivalued behaviour of interacting fields at the corresponding lowest levels of the (now completely causal) structure of reality. Incorporating the results of the canonical theories as an over-simplified limiting case, this new approach urgently needs support, since its causality and completeness are directly extendible to arbitrary cases of complex behaviour of real systems, in sharp contrast to the dominating inefficient empiricism of 'computer experimentation' with primitive mechanistic (i. e. dynamically single-valued) 'models' of the irreducibly multivalued reality.
The physical consequences of the analysis performed in Parts I-IV are outlined within a scheme of the complete quantum (wave) mechanics called quantum field mechanics and completing the original ideas of Louis de Broglie by the dynamic complexity concept. The total picture includes the formally complete description at the level of the "average" wave function of Schroedinger type that shows dynamically chaotic behaviour in the form of either quantum chaos (Parts I-III), or quantum measurement (Part IV) with causal indeterminacy and wave reduction. This level is only an approximation, though often sufficient, to a lower (and actually the lowest accessible) level of complexity containing the causally complete version of the unreduced, nonlinear "double solution" proposed by Louis de Broglie. The extended 'double solution with chaos' describes the state of a nonlinear material field and includes the unstable high-intensity "hump" moving chaotically within the embedding smooth wave (quant-ph/9902015,16). The involvement of chaos causally understood within the same concept of dynamic complexity (multivaluedness) provides, at this lower level, de Broglie's "hidden thermodynamics" now, however, without the necessity for any real "hidden thermostat". The chaotic reduction of the "piloting" Schroedinger wave, at the higher sublevel of complexity, conforms with the detailed 'wandering' of the virtual soliton at the lower sublevel. The proposed dynamic multivaluedness (redundance) paradigm serves as the basis for a self-consistent hierarchic picture of the world with a (high) non-zero complexity (and thus irreducible randomness), where the complete extension of quantum mechanics is causally interpreted as several lowest levels of complexity.
The universal dynamic uncertainty, discovered in Parts I and II of this series of papers for the case of Hamiltonian quantum systems, is further specified to reveal the hierarchical structure of levels of dynamically redundant 'realisations' which takes the form of the intrinsically probabilistic 'fundamental dynamical fractal' of a problem and determines fractal character of the observed quantities. This intrinsic fractality is obtained as a natural, causally derived property of dynamic behaviour of a system with interaction and the corresponding complete solution. Every branch of the fundamental dynamical fractal of a problem, as well as the probability of its emergence, can be obtained within the extended nonperturbative analysis of the main dynamic equation (Schroedinger equation in our case), contrary to basically restricted imitations of fractality within the canonical, single-valued approach. The results of the dynamical chaos analysis in Hamiltonian quantum systems, Parts I-III, are then subjected to discussion and generalisation. The physical origins of the dynamic uncertainty are analysed from various points of view. The basic consequences, involving essential extension of the conventional, unitary (= single-valued) quantum mechanics, are summarised. Finally, we emphasize the universal character of the emerging notions of dynamic multivaluedness (or redundance), causal randomness (or dynamic uncertainty), first-principle probability, (non)integrability, general solution, and physical complexity applicable to real dynamical systems of any kind.
A system of two initially homogeneous, physically real fields uniformly attracted to each other is considered as the simplest basis of the self-developing world structure. It is shown that the system is unstable against periodic cycles of self-amplified, essentially nonlinear squeeze of its extended part to a small volume around randomly chosen centre, followed by the reverse extension. The resulting spatially random pulsation, or "quantum beat", is observed as (massive) elementary particle such as the electron. The property of mass is then universally and consistently defined as temporal rate of such dynamically chaotic and essentially nonlinear quantum beat, without introduction of any additional entities. The obtained picture can be considered as complex-dynamical completion of the "double solution" concept of Louis de Broglie. The dynamically emerging wave-particle duality, quantum discreteness, indeterminacy, space, and time lead to the equations of special relativity and quantum mechanics, providing their causal explanation and explicit unification. The elementary particle structure, its intrinsic properties, quantum and relativistic behaviour are obtained thus all together, within the unified analysis of the unreduced interaction process leading to the universal concept of dynamic complexity. The same complex-dynamical process accounts for the universal gravitation and general relativity. The electromagnetic, weak, and strong types of interaction between particles also constitute integral, dynamically unified parts of quantum beat processes inside elementary particles. The classical, dynamically localised behaviour emerges in a closed system as a higher complexity level corresponding to formation of elementary bound systems (like atoms).
Two major deviations from causality in the existing formulations of quantum mechanics, related respectively to quantum chaos and indeterminate wave reduction, are eliminated within the new, universal concept of dynamic complexity. The analysis involves a new paradigm for description of a system with interaction, the principle of dynamic multivaluedness (redundance), and the ensuing concept of the fundamental dynamic uncertainty. It is shown that both the wave reduction and truly unpredictable (chaotic) behaviour in quantum systems can be completely and causally understood as a higher sublevel of the same dynamic complexity that provides the causally complete picture of the unified wave-particle duality and relativity at its lowest level (quant-ph/9902015,16). The presentation is divided into five parts. The first three parts deal with intrinsic randomness in Hamiltonian (isolated) quantum systems as the basic case of dynamical chaos. In the last two parts a causal solution to the problem of quantum indeterminacy and wave reduction is proposed. Part I introduces the method of effective dynamical functions as a generalisation of the optical potential formalism. The method provides a legal transformation of the Schroedinger equation revealing the hidden multivaluedness of interaction process, i. e. its self-consistent, dynamical splitting into many equally real, but mutually incompatible branches, called 'realisations'. Each realisation incorporates the usual "complete" set of eigenfunctions and eigenvalues for the entire problem. The method is presented in detail for the Hamiltonian system with periodic (not small) perturbation, both in its time-independent and time-dependent versions.
Any real interaction process produces many incompatible system versions, or realisations, giving rise to the omnipresent dynamic randomness and universally defined complexity (physics/9806002). Since quantum behaviour dynamically emerges as the lowest complexity level (quant-ph/9902016), quantum interaction randomness can only be relatively strong, which reveals the causal origin of quantum indeterminacy (quant-ph/9511037) and true quantum chaos (quant-ph/9511035), but rigorously excludes a possibility of unitary quantum computation, even in the 'ideal', noiseless system. Any real computation is an internally chaotic (multivalued) process of system complexity development realised in different regimes. The unitary quantum machines, including their postulated 'magic', cannot be realised as such because their dynamically single-valued scheme is incompatible with the irreducibly high dynamic randomness at quantum complexity levels and should be replaced by the explicitly chaotic, intrinsically creative machines already realised in living organisms and providing their quite different, realistic kind of magic. The related concepts of reality-based, complex-dynamical nanotechnology, biotechnology, and intelligence are outlined, together with the ensuing change in research strategy. The unreduced solution of the many-body problem reveals the true, complex-dynamical basis of solid-state dynamics, including the origin and internal dynamics of macroscopic quantum states. The critical, 'end-of-science' state of the unitary knowledge and the way to positive change are causally specified within the same, universal concept of complexity.