A system of two interacting protofields with generic parameters is unstable with respect to unceasing cycles of nonlinear squeeze (reduction) to randomly chosen centres and reverse extension which form the causally probabilistic process of quantum beat observed as elementary particle (quant-ph/9902015). Here we show that the emerging wave-particle duality, space, and time lead to the equations of special relativity and quantum mechanics thus providing their causal extension and unification. Relativistic inertial mass (energy) is universally defined as the temporal rate (frequency) of the chaotic quantum beat process(es). The same complex dynamical processes and mass account for universal gravitation, since any reduction event in the electromagnetic protofield involves also the (directly unobservable) gravitational protofield thus increasing its tension and influencing quantum beat frequencies of other particles. This complex dynamical mechanism of universal gravitation provides causal extension of general relativity intrinsically unified with causal quantum mechanics and special relativity, as well as physical origin and unification of all the four 'fundamental forces' (also gr-qc/9906077). The dynamic origin of the Dirac quantization rules is also revealed and used for the first-principles derivation of the Dirac and Schroedinger equations describing the same irreducibly complex, internally nonlinear interaction processes within field-particles and their simplest systems (quant-ph/9511034 - quant-ph/9511038). The classical, dynamically localised behaviour naturally emerges as a higher level of complexity appearing as formation of elementary bound systems (like atoms).
A system of two interacting protofields with generic parameters is unstable with respect to unceasing cycles of nonlinear squeeze (reduction) to randomly chosen centres and reverse extension which form the causally probabilistic process of quantum beat observed as elementary particle (quant-ph/9902015). Here we show that the emerging wave-particle duality, space, and time lead to the equations of special relativity and quantum mechanics thus providing their causal extension and unification. Relativistic inertial mass (energy) is universally defined as the temporal rate (frequency) of the chaotic quantum beat process(es). The same complex dynamical processes and mass account for universal gravitation, since any reduction event in the electromagnetic protofield involves also the (directly unobservable) gravitational protofield thus increasing its tension and influencing quantum beat frequencies of other particles. This complex dynamical mechanism of universal gravitation provides causal extension of general relativity intrinsically unified with causal quantum mechanics and special relativity, as well as physical origin and unification of all the four 'fundamental forces' (also gr-qc/9906077). The dynamic origin of the Dirac quantization rules is also revealed and used for the first-principles derivation of the Dirac and Schroedinger equations describing the same irreducibly complex, internally nonlinear interaction processes within field-particles and their simplest systems (quant-ph/9511034 - quant-ph/9511038). The classical, dynamically localised behaviour naturally emerges as a higher level of complexity appearing as formation of elementary bound systems (like atoms).
A system of two interacting, physically real, initially homogeneous fields is considered as the simplest basis for the world construction in which one of them, a 'protofield' of electromagnetic nature, is attracted to another protofield, or medium, responsible for the eventually emerging gravitational effects. The interaction process is analysed within the generalised 'effective (optical) potential method' in which we avoid any usual perturbative reduction. It then appears that for generic system parameters the protofields, instead of simply 'falling' one onto another and forming a fixed 'bound state', are engaged in a self-sustained process of nonlinear pulsation, or 'quantum beat', consisting in unceasing cycles of self-amplified auto-squeeze, or 'collapse' ('reduction'), of a portion of the extended protofields to a small volume followed by the inverse phase of extension. Centres of consecutive reductions form the physical 'points' of thus emerging, intrinsically discrete space, and each of them is 'selected' by the system in a causally random fashion among many equally possible versions (or 'realisations'). This is a manifestation of the dynamic redundance forming the unified basis of dynamically complex (chaotic) behaviour of any real system with interaction (physics/9806002). The sequence of reduction events constitutes the elementary physical 'clock' of the world providing it with the unceasing, intrinsically irreversible time flow. The complex-dynamical quantum beat process in the system of two interacting protofields is observed as the massive elementary particle (like the electron) which naturally possesses the property of physically real wave-particle duality completing the double solution concept of Louis de Broglie (see also quant-ph/9902016, gr-qc/9906077).
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).
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.
On 14 December 1900 Max Planck first formulated the idea of energy quanta related to a new universal constant now known as Planck's constant. Despite the following progress of thus initiated "quantum mechanics", the physical origin of both quantization and universality of Planck's constant remains mysterious, as well as other "peculiar" properties of quantum dynamics. In this paper we review a recent causal extension of quantum mechanics consistently explaining all its "mysteries" by irreducibly complex, "dynamically multivalued" behaviour of the underlying system of two interacting protofields (quant-ph/9902015, quant-ph/9902016). The theory contains no imposed postulates or entities except one, unavoidable assumption about the physical nature of the protofields. All the observed entities and their properties, starting from physically real space, time, and elementary particle structure, are consistently derived, in exact correspondence with their emergence in real, irreducibly complex system dynamics. The latter provides also natural (dynamic) unification of the causally extended versions of quantum mechanics, relativity, and field theory, including unification and causal understanding of particle interaction forces. Realism and wholeness of the obtained world picture are in agreement with the "absolute reality" quest of Max Planck and confirm his famous doubts about the conventional scheme of quantum mechanics (cf. quant-ph/9911107, quant-ph/0101129). We describe various applications of the obtained results providing successful solution to many fundamental and practical problems dangerously stagnating within conventional approaches.
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.
This report provides a brief review of recently developed extended framework for fundamental physics, designated as Quantum Field Mechanics and including causally complete and intrinsically unified theory of explicitly emerging elementary particles, their inherent properties, quantum and relativistic behaviour, interactions and their results. Essential progress with respect to usual theory is attained due to the unreduced, nonperturbative analysis of arbitrary interaction process revealing a qualitatively new phenomenon of dynamic multivaluedness of interaction results and their dynamically entangled structure giving rise to universally defined dynamic complexity (physics/9806002) and absent in usual, always perturbative and dynamically single-valued models with the zero value of unreduced complexity (including substitutes used for "complexity", "chaoticity", "self-organisation", etc.). It is shown how the observed world structure, starting from elementary particles and their interactions, dynamically emerges from the unreduced interaction between two initially homogeneous, physically real protofields (quant-ph/9902015, quant-ph/9902016). In that way one avoids arbitrary imposition of abstract entities and unprovable postulates or "principles", let alone "mysteries", of conventional theory, which now obtain unified, consistent and realistic explanation in terms of unreduced dynamic complexity. We complete the description of fundamental world structure emergence and properties by an outline of experimental implications and resulting causally substantiated change of research strategy.