Complex Dynamics of Real Quantum, Classical and Hybrid Micro-Machines A.P. KIRILYUK* Institute of Metal Physics, Kiev, Ukraine ABSTRACT. Any real interaction process produces many equally possi- ble, but mutually incompatible system versions, or realisations, giving rise to the omnipresent, purely dynamic randomness (chaoticity) and universal- ly defined complexity (sections 3-4). Since quantum behaviour dynamical- ly emerges as the lowest level of unreduced world complexity (sections 4.6-7, 5.3), quantum interaction randomness can only be relatively strong (explicit), which reveals the causal origin of quantum indeterminacy (sec- tions 4.6.1, 5.3(A)) and true quantum chaos (sections 4.6.2, 5.2.1, 6), but rigorously excludes the possibility of unitary quantum computation, even in an ‘ideal’, noiseless system (sections 5-7). Any real computation is an in- ternally chaotic (multivalued) process of system complexity development occurring in different regimes at various complexity levels (sections 7.1-2). Unitary quantum machines, including their postulated ‘magic’, cannot be realised as such because their dynamically single-valued scheme is incom- patible with the irreducibly high dynamic randomness at quantum complex- ity levels (sections 4.5-7, 5.1, 5.2.2, 7.1-2) 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, bio- technology and intelligence are outlined, together with the ensuing change in research strategy and content (sections 7.3, 8). The unreduced, dynami- cally multivalued solution of the quantum (and classical) many-body prob- lem reveals the true, complex-dynamical basis of solid-state dynamics, in- cluding the origin and internal dynamics of macroscopic quantum states (section 5.3(C)). The critical, ‘end-of-science’ state of conventional, uni- tary knowledge and the way to positive change are causally specified with- in the same, universal concept of complexity (section 9). * Address for correspondence: Institute of Metal Physics, Solid State Theory Department, 36 Vernadsky Av., Kyiv 03142, Ukraine. E-mail address: [email protected]. 2 Complex Dynamics of Real Quantum, Classical and Hybrid Micro-Machines From Causally Complete Quantum Mechanics to the Efficient Nanotechnology and Development Concept Back-cover book description. The lasting stagnation of fundamental sci- ence becomes an increasingly urgent problem, especially by contrast to ap- parent success of its previous discoveries. In particular, the unsolved prob- lems of quantum mechanics and particle theory strangely correlate with the stable absence of key advance in quantum computation and full-scale nano- technology, despite the high promises and huge efforts applied. In this book the decisive extension of conventional science basis is introduced in the form of unreduced solution to the arbitrary interaction problem. It is shown how the qualitatively new, “dynamically multivalued” structure of the un- reduced solution and real system behaviour leads to the intrinsically uni- versal and problem-solving concept of dynamic complexity and chaos. It is applied here to problems of full-scale quantum computation and na- nomachines, where the impossibility of unitary quantum machines is demonstrated together with the high potentialities of their extended, com- plex-dynamical version, already realised in natural living systems. The book is a mixture of rigorous basis, popular explanation and new paradigm discussion oriented to a wide range of educated readers. 3 4 CONTENTS 1. Introduction . 9 2. Impossibility of unitary quantum computation: Qualitative considerations . 16 (i) Non-creative character of unitary dynamics vs real computation nature and demands . 19 (ii) Contradiction between unitary description of quantum devices and quantum postulates . 24 (iii) Contradiction between unitary computation and entropy growth law . 30 (iv) Contradiction between quantum computer coherence and its irreducible structure . 33 (v) Transition from quantum to classical computation and back . 35 3. Dynamic origin of randomness in a noiseless system . 42 3.1. Generalised many-body problem and micro-machine dynamics 42 3.2. Universally nonperturbative problem solution by the unreduced effective potential method . 51 3.3. Dynamically multivalued interaction result as the unified origin of randomness and the a priori probability values . 55 4. Universal dynamic complexity, its properties and manifestations in micro-system dynamics . 65 4.1. Universal concept of complexity and chaoticity by the dynamic redundance paradigm . 65 4.2. Dynamic entanglement, causal wavefunction and the internal structure of real interaction processes . 68 4.3. Omnipresent dynamic instability, essential nonlinearity, generalised dynamical collapse, physical space, time and quantisation . 73 4.4. Probabilistic dynamic fractality, interactive adaptability and universal complexity development . 80 5 4.5. Generic types of system behaviour as particular cases of dynamically multivalued interaction process . 86 4.5.1. Dynamically multivalued self-organisation and control of chaos . 86 4.5.2. Uniform (global) chaos, its universal criterion and physical origin . 92 4.6. Causally complete description of quantum behaviour as the lowest level of unreduced dynamic complexity . 98 4.6.1. The dynamic origin of elementary particles, their properties and wave-particle duality . 98 4.6.2. Complex-dynamical particle interaction, genuine quantum chaos and quantum measurement dynamics . 102 4.7. Interaction complexity development and dynamic origin of classical behaviour in noiseless micro-systems . 107 5. Dynamically multivalued computation by real quantum and hybrid machines . 121 5.1. The myth of unitary quantum computation: its formal origin and impossibility of realisation . 121 5.2. Dynamically chaotic (multivalued) operation of real micro-machines: general principle, universal properties and particular features . 139 5.2.1. Time-periodic perturbation of bound quantum motion: Complex dynamics of elementary interaction act . 139 5.2.2. Fundamental properties and causally derived general principle of real quantum machine operation . 151 5.3. Complex-dynamical reality behind the mystified abstractions of official unitarity . 175 (A) Quantum coherence, ‘decoherence’, randomness, chaos and density matrix . 178 (B) Quantum entanglement, nonlocality/‘correlations’, ‘teleportation’, reduction/measurement and duality/complementarity . 181 (C) Classicality, macroscopic quantum states and complex solid state dynamics . 189 6. Genuine quantum chaos and its consistent transition to the true dynamical randomness in classical mechanics . 200 6 7. Computation as a complexity development process: The physical information theory . 221 7.1. Dynamic information as a form of dynamic complexity, its unceasing transformation into dynamic entropy and the universal symmetry of complexity . 221 7.2. Computation as complexity conservation by transformation of information into entropy and its particular features at the level of micro-machine dynamics . 262 7.3. Universal direction of system evolution, causal interpretation of intelligence and transition to creative computation/production processes . 269 8. Dynamically multivalued, not unitary or stochastic, micro-machines as the real basis for the next technological revolution . 280 9. Human implications of quantum computation story: Unitary calculations and show-business kind of ‘science’ vs real problem solution within intrinsically creative knowledge . 289 References . 320 Il me paraît plus naturel et plus conforme aux idées qui ont toujours heureusement orienté la recherche scientifique de supposer que les transitions quantiques pourront un jour être interprétées, peut-être à l'aide de moyens analytiques dont nous ne disposons pas encore, comme des processus très rapides, mais en principe descriptibles en termes d'espace et de temps, analogues à ces passages brusques d'un cycle limite à un autre que l'on rencontre très fréquemment dans l'étude des phénomènes mécaniques et électromagnétiques non linéaires. Louis de Broglie, Les idées qui me guident dans mes recherches (1965) [381] 7 ABBREVIATIONS used in the text EP for Effective Potential (introduced in Section 3.2) SOC for Self-Organised Criticality (introduced in Section 4.5.1) 8 1. Introduction The end of a big enough stage of evolution of any complex system is characterised by critically sharp instabilities marking the ‘last breath’ of the disappearing regime and possible beginning of transition to a qualitatively new level of development. This universal expression of the ‘generalised phase transition’ [1] in the complex system dynamics is readily observed for the whole variety of real world phenomena, from a brightly blinking and then forever fading light source (a lamp or a star) to the modern ‘sud- den’ revival of activity in the fundamental ‘new physics’ as if repeating the excitement of its birth period a hundred years ago (see e. g. [2-4] and refer- ences therein). Concentrating especially around ‘quantum’ phenomena (though they are often arbitrary extended to any weird-looking, ‘mysteri- ous’ things and ideas), this latest ‘advance’ of ‘quantum computation’, ‘quantum teleportation’, ‘entanglement’ and other announced ‘quantum miracles’ produces much promise of ‘fantastic’, extraordinary new possi- bilities, but uses