Considering the highly complex structure of quantum chaos and the nonstationary characteristics of speech signals, this paper proposes a quantum chaotic encryption and quantum particle swarm extraction method based on an underdetermined model. The proposed method first uses quantum chaos to encrypt the speech signal and then uses the local mean decomposition method to construct a virtual receiving array and convert the underdetermined model to a positive definite model. Finally, the signal is extracted using (...) the Levi flight strategy based on kurtosis and the quantum particle swarm optimization optimized by the greedy algorithm. The bit error rate and similarity coefficient of the voice signal are extracted by testing the source voice signal SA1, SA2, and SI943 under different SNR, and the similarity coefficient, uncertainty, and disorder of the observed signal and the source voice signal SA1, SA2, and SI943 verify the effectiveness of the proposed speech signal extraction method and the security of quantum chaos used in speech signal encryption. (shrink)

This paper discusses the problem of finding and defining chaos in quantum mechanics. While chaotic time evolution appears to be ubiquitous in classical mechanics, it is apparently absent in quantum mechanics in part because for a bound, isolated quantum system, the evolution of its state is multiply periodic. This has led a number of investigators to search for semiclassical signatures of chaos. Here I am concerned with the status of semiclassical mechanics as a distinct third (...) theory of the asymptotic domain between classical and quantum mechanics. I discuss in some detail the meaning of such crucial locutions as the " classical counterpart to a quantum system " and a quantum system ' s " underlying classical motion ". A proper elucidation of these concepts requires a semiclassical association between phase space surfaces and wave - functions. This significance of this association is discussed in some detail. (shrink)

A simple model of an exciton-phonon system is studied in connection with quantum chaos.

In this paper, we report on some machine experiments which suggest that waveforms of CM-type are asymptotically Gaussian-distributed.

We report here on an ongoing study of a self-defining community of physicists whose work spans an interestingly diverse set of subjects, typically in the borderland between macroscopic and microscopic description and between quantum and classical domains. Its methods are typically semi-classical. It is this borderland—of people, subject, and methods—in which we are primarily interested and which we will attempt to characterise. For concreteness, we will focus on the subset of ‘quantum chaos’ and more particularly on the (...) work that the physicists Eric Heller and Steven Tomsovic have called ‘postmodern quantum mechanics’, using their characterisation to ground a somewhat more expansive interpretation. (shrink)

Conventional wisdom has it that chaotic behavior is either strongly suppressed or absent in quantum models. Indeed, some researchers have concluded that these considerations serve to undermine the correspondence principle, thereby raising serious doubts about the adequacy of quantum mechanics. Thus, the quantum chaos question is a prime subject for philosophical analysis. The most significant reasons given for the absence or suppression of chaotic behavior in quantum models are the linearity of Schrödinger’s equation and the (...) unitarity of the time-evolution described by that equation. Both are shown in this essay to be irrelevant by demonstrating that the crucial feature for chaos is the nonseparability of the Hamiltonian. That demonstration indicates that quantum chaos is likely to be exhibited in models of open quantum systems. A measure for probing such models for chaotic behavior is developed, and then used to show that quantum mechanics has chaotic models for systems having a continuous energy spectrum. The prospects of this result for vindicating the correspondence principle (or the motivation behind it, at least) are then briefly examined. (shrink)

The ubiquity of chaos in classical mechanics (CM), as opposed to the situation in standard quantum mechanics (QM), might be taken as speaking against QM being the fundamental theory of physical phenomena. Bohmian mechanics (BM), as a formulation of quantum theory, may clarify both the existence of chaos in the quantum domain and the nature of the classical limit. Two interesting possibilities are (i) that CM and classical chaos are included in and underwritten by (...) quantum mechanics (BM) or (ii) that BM and CM simply possess a common region of (noninclusive) overlap. In the latter case, neither CM nor QM alone would be sufficient, even in principle, to account for all of the physical phenomena we encounter. In this talk I shall summarize and discuss the implications of some recent work on chaos and on the classical limit within the framework of BM. (shrink)

A vast amount of ink has been spilled in both the physics and the philosophy literature on the measurement problem in quantum mechanics. Important as it is, this problem is but one aspect of the more general issue of how, if at all, classical properties can emerge from the quantum descriptions of physical systems. In this paper we will study another aspect of the more general issue-the emergence of classical chaos-which has been receiving increasing attention from physicists (...) but which has largely been neglected by philosophers of science. (shrink)

A recent noninterventionist account of divine agency has been proposed that marries the probabilistic nature of quantum mechanics to the instability of chaos theory. On this account, God is able to bring about observable effects in the macroscopic world by determining the outcome quantum events. When this determination occurs in the presence of chaos, the ability to influence large systems is multiplied. This paper argues that although the proposal is highly intuitive, current research in dynamics shows (...) that it is far less plausible than previously thought. Chaos coupled to quantum mechanics proves to be a shaky foundation for models of divine agency. (shrink)

This article explores the relationships between the philosophical foundations of quantum field theory, the currently dominant form of quantum physics, and Deleuze's concept of the virtual, most especially in relation to the idea of chaos found in Deleuze and Guattari's What is Philosophy?. Deleuze and Guattari appear to derive this idea partly from the philosophical conceptuality of quantum field theory, in particular the concept of virtual particle formation. The article then goes on to discuss, from this (...) perspective, the relationships between philosophy and science, and between their respective ways of confronting chaos, a great enemy but also a great friend of thought, and its greatest ally in its struggle against opinion. (shrink)

We review the dissipative quantum model of the brain and present recent developments related to the role of entanglement, quantum noise and chaos in the model.

In a previous essay I argued that quantum chaos cannot be exhibited in models of quantum systems within von Neumann's mathematical framework for quantum mechanics, and that it can be exhibited in models within Dirac's formal framework. In this essay, the negative thesis concerning von Neumann's framework is elaborated further by extending it to the case of Hamiltonian operators having a continuous spectrum. The positive thesis concerning Dirac's formal framework is also elaborated further by constructing a (...) chaotic model of an open quantum system in which an entropy measure is shown to approach its maximum value as time goes to infinity. Having such an entropy measure is a characteristic that is closely connected to chaotic behavior in phase space models of classical systems. (shrink)

A model is described in which subjective consciousness is generated through an unusual property of quantum non-locality. Chaos and bifurcation serve to link quantum transactions to global brain dynamics through the fractal architecture and dynamics of the central nervous system. The resulting process operates at the boundary between quantum computation and wave-particle reduction, thus combining optimality and free-choice. It is concluded that subjective consciousness has an evolutionary role as a non-computational predictive faculty, first emerging from chaotic (...) excitations in single-celled organisms; and that conscious anticipation, rather than computation, has been the principal factor promoting selective advantage in the development of the brain. (shrink)

Level statistics and nodal point distribution in a rectangular semiconductor quantum dot are studied for different degrees of spin-orbit coupling. The chaotic features occurring from the spin-orbit coupling have no classical counterpart. Using experimental values for GaSb/InAs/GaSb semiconductor quantum wells we find that level repulsion can lead to the semi-Poisson distribution for nearest level separations. Nodal lines and nodal points are also investigated. Comparison is made with nodal point distributions for fully chaotic states.

Bogolubov's classical example of statistical relaxation in a many-dimensional linear oscillator is discussed. The relation of the discovered relaxation mechanism to quantum dynamics as well as to some new problems in classical mechanics is considered.

Explores the confusion among physicists at the beginning of the 20th century when experimental findings kept not fitting into their mechanical view of the universe, the theoretical speculations and experimental innovations they responded with, and the new science that emerged. The mathematical details are set apart in boxes to allow nontechnical readers to engage the flow of the narrative uninterrupted. Paper edition (unseen), $29.95. Annotation copyright by Book News, Inc., Portland, OR.

We discuss the intimate connection between the chaotic dynamics of a classical field theory and the instability of the one-loop effective action of the associated quantum field theory. Using the example of massless scalar electrodynamics, we show how the radiatively induced spontaneous symmetry breaking stabilizes the vacuum state against chaos, and we speculate that monopole condensation can have the same effect in non-Abelian gauge theories.

The presented study introduces a new theoretical model of collapse for social, cultural, or political systems. Based on the current form of quantum anthropology conceptualized by Heidi Ann Russell, further development of this field is provided. The new theoretical model is called the spiral model of collapses, and is suggested to provide an analytical framework for collapses in social, cultural, and political systems. The main conclusions of this study are: 1) The individual crises in the period before a collapse (...) of social, cultural, and political systems form the trajectory of a conical helix similar to a vortex. 2) The occurrences of crises in the period before a collapse have the shape of the trajectory on the surface of the circular cone with a convex wall narrowing up to its peak. The shape of this cone is based on the Fibonacci sequence coiled into the three-dimensional space. 3) The constant circular movement along the trajectory of crises can occur in exceptional situations in the development of social, cultural, and political systems; however, such a state is always temporary. In such cases, the trajectory of the crisis does not follow the Fibonacci sequence, but the shape of a regular helix. Remaining on the trajectory of a regular helix in the long-term is highly improbable for social, cultural, and political systems. 4) The creation of new potentialities after the final collapse of a system is explained by the conception of topological inversion, when the heretofore embodied part of the energy-information field returns to the global, wave-particle energy-information potential. 5) The global, wave-particle energy-information potential is a source of energy-information for future embodiments in the sense of the future collapses of wave functions. (shrink)

With the increasing volume of data transmission through insecure communication channels, big data security has become one of the important concerns in the cybersecurity domain. To address these concerns and keep data safe, a robust privacy-preserving cryptosystem is necessary. Such a solution relies on chaos encryption algorithms over standard cryptographic methods that possess multistage encryption levels, including high speed, high security, low compute overheads, and procedural power, among other characteristics. In this work, a secure image encryption scheme is proposed (...) using linear feedback shift register and chaos-based quantum chaotic map. The focus of the scheme is mainly dependent on the secret keys from the input of the algorithm. The threat landscape, the statistical test analysis, along critical comparisons with other schemes indicate that the presented algorithm is significantly secure and is resistant to a wide range of different attacks such as differential and statistical attacks. The proposed method has sufficiently higher sensitivity and security when compared to existing encryption algorithms. Several security parameters validated the security of proposed work such as correlation coefficient analyses among the neighboring pixels, entropy, the number of pixels change rate, unified average change intensity, mean square error, brute force, key sensitivity, and peak signal to noise ratio analyses. The randomness of the ciphers produced by the proposed technique is also passed through NIST-800-22. The results of NIST indicate that the ciphers are highly random and do not produce any type of periodicity or pattern. (shrink)

This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link (...) these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws. (shrink)

Being based on the observation that a conjugate pair of representations, or dual logic, is a necessity under the presence of chaos, a new interpretation of quantum theory is proposed as describingproto-chaos. This chaos has to be a result of basic nonlinearity in the dynamic structure, of which, however, the nonchaotic phase seems to lie ourside the reach of experimental technique, thus the term proto-chaos. Nevertheless, assuming no extra degrees of freedom, the interpretation clarifies a (...) number of riddles posed hitherto and throws some light on the overall hierarchical structure of our understanding and description of nature. (shrink)

Chaotic dynamics has been hailed as the third great scientific revolution in physics this century, comparable to relativity and quantum mechanics. In this book, Peter Smith takes a cool, critical look at such claims. He cuts through the hype and rhetoric by explaining some of the basic mathematical ideas in a clear and accessible way, and by carefully discussing the methodological issues which arise. In particular, he explores the new kinds of explanation of empirical phenomena which modern dynamics can (...) deliver. Explaining Chaos will be compulsory reading for philosophers of science and for anyone who has wondered about the conceptual foundations of chaos theory. (shrink)

Nonclarity around the understandingof the concept of chaos has caused someconfusion in the contemporary natural science.For instance, not making a clear distinctionbetween the deterministic and quantum chaos hasmade it impossible to evaluate the approach ofIlya Prigogine in an appropriate way. It isshown that Jean Bricmont has missed the targetin his critique of I. Prigogine's ideas, as thelatter has concentrated his interest on systemsconsisting of infinite (arbitrarily large)number of particles in incessant mutualimpact, the former on systems that have (...) afinite (not necessarily large, althoughsometimes very large) number of particles,which move freely of any mutual impact orparticipate only in transient interaction. Thedifference may sometimes be quite crucial. Itis also suggested that if we consider theirreversibility as the basic element ofdescription of physical world, the world oftrajectories and wave functions cannot beresearched apart from this real irreversibility. (shrink)

Classical mechanics and quantum mechanics are two of the most successful scientific theories ever discovered, and yet how they can describe the same world is far from clear: one theory is deterministic, the other indeterministic; one theory describes a world in which chaos is pervasive, the other a world in which chaos is absent. Focusing on the exciting field of 'quantum chaos', this book reveals that there is a subtle and complex relation between classical and (...) quantum mechanics. It challenges the received view that classical and quantum mechanics are incommensurable, and revives another, largely forgotten tradition due to Niels Bohr and Paul Dirac. By artfully weaving together considerations from the history of science, philosophy of science, and contemporary physics, this book offers a new way of thinking about intertheory relations and scientific explanation. It will be of particular interest to historians and philosophers of science, philosophically-inclined physicists, and interested non-specialists. (shrink)

Laplacean determinism remains a popular theory among philosophers and scientists alike, in spite of the fact that the Copenhagen Interpretation of quantum mechanics, with which it is inconsistent, has been around for more than fifty years. There are a number of reasons for its continuing popularity. One, recently articulated by Honderich, is that there are too many possible interpretations of quantum mechanics, and the subject is too controversial even among physicists to be an adequate basis for overturning determinism. (...) Nevertheless, quantum mechanics is an enormously successful theory, considering the quantity and variety of its predictions which have been verified under conditions never dreamt of by its originators; and the Copenhagen Interpretation is the only widely accepted interpretation of it. Although a hidden variable theory consistent with the results of quantum mechanics is not impossible, one of its major advocates admits that it is highly speculative, and far from adequately developed. Yet such a theory would be needed to reconcile Laplacean determinism with quantum mechanics; most of the controversies alluded to by Honderich are irrelevant. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Chaos and Clinical TheoryDouglas W. Heinrichs (bio)In considering the specific issues raised by these three very thoughtful commentaries, it is helpful to reflect on the status of a theory or model for a specifically clinical discipline—what is it trying to accomplish and how might it proceed to do so? Kellert (2005) sees my proposal in terms of "borrowed knowledge"—the metaphorical application of a theory established in one field (...) of inquiry to another field—and views my application of chaos theory as a "nonliteral use of knowledge from the natural sciences" (p. 239). He likens it to attempts to explore consequences of relativity theory or quantum mechanics for areas other than those for which they were developed. He notes the rhetorical functions—including appeal to the disciplinary prestige of natural science—of such metaphorical borrowings.Although clearly there are significant metaphorical aspects at work here, there are at least two factors that distinguish this model from, say, the metaphorical application of quantum mechanics to a field other than subatomic physics. First, quantum mechanics purports to say something specific about the behavior of the subatomic world. Its development is wed to that specific content area. On the other hand, nonlinear dynamics, including chaos theory, is a formal mathematical model intending to characterize the behavior of any system of elements that possess certain formal relational properties. It does not start out as field or discipline specific. In fact it is not uniquely tied to the natural sciences at all, beyond the fact that it may be easier to obtain the sort of detailed repeated measures needed to demonstrate chaotic behavior in physical systems. So it is not just a question of whether chaos theory is a useful intuitive device for thinking freshly about clinical psychiatry. Rather, it is the quite literal and nonmetaphorical question as to whether some of the observable aspects of persons that are relevant to their psychiatric care behave chaotically, and if so what are the implications.Now it is quite true that direct, mathematically rigorous demonstrations of chaos in clinically relevant data sets is currently limited. In fact, one hoped for consequence of presenting this model is to encourage just such studies, and I suggest several promising directions for doing so. However, there are good reasons for thinking the presence of such chaotic behavior to be likely, and this relates to the notion of a clinical theory.One of the consequences of what Globus (2005) calls "triumphalist biological psychiatry" (p. 229) is the frequent assumption that the model or paradigm of psychiatry—an applied clinical practice, a techne—is synonymous with the paradigm of neuroscience—a basic science or episteme. This is clearly not so for many reasons, including the fact that the former has to incorporate the comprehensive treatment of discrete individuals in a way that the latter does not. Yet the respective theories are related more than metaphorically. [End Page 243] The paradigms of neuroscience and those of other relevant basic sciences, such as psychology, substantially inform the clinical paradigm and the clinical model must be at least compatible with those of the relevant basic sciences. Thus, it is reasonable to assume that if chaotic processes are demonstrable in the nervous system, for which significant evidence already exists, there is good reason to expect them to be reflected in clinically relevant domains. The clinical paradigm should make room for it and its consequences, rather than thinking within an outmoded neuroscience model that makes no room for the implications of nonlinear dynamics. And when this generates a picture more compatible than the old model with our usual sense of what it is to be human, the odds that we are on to something is further enhanced. Of course until such time that enough clinical research based on this model is completed, considerable speculation—indeed aided by metaphorical devices—is involved in generating a concrete sense of how the model would be applied to specific clinical problems, such as the treatment of depressed persons.One clear task of the clinical paradigm is the methodologic integration of interventions growing out of different informing basic sciences. Because chaotic modeling can be applied across various content domains and... (shrink)

An examination of determinism in the context of chaotic dynamics.

When the fuzzy indeterminacy of quantum mechanics overthrew the orderly world of Isaac Newton, Albert Einstein and Erwin Schrödinger were at the forefront of the revolution. Neither man was ever satisfied with the standard interpretation of quantum mechanics, however, and both rebelled against what they considered the most preposterous aspect of quantum mechanics: its randomness. Einstein famously quipped that God does not play dice with the universe, and Schrödinger constructed his famous fable of a cat that was (...) neither alive nor dead not to explain quantum mechanics but to highlight the apparent absurdity of a theory gone wrong. But these two giants did more than just criticize: they fought back, seeking a Theory of Everything that would make the universe seem sensible again. In Einstein’s Dice and Schrödinger’s Cat, physicist Paul Halpern tells the little-known story of how Einstein and Schrödinger searched, first as collaborators and then as competitors, for a theory that transcended quantum weirdness. This story of their quest—which ultimately failed—provides readers with new insights into the history of physics and the lives and work of two scientists whose obsessions drove its progress. Today, much of modern physics remains focused on the search for a Theory of Everything. As Halpern explains, the recent discovery of the Higgs Boson makes the Standard Model—the closest thing we have to a unified theory— nearly complete. And while Einstein and Schrödinger failed in their attempt to explain everything in the cosmos through pure geometry, the development of string theory has, in its own quantum way, brought this idea back into vogue. As in so many things, even when they were wrong, Einstein and Schrödinger couldn’t help but get a great deal right. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Chaos and LiteratureCarl Matheson and Evan KirchhoffIChaos theory was the intellectual darling of pop-science writers of the late 1980s. 1 In their eyes, it would provide a new paradigm by which to describe the world, one that liberated scientists from clockwork determinism—or, alternatively, from incomprehensible randomness. In an introductory textbook of the period, Robert Devaney called chaos theory “the third great scientific revolution of the 20th century, (...) along with relativity and quantum mechanics.” Similar attitudes propagated into philosophy; for example, Stephen Kellert argued that an acceptance of chaos theory would involve a reconfiguration of scientific methodology. 2It was in the domain of literary theory, however, that chaos found its most enthusiastic reception in the humanities, and the enthusiasm lives on. Many literary theorists display no hesitation in touting the supposedly revolutionary implications of chaos science. Katherine Hayles, the chief among them, argues that because the concept of order has undergone a “radical reevaluation” in recent decades, “textuality is conceived in new ways within critical theory and literature, and new kinds of phenomena are coming to the fore within an emerging field known as the science of chaos” (CO, p. 1). She infers that the new “paradigm of orderly disorder” (CB, p. xiii) represented by chaos theory signifies a conceptual revolution in modern culture as a whole. 3 She attempts to establish a parallel between chaos theory and various poststructuralist philosophical positions, including those of Derrida and Foucault, claiming that this new paradigm “may well prove to be as important to the second half of the century as the field concept was to [End Page 28] the first half” (CB, p. xiii), and that chaos may soon be “on a par with evolution, relativity, and quantum mechanics in its impact on the culture” (CO, p. 4). Other theorists make claims for the interpretive power of chaos; according to William Demastes, “chaos theory can help in comprehending several paths that the theatre has followed since the inception of postmodernism” (p. 242). 4 By a conservative estimate, over fifty papers have been published which link chaos theory to literature or literary theory. Clearly, the idea that chaos theory has application outside of science is not restricted to one or two over-eager humanists.In this essay, we wish to address some of the claims which concern the relationship between chaos science and the study of literature. Three such claims are:a. There are significant similarities between the science of chaos, contemporary literary theory, and/or philosophy.b. We can trace a common etiology for chaos theory and poststructuralist criticism. The two are so intimately related that they are really different formulations of a common claim, as filtered through two different fields.c. The science of chaos can help us interpret and understand specific literary works, and perhaps contemporary literature in general.However, before assessing the relationship between chaos and literature, we will briefly introduce chaos theory itself and demonstrate that even a minimal understanding is sufficient to undercut the supposed revolutionary significance of chaos theory. 5IIChaotic systems are deterministic: an exact description of a system at any given time, together with the laws of nature that apply to it, will entail the entire future behavior of the system. In this sense, chaotic systems form a subclass of classical systems (and are to be distinguished from quantum systems, which are indeterministic). However, chaotic systems differ from the systems studied throughout most of the history of science in two major ways. First, the differential equations used to model them are nonlinear, while the history of mathematical physics is largely devoted to a treatment of linear differential equations. Technical issues aside, the ramifications of nonlinearity are: (i) equations which are impossible to solve using the general strategies designed for [End Page 29] linear equations; and consequently (ii) the need for solutions by methods of numerical approximation, generally performed on a computer. Second, chaotic systems exhibit a feature known as “sensitive dependence”—or, more colorfully, as “the butterfly effect,” a figure of speech intended to evoke the worry that our long-term forecasts of the weather can be hopelessly disrupted by the atmospheric fluctuations due to a single butterfly... (shrink)

We consider the Bohmian trajectories in a 2-d quantum harmonic oscillator with non commensurable frequencies whose wavefunction is of the form Ψ=aΨm1,n1+bΨm2,n2+cΨm3,n3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Psi =a\Psi _{m_1,n_1}+b\Psi _{m_2,n_2}+c\Psi _{m_3,n_3}$$\end{document}. We first find the trajectories of the nodal points for different combinations of the quantum numbers m, n. Then we study, in detail, a case with relatively large quantum numbers and two equal m′s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m's$$\end{document}. (...) We find fixed nodes independent of time and moving nodes which from time to time collide with the fixed nodes and at particular times they go to infinity. Finally, we study the trajectories of quantum particles close to the nodal points and observe, for the first time, how chaos is generated in a complex system with multiple nodes scattered on the configuration space. (shrink)

An investigation is made into how the foundations of statistical mechanics are affected once we treat classical mechanics as an approximation to quantum mechanics in certain domains rather than as a theory in its own right; this is necessary if we are to understand statistical-mechanical systems in our own world. Relevant structural and dynamical differences are identified between classical and quantum mechanics (partly through analysis of technical work on quantum chaos by other authors). These imply that (...) quantum mechanics significantly affects a number of foundational questions, including the nature of statistical probability and the direction of time. (shrink)

It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can’t contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is “random numbers”, as their series of bits are truly random. I propose an alternative classical mechanics, which is (...) empirically equivalent to classical mechanics, but uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic. Most physicists straightforwardly supplement classical theory with real numbers to which they attribute physical existence, while most physicists reject Bohmian mechanics as supplemented quantum theory, arguing that Bohmian positions have no physical reality. (shrink)

Topic of quantum chaos has begun to draw increasing attention in recent years. So, to ensure the security of digital image, an image encryption algorithm based on combining a hyperchaotic system and quantum 3D logistic map is proposed. This algorithm is applied in four stages. Initially, the key generator builds upon the foundation of mean for any row or column of the edges of the plain image. Its output value is used to yield initial conditions and parameters (...) of the proposed image encryption scheme. Next, it diffuses the plain image by the random sequences generated by 3D hyperchaotic system, and the diffusion process is realized by implementing XOR operation. Then, the diffused image and chaotic sequences are produced by the 3D quantum chaotic logistic map, expressed as a quantum superposition state using density matrix which is a representation of the state of a quantum system, and finally the resulting quantum image is then confused and diffused simultaneously by a unitary matrix generated by logistic chaos using XNOR operation to obtain the final cipher image. Because of the dependence on the plain image, the algorithm can frustrate the chosen-plaintext and known-plaintext attacks. Simulation results and theoretical analysis verify that the presented scheme has high safety performance, a good encryption effect, and a large key space. The method can effectively resist exhaustive, statistical, and differential attacks. Moreover, the encryption time of the proposed method is satisfactory, and the method can be efficiently used in practice for the secure transmission of image information. (shrink)

It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can’t contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is “random numbers”, as their series of bits are truly random. I propose an alternative classical mechanics, which is (...) empirically equivalent to classical mechanics, but uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic. Most physicists straightforwardly supplement classical theory with real numbers to which they attribute physical existence, while most physicists reject Bohmian mechanics as supplemented quantum theory, arguing that Bohmian positions have no physical reality. (shrink)

This paper aims at a logico-mathematical analysis of the concept of chaos from the point of view of a constructivist philosophy of physics. The idea of an internal logic of chaos theory is meant as an alternative to a realist conception of chaos. A brief historical overview of the theory of dynamical systems is provided in order to situate the philosophical problem in the context of probability theory. A finitary probabilistic account of chaos amounts to the (...) theory of measurement in the line of a quantum-theoretical foundational perspective and the paper concludes on the non-classical internal logic of chaos theory. Finally, deterministic chaos points to a philosophy which asserts that chaotic systems are no less measurable than other physical systems where predictable and non–predictable phenomena intermingle in a constructive theory of measurement. (shrink)

I now understand why the invitation to contribute an article on “chaos theory” invoked both my excitement and reticience. Let me first explain my excitement in terms of intriguing developments generated by the Cosmic Background Explorer satellite. Since COBE strengthened an “inflationary” Big Bang Theory wherein the structure of the universe was induced by random statistical fluctuations, there are implications inter alia of thermodynamics for chaotic fluctuations in both the structure and biological systems formed from it. I shall then (...) explain my reticence concerning a chaosladen cosmology. Though it seems to call for an epistemological revision of deterministic scientific truth, the cosmology is as likely as one influenced by quantum mechanics to lead to either a pseudo-scientific connection of indeterminism to freedom and purpose or their dogmatic exclusion as possible “realities” by the natural and social sciences. What I will be concerned about are the conflation of physics with metaphysics and the need to metaphysically articulate the continuity between a primordial quantum fluctuation, biological “possibilities,” and human freedom. (shrink)

Later works of C.G. Jung contain comprehensive descriptions of the relationship between psychological and physical research. These considerations described in Jung’s works and in his correspondence with Wolfgang Pauli represent interesting philosophical ideas that are related to interpretation of psychological data. The so-called “collective unconscious” studied by Jung in analysis of dream material, mythology, psychopathological symptoms, and several cultural manifestations led him to postulate complementarity and unity of scientific principles, and to define the psyche as complementary to physical reality. Likewise (...) recent neuroscientific studies and physical analyses on the role of the observer in physical reality led to the study of “quantum consciousness.” This review compares the philosophical postulates by Roger Penrose with Jung’s and Pauli’s studies, and suggests novel links of these concepts to recent findings of chaos theory in the brain. (shrink)

The causal indeterminacy suggested by quantum mechanics has led to its being the centerpiece of several proposals for divine action that does not contradict natural laws. However, even if the theoretical concerns about the reality of causal indeterminacy are ignored, quantum-level divine action fails to resolve the problem of ongoing, responsive divine activity. This is because most quantum-level actions require a significant period of time in order to reach macroscopic levels whether via chaotic amplification or complete divine (...) control of quantum events. Therefore, quantum-level divine action either requires divine foreknowledge of purportedly free or random events or imposes such limitations on divine actions that they become late, potentially impotent, and confused. I argue that the theological problem of divine action remains; even at its most promising, quantum mechanics offers insufficient resolution. This failure suggests a reexamination of the assumptions that God is temporal and lacks foreknowledge of future contingencies. (shrink)