All Entanglements of Elementary Particles are Elements of upper level above normal level. Our dynamic mathematics explains the mechanisms of Entanglement and provides new mathematical possibilities for working with it. Here are given mathematical fundamentals of interpretations theory (future science) and fundamentally new approach to elementary particles, energy conservation. Here is studying Energy-space with scalar product and norm of its elements by format-numbers. Digitization of interpretations forms allows the use of digital technologies through appropriate programming. In science, there are two approaches to studying nature beyond classical science (conditionally, the (1, 1)-interpretation): the approach through quantum mechanics (conditionally, the (1, 2)-interpretation) and dynamic mathematics (conditionally, the (2, 1)-interpretation) [1, 2]. In contrast to the probabilistic approach of quantum mechanics with dimension doubling for quantum entanglement, we propose a deterministic approach via an energy hierarchy. Both approaches have the same "root": |||, but at two opposite ends: quantum mechanics ((1, 2)-interpretation) by |||^(-1)by and dynamic mathematics (2, 1)-interpretation) by ||| and ((1, 2)-interpretation) by |||^(-1) and other interpretations with using hierarchical structures of measures, some equations [1, 2]. Therefore, the conclusions are similar, but for different objects and processes. Either we take what we need from emptiness by |||^(-1) or through substitution by |||. We also demonstrate the possibilities of not only using the effects of quantum entanglement for calculations, but also for manipulating energies, objects, their actions, and processes through the upper level. Let us call the interpretation formats by format-numbers and quantum levels of connections. Elements of format-numbers mathematics were considered partially [1, 2]. And for manipulating these numbers, the interpretation (1, 1) is already suitable, i.e., ordinary traditional science is suitable. This is a different approach to complex processes, not through probability. This article applies to physics and neural networks of the new direct-parallel and direct-accumulative types. For now, this is only an introductory article. The first task: to understand hierarchy of energies in the Universe and the principles of functioning of living energy (living organism, in particular, human, subtle energies), and then using these principles to "construct" artificial living energies (let's call them pseudo-living energies). It is possible to significantly expand the horizons of science, in particular physics, by studying the subtle energies in the Universe. For this, some aspects are proposed for consideration of Dynamic Science. self_science^(our theory) - science here acts as a space for the application of our theory in the self-format, i.e., any place of science, in particular physics, can act as a place for the "location" of the self. It contains itself (accommodates any action C) in any place of science. On the basis of mathematical uncertainties, new mathematical structures are formed, allowing us to describe processes and objects that are fundamentally not determined by conventional deterministic methods. Objective uncertainties in any case can mean manifestations of processes and objects that are fundamentally not determined by conventional deterministic methods. Since dynamic mathematics places the primary emphasis on the dynamics of energy, rather than on objectivity, the level of approach to studying processes expands. Here are the formulas of dynamic mathematics that determine the spirit of actions and objects (i.e., the energy of the upper level that generates their self-energy); that determine the double of the magician, etc. Many energies are indeterminate because they are based on uncertainties from the perspective of traditional science—large concentrations of specific energy in a chaotic state. The foundation of dynamic mathematics lies in working with uncertainties, which makes it possible to manipulate these indeterminate energies using direct-accumulative direct-parallel neural networks. Ordinary regular work with them in ordinary science is fundamentally unable to realize their capabilities. Therefore, singular science realized on a neural network - an analogue of the human CNS - will be much more natural. Unfortunately, we do not have funding to perform the necessary experiments and the practical creation of a technical model of such a neural network. There is a need to develop an instrumental mathematical base for new technologies. The task of the work is to create new approaches for this by introducing new concepts and methods. Our mathematics is unusual for a mathematician, because here the fulcrum is the action, and not the result of the action as in classical mathematics. Therefore, our mathematics is adapted not only to obtain results, but also to directly control actions, which will certainly show its benefits on a fundamentally new type of neural networks with directly parallel calculations, for which it was created. Any action has much greater potential than its result. Social justice is fundamentally impossible as long as education (training) is based on achieving results, and not on the process. It is time for physicists to begin studying not only the manifestations of living energies, but also the living energies themselves, which are by no means expressed through objectivity and ordinary energies, although they are capable of manifesting themselves through a lower level - objectivity and ordinary energies. We, as mathematicians, offer a new corresponding apparatus for understanding nature and studying living energies. Significance of the article: in a new qualitatively different approach to the study of complex processes through new mathematical, hierarchical, dynamic structures, in particular those processes that are dealt with by Synergetics. The significance of our monograph is in the formation of the presumptive mathematical structure of subtle energies, this is being done for the first time in science, and the presumptive classification of the mathematical structures of subtle energies for the first time. The experiments of the 2022 Nobel laureates Asle Ahlen, John Clauser, Anton Zeilinger and the experiments in chemistry Nazhipa Valitov eloquently demonstrate that we are right and that these studies are necessary. Be that as it may, we created classes of new mathematical structures, new mathematical singularities, i.e., made a contribution to the development of mathematics. Conventional science changes numbers. Ours changes levels by SmnSprt. Connection is fundamental to understanding our world. Everything is expressed through connections; an object (matter) is a self-connection in the form of energy closed in on itself; all forms of energy are forms of connection, information, thoughts are forms of connection, in particular, Vernadsky's noosphere is an example of this, and so on.
All Entanglements of Elementary Particles are Elements of upper level above normal level. Our dynamic mathematics explains the mechanisms of Entanglement and provides new mathematical possibilities for working with it. Here are given mathematical fundamentals of interpretations theory (future science) and fundamentally new approach to elementary particles, energy conservation. Here is studying Energy-space with scalar product and norm of its elements by format-numbers. Digitization of interpretations forms allows the use of digital technologies through appropriate programming. In science, there are two approaches to studying nature beyond classical science (conditionally, the (1, 1)-interpretation): the approach through quantum mechanics (conditionally, the (1, 2)-interpretation) and dynamic mathematics (conditionally, the (2, 1)-interpretation) [1, 2]. In contrast to the probabilistic approach of quantum mechanics with dimension doubling for quantum entanglement, we propose a deterministic approach via an energy hierarchy. Both approaches have the same "root": |||, but at two opposite ends: quantum mechanics ((1, 2)-interpretation) by |||^(-1)by and dynamic mathematics (2, 1)-interpretation) by ||| and ((1, 2)-interpretation) by |||^(-1) and other interpretations with using hierarchical structures of measures, some equations [1, 2]. Therefore, the conclusions are similar, but for different objects and processes. Either we take what we need from emptiness by |||^(-1) or through substitution by |||. We also demonstrate the possibilities of not only using the effects of quantum entanglement for calculations, but also for manipulating energies, objects, their actions, and processes through the upper level. Let us call the interpretation formats by format-numbers and quantum levels of connections. Elements of format-numbers mathematics were considered partially [1, 2]. And for manipulating these numbers, the interpretation (1, 1) is already suitable, i.e., ordinary traditional science is suitable. This is a different approach to complex processes, not through probability. This article applies to physics and neural networks of the new direct-parallel and direct-accumulative types. For now, this is only an introductory article. The first task: to understand hierarchy of energies in the Universe and the principles of functioning of living energy (living organism, in particular, human, subtle energies), and then using these principles to "construct" artificial living energies (let's call them pseudo-living energies). It is possible to significantly expand the horizons of science, in particular physics, by studying the subtle energies in the Universe. For this, some aspects are proposed for consideration of Dynamic Science. self_science^(our theory) - science here acts as a space for the application of our theory in the self-format, i.e., any place of science, in particular physics, can act as a place for the "location" of the self. It contains itself (accommodates any action C) in any place of science. On the basis of mathematical uncertainties, new mathematical structures are formed, allowing us to describe processes and objects that are fundamentally not determined by conventional deterministic methods. Objective uncertainties in any case can mean manifestations of processes and objects that are fundamentally not determined by conventional deterministic methods. Since dynamic mathematics places the primary emphasis on the dynamics of energy, rather than on objectivity, the level of approach to studying processes expands. Here are the formulas of dynamic mathematics that determine the spirit of actions and objects (i.e., the energy of the upper level that generates their self-energy); that determine the double of the magician, etc. Many energies are indeterminate because they are based on uncertainties from the perspective of traditional science—large concentrations of specific energy in a chaotic state. The foundation of dynamic mathematics lies in working with uncertainties, which makes it possible to manipulate these indeterminate energies using direct-accumulative direct-parallel neural networks. Ordinary regular work with them in ordinary science is fundamentally unable to realize their capabilities. Therefore, singular science realized on a neural network - an analogue of the human CNS - will be much more natural. Unfortunately, we do not have funding to perform the necessary experiments and the practical creation of a technical model of such a neural network. There is a need to develop an instrumental mathematical base for new technologies. The task of the work is to create new approaches for this by introducing new concepts and methods. Our mathematics is unusual for a mathematician, because here the fulcrum is the action, and not the result of the action as in classical mathematics. Therefore, our mathematics is adapted not only to obtain results, but also to directly control actions, which will certainly show its benefits on a fundamentally new type of neural networks with directly parallel calculations, for which it was created. Any action has much greater potential than its result. Social justice is fundamentally impossible as long as education (training) is based on achieving results, and not on the process. It is time for physicists to begin studying not only the manifestations of living energies, but also the living energies themselves, which are by no means expressed through objectivity and ordinary energies, although they are capable of manifesting themselves through a lower level - objectivity and ordinary energies. We, as mathematicians, offer a new corresponding apparatus for understanding nature and studying living energies. Significance of the article: in a new qualitatively different approach to the study of complex processes through new mathematical, hierarchical, dynamic structures, in particular those processes that are dealt with by Synergetics. The significance of our monograph is in the formation of the presumptive mathematical structure of subtle energies, this is being done for the first time in science, and the presumptive classification of the mathematical structures of subtle energies for the first time. The experiments of the 2022 Nobel laureates Asle Ahlen, John Clauser, Anton Zeilinger and the experiments in chemistry Nazhipa Valitov eloquently demonstrate that we are right and that these studies are necessary. Be that as it may, we created classes of new mathematical structures, new mathematical singularities, i.e., made a contribution to the development of mathematics. Conventional science changes numbers. Ours changes levels by SmnSprt. Connection is fundamental to understanding our world. Everything is expressed through connections; an object (matter) is a self-connection in the form of energy closed in on itself; all forms of energy are forms of connection, information, thoughts are forms of connection, in particular, Vernadsky's noosphere is an example of this, and so on.
Connection is fundamental to understanding our world. Everything is expressed through connections: an object (matter) may be understood as a self-connection in the form of energy closed in on itself, while energy, information, and thoughts are forms of connection. We therefore proceed from connections to connection structures. In this approach, connections are more comprehensive than energy, and energy is more comprehensive than objects. Dynamic science is thus proposed as broader than traditional science because it is based on more general foundations. A central instrument of this approach is the format-number, which defines hierarchical structures of interpretations, energies, actions, and processes. Digitization of interpretation forms by format-numbers makes their use in digital technologies possible through appropriate programming. The format-number (2(1, 2, 1), (1, 2, 1)) characterizes the transition of quantum numbers through the tensor product to entanglement. The (1, 2)- and (2, 1)-interpretations are simplified models of a more complex reality. Beyond classical science, two approaches are distinguished: quantum mechanics, conditionally associated with the (1, 2)-interpretation, and dynamic mathematics, associated with the (2, 1)-interpretation. In contrast to the probabilistic approach of quantum mechanics, dynamic mathematics proposes a deterministic approach through an energy hierarchy. These approaches have a common “root” but operate from opposite positions and may lead to similar conclusions. The proposed framework extends the use of hierarchical structures beyond calculations to the manipulation of energies, objects, actions, and processes through higher levels. Interpretation formats are represented by format-numbers and quantum levels of connections. Traditional science, corresponding to the (1, 1)-interpretation, can be used for manipulating such numbers, thereby providing a bridge between dynamic and traditional science. The first task of the framework is to understand the hierarchy of energies in the Universe and the functioning principles of living energy, including living organisms and subtle energies. On this basis, artificial “pseudo-living energies” could be constructed. Dynamic science studies Energy-space with scalar product and norms of its elements described through format-numbers. Its mathematical basis emphasizes uncertainty and the dynamics of energy rather than objectivity alone. Mathematical uncertainties are used to form new structures for describing processes and objects that cannot be determined by conventional deterministic methods. Many energies are treated as indeterminate from the perspective of traditional science because they arise from uncertainties and may represent large concentrations of specific energy in chaotic states. Dynamic mathematics is designed to work with such uncertainties and proposes their manipulation using direct-accumulative, direct-parallel neural networks. Within this concept, a singular science realized through a neural network analogous to the human central nervous system would be more natural than ordinary computational approaches. Quantum computers are considered only an initial stage. The proposed SmnSprt network is intended to use format-numbers to construct or access levels of subtle energies, including transformations or “shifts” of ordinary energy into subtle energies. The practical development of such a network requires an instrumental mathematical basis and experimental verification. The aim of the work is therefore to introduce concepts and methods for developing new technologies based on this framework. Unlike classical mathematics, which focuses primarily on results, dynamic mathematics places the action itself at the center. It is intended not only to obtain results but also to directly control actions, especially within direct-parallel neural networks. The authors argue that any action has greater potential than its result and that this process-oriented view may be useful not only in mathematics and physics but also in other complex systems. The proposed apparatus is intended for studying living and subtle energies that are not directly expressed through ordinary objectivity and conventional forms of energy, although they may manifest themselves through lower levels. The significance of the work lies in offering a qualitatively different approach to complex processes through new mathematical, hierarchical, and dynamic structures, including processes studied in synergetics. The authors propose a presumptive mathematical structure and classification of subtle energies and introduce new classes of mathematical structures and singularities. The methodological distinction between classical and dynamic mathematics also concerns their application in technical devices. Classical mathematics operates indirectly through numbers, whereas dynamic mathematics is proposed to act directly through energies, including specific energies that determine numerical values at particular moments in technical systems. The uniqueness of a given energy is treated as a key feature for constructing and manipulating subtle energies. The authors do not claim that traditional science currently recognizes dynamic mathematics, since the two approaches occupy different perceptual positions. Traditional science and dynamic science are nevertheless regarded as intersecting domains. Dynamic models identified with traditional mathematics are termed dynamic mathematics, and the corresponding broader framework is termed dynamic science. Concepts such as self, oself, pself and other singularities are presented as instruments for creating order from chaos, while intention is treated as a mechanism for switching the assemblage point to a desired position.
Connection is fundamental to understanding our world. Everything is expressed through connections; an object (matter) is a self-connection in the form of energy closed in on itself; all forms of energy are forms of connection, information, thoughts are forms of connection, in particular, Vernadsky's noosphere is an example of this, and so on. We proceed through connections, then through connection structures. Connections are energy. Connections are more comprehensive than energy, which is a special case of a connection; an object is a special case of energy. That is, dynamic science is more comprehensive than traditional science due to its more general foundations. The format-number defines the hierarchy structure of interpretations, energies, actions, process etc. Digitization of interpretations forms by format-numbers allows the use of digital technologies through appropriate programming. Format-number (2(1, 2, 1), (1, 2, 1)) characterizes the transition of quantum numbers through the tensor product to entanglement. Of course, (1, 2)-interpretation and (2, 1)-interpretation are simplifications; in reality, reality is much more complex. Quantum computers are just the beginning; our dynamic science constructs corresponding pseudo-living energies to achieve desired goals through network SmnSprt. In science, there are two approaches to studying nature beyond classical science (conditionally, the (1, 1)-interpretation): the approach through quantum mechanics (conditionally, the (1, 2)-interpretation: (1, 2) ((2, 1)) = (1, 1)) and dynamic mathematics (conditionally, the (2, 1)-interpretation) [1, 2]. In contrast to the probabilistic approach of quantum mechanics with dimension doubling for quantum entanglement, we propose a deterministic approach via an energy hierarchy. Both approaches have the same "root": |||, but at two opposite ends: quantum mechanics ((1, 2)-interpretation) by |||^{-1}by and dynamic mathematics (2, 1)-interpretation) by ||| and ((1, 2)-interpretation) by |||^{-1} and other interpretations with using hierarchical structures of measures, some equations [1, 2]. Therefore, the conclusions are similar, but for different objects and processes. Either we take what we need from emptiness by |||^{-1} or through substitution by |||. We also demonstrate the possibilities of not only using the effects of quantum entanglement for calculations, but also for manipulating energies, objects, their actions, and processes through the upper level. Let us call the interpretation formats by format-numbers and quantum levels of connections. Elements of format-numbers mathematics were considered partially [1, 2]. And for manipulating these numbers, the interpretation (1, 1) is already suitable, i.e., ordinary traditional science is suitable. This is a different approach to complex processes, not through probability. The format-number of connecting traditional science with our dynamic science is ((1,2), (2, 1), 1) ((1,2) ((1, 1))). (2, 1)3/2 is the format-number for spirit. ((1,2),(2,1),1)((1,2) ((1, 1) A)) ⱯA is a bridge for the transition from our dynamic science to traditional science and vice versa. For now, this is only an introductory article. The first task: to understand hierarchy of energies in the Universe and the principles of functioning of living energy (living organism, in particular, human, subtle energies), and then using these principles to "construct" artificial living energies (let's call them pseudo-living energies). It is possible to significantly expand the horizons of science, in particular physics, by studying the subtle energies in the Universe. Here is studying Energy-space with scalar product and norm of its elements by format-numbers. For this, some aspects are proposed for consideration of Dynamic Science. \mathrm{sel}{\mathrm{f}}_{\mathrm{science}}^{\mathrm{our}\ \mathrm{theory}} - science here acts as a space for the application of our theory in the self-format, i.e., any place of science, in particular physics, can act as a place for the "location" of the self. It contains itself (accommodates any action C) in any place of science. On the basis of mathematical uncertainties, new mathematical structures are formed, allowing us to describe processes and objects that are fundamentally not determined by conventional deterministic methods. Objective uncertainties in any case can mean manifestations of processes and objects that are fundamentally not determined by conventional deterministic methods. Since dynamic mathematics places the primary emphasis on the dynamics of energy, rather than on objectivity, the level of approach to studying processes expands. Many energies are indeterminate because they are based on uncertainties from the perspective of traditional science—large concentrations of specific energy in a chaotic state. The foundation of dynamic mathematics lies in working with uncertainties, which makes it possible to manipulate these indeterminate energies using direct-accumulative direct-parallel neural networks. Ordinary regular work with them in ordinary science is fundamentally unable to realize their capabilities. Therefore, singular science realized on a neural network - an analogue of the human CNS - will be much more natural. Quantum computers are just the beginning; our dynamic science constructs corresponding pseudo-living energies to achieve desired goals through network SmnSprt. SmnSprt must use format numbers to construct subtle energies, or rather, to access their levels (transform or "shift" ordinary energy into subtle energies, or "shift"). It's clear that the physical part of SmnSprt cannot exist in other worlds except for those close to our world or those whose parts intersect with our world. Unfortunately, we do not have funding to perform the necessary experiments and the practical creation of a technical model of such a neural network. There is a need to develop an instrumental mathematical base for new technologies. The task of the work is to create new approaches for this by introducing new concepts and methods. Our mathematics is unusual for a mathematician, because here the fulcrum is the action, and not the result of the action as in classical mathematics. Therefore, our mathematics is adapted not only to obtain results, but also to directly control actions, which will certainly show its benefits on a fundamentally new type of neural networks with directly parallel calculations, for which it was created. Any action has much greater potential than its result. Social justice is fundamentally impossible as long as education (training) is based on achieving results, and not on the process. It is time for physicists to begin studying not only the manifestations of living energies, but also the living energies themselves, which are by no means expressed through objectivity and ordinary energies, although they are capable of manifesting themselves through a lower level - objectivity and ordinary energies. We, as mathematicians, offer a new corresponding apparatus for understanding nature and studying living energies. Significance of the article: in a new qualitatively different approach to the study of complex processes through new mathematical, hierarchical, dynamic structures, in particular those processes that are dealt with by Synergetics. The significance of our article is in the formation of the presumptive mathematical structure of subtle energies, this is being done for the first time in science, and the presumptive classification of the mathematical structures of subtle energies for the first time. The experiments of the 2022 Nobel laureates Asle Ahlen, John Clauser, Anton Zeilinger and the experiments in chemistry Nazhipa Valitov eloquently demonstrate that we are right and that these studies are necessary. Be that as it may, we created classes of new mathematical structures, new mathematical singularities, i.e., made a contribution to the development of mathematics. Conventional science changes numbers. Ours changes levels by SmnSprt.
In recent decades, substantial theoretical and experimental progress was achieved in understanding the quantum nature of physical phenomena that serves as the foundation of present and future quantum technologies. Quantum correlations like the entanglement of the states of composite systems, the phenomenon of quantum discord, which captures other aspects of quantum correlations, quantum contextuality and, connected with these phenomena, uncertainty relations for conjugate variables and entropies, like Shannon and Rényi entropies, and the inequalities for spin states, like Bell inequalities, reflect the recently understood quantum properties of micro and macro systems. The mathematical methods needed to describe all quantum phenomena mentioned above were also the subject of intense studies in the end of the last, and beginning of the new, century. In this section of CAMOP 'Mathematical Methods of Studying Physical Phenomena' new results and new trends in the rapidly developing domain of quantum (and classical) physics are presented. Among the particular topics under discussion there are some reviews on the problems of dynamical invariants and their relations with symmetries of the physical systems. In fact, this is a very old problem of both classical and quantum systems, e.g. the systems of parametric oscillators with time-dependent parameters, like Ermakov systems, which have specific constants of motion depending linearly or quadratically on the oscillator positions and momenta. Such dynamical invariants play an important role in studying the dynamical Casimir effect, the essence of the effect being the creation of photons from the vacuum in a cavity with moving boundaries due to the presence of purely quantum fluctuations of the electromagnetic field in the vacuum. It is remarkable that this effect was recently observed experimentally. The other new direction in developing the mathematical approach in physics is quantum tomography that provides a new vision of quantum states. In the tomographic picture of quantum mechanics, the states are identified with fair conditional probability distributions, which contain the same information on the states as the wave function or the density matrix. The mathematical methods of the tomographic approach are based on studying the star-product (associative product) quantization scheme. The tomographic star-product technique provides an additional understanding of the associative product, which is connected with the existence of specific pairs of operators called quantizers and dequantizers. These operators code information on the kernels of all the star-product schemes, including the traditional phase-space Weyl–Wigner–Moyal picture describing the quantum-system evolution. The new equation to find quantizers, if the kernel of the star product of functions is given, is presented in this CAMOP section. For studying classical systems, the mathematical methods developed in quantum mechanics can also be used. The case of paraxial-radiation beams propagating in waveguides is a known example of describing a purely classical phenomenon by means of quantum-like equations. Thus, some quantum phenomenon like the entanglement can be mimicked by the properties of classical beams, for example, Gaussian modes. The mathematical structures and relations to the symplectic symmetry group are analogous for both classical and quantum phenomena. Such analogies of the mathematical classical and quantum methods used in research on quantum-like communication channels provide new tools for constructing a theoretical basis of the new information–transmission technologies. The conventional quantum mechanics and its relation to classical mechanics contain mathematical recipes of the correspondence principle and quantization rules. Attempts to find rules for deriving the quantum-mechanical formalism starting from the classical field theory, taking into account the influence of classical fluctuations of the field, is considered in these papers. The methods to solve quantum equations and formulate the boundary conditions in the problems with singular potentials are connected with the mathematical problems of self-adjointness of the Hamiltonians. The progress and some new results in this direction are reflected in this CAMOP section. The Gaussian states of the photons play an important role in quantum optics. The multimode electromagnetic field and quantum correlations in the Gaussian states are considered in this section. The new results in the statistical properties of the laser radiation discussed here are based on applications of mathematical methods in this traditional domain of physics. It is worth stressing that the universality of the mathematical procedures permitted to consider the physical phenomena in the ocean is on the same footing as the phenomena in the microworld. In this CAMOP section, there are also papers devoted to traditional problems of solving the Schrödinger equation for interesting quantum systems. Recently obtained results related to different domains of theoretical physics are united by applying mathematical methods and tools, that provide new possibilities to better understand the theoretical foundations needed to develop new quantum technologies like quantum computing and quantum communications. The papers are arranged alphabetically by the name of the first author. We are grateful to all authors who accepted our invitation to contribute to this CAMOP section.
While it is widely acknowledged that quantum theory is strange, and that the world view it implies is elusive, there is considerably less consensus as to why this is the case. This article will explore the possibility that the theory may be opaque because the mathematical language it employs is inarticulate. To address this possibility, three interconnected mathematical theories will be developed, each specifically designed to handle aspects of quantum theory's subject matter. The first will describe dynamic systems in terms that are general enough to be applicable to any kind dynamics, including both classical and quantum. That description will then be used to construct a theory of experiments, with the aim of understanding what types of experiments scientific methodology allows. Finally, the theory of experiments will found a theory of experimental probabilities applicable to any collection of experiments, so long as their probabilities are internally consistent. The resulting over-arching mathematical language will then be applied to quantum theory. In the initial application, it will be used to explain the core nature and structure of quantum measurement and probability. Following that, it will be used to explore quantum theory's models. Like any theory written in a mathematical language, quantum theory derives its meaning from its class of models. To understand the class quantum models, two models of central importance will be described. The first will be a conceptually simple construction that follows almost immediately from the above theory of dynamics. It fully satisfies both quantum theory and the above mentioned theory of experimentation; additionally, its macroscopic objects obey classical mechanics. The second will utilize a minimal amount of mathematical structure to satisfy the same conditions.
Introduction In the processes of adaptation, development and evolution, living systems interpret themselves in the environment resulting in changes of both. This leads to the growth of information via rescaling of internal time (heterochrony) followed by spatial reconstructions of morphology (heterotopy). The growth of information is based on perpetual changes in its interpretation in the changing world. Biological evolution involves the anticipatory epigenetic changes in interpretation of the genetic information which cannot be generally forecasted but can provide canalization of structural changes defined by the existing organization leading to predictable patterns of form generation. Social evolution is accompanied by unprecedented growth of the informational field that leads to progressive development of human society. In modern theoretical biology, the internal measurement concept was suggested as a background for explanation of the phenomenon of life (Matsuno, 1995). The quantum measurement represents the action of a measuring device on the measured system. The quantum measurement is an irreversible phenomenon exhibiting itself as a reduction of the potential field. It has also a relation to the irreversibility of time (Igamberdiev, 1993). The collapse of wave function is not equivalent to time until it does not generate a measurable duration, but when its pattern is repeated consistently, the clock can be set, and the system becomes organized in time. When the measuring device is a part of measured system, the measurement proceeds internally in relation to the whole system and the latter becomes more complex as a result of measurement itself. The aim of this study is to discuss the role of internal measurement in the growth of information in evolving systems. This can refer to biological evolution, social evolution, and as well to the cosmic evolution, which is represented in the phenomenon of expansion of the Universe. Internal Measurement and the Generation of New Information The internal measurement leads to an iterative recursive process which appears as the development and evolution of the combined system containing the measuring device and the measured object. The quantum measuring device can be organized in such way that it “encodes” the system in the course of interaction with the measured object, and makes it possible for the measurement to proceed in a regular way. In this case, such system can memorize the evolutionary complication of organization in a digital information-bearing subsystem and evolve further; in other words it contains an internal description memorizing the result of measurement. The logical precondition of the growth of information in this evolving process is the incompleteness of biosystem’s internal description, while the physical precondition is the uncertainty of quantum measurement. The evolutionary increase of complexity becomes possible when genotype appears as a system distinct from phenotype and is embedded into it, which separates energy-degenerate rate-independent genetic symbols from the rate-dependent dynamics of construction that they control (Pattee, 2001). Evolutionary growth of information becomes its own cause, a universal property of our world. The growth of information accompanies the appearance of measurable time that occurs in the systems performing quantum measurements in a regular way, with low dissipation of energy (Igamberdiev, 1993, 2004). These systems are modelled as hypercycles and can be defined as structures in which the subset of a substrate set of the catalytic system happens to be the matrix for generating and reproducing the set of catalysts itself (Igamberdiev, 1999). This definition keeps the main features of the original notion of hypercycle given by Eigen and Schuster (1979). The hypercyclic system is closed in the way that all of the catalysts needed for an organism to stay alive (representing an efficient causation according to Aristotle and forming organism’s spatiotemporal structure) must be produced by the organism itself, only relying on matter and energy from the outside (Letelier et al., 2011). When hypercycles appear in evolution, time becomes an independent measurable variable due to the internal reproducible changes. Hypercycle organizes irreversibility of quantum measurement into a measurable duration. Eigen’s hypercycle is a formalized representation of the autopoietic system of Maturana and Varela or Rosen’s (M,R) system (Leteiler et al., 2011). The system becomes an internal autonomous clock that distinguishes the past (memory), the present (life), and the future (anticipation based on the reproducible model), so the modeling, logic and digital information growth become possible within the system (Rosen, 1985). The hypercycle having own embedded description, becomes a structure that realizes computation in accordance with its internal logic defined by the embedded description. The latter has the property of incompleteness which is reflected in the fact that quantum correlations of the states of the system are associated with undecidable logic theories, i.e., they can potentially generate the statements not defined within the system. The undecidability can be interpreted in the sense similar to the Gödel’s incompleteness theorem, meaning that there exist propositions, expressible in the formal logic, which cannot be proven or disproven (Briegel et al., 2009). These propositions become the grounds of expansion of the system and its informational growth. From the quantum mechanical point of view, the emergence of a new statement results in acquiring a new error-correction meaning to support the internal quantum state (IQS) (Igamberdiev, 2004, 2007). The IQS keeps the system organizationally invariant. It is supported by the set of error-correcting commands that aim to keep IQS free from external demolitions. The error-correction information becomes an important part of the whole informational field. A new statement makes the system more complex (it leads to an increase of its informational content), with its all spatiotemporal organizational invariance be rescaled. In the course of evolution, an available element of a formal system (similarly to a word when used as a metaphor) can acquire another (in addition to already existing) value that contributes to formation of a new level of organization in the system. The logical basis of this action is the incompleteness of the existing formal system that allows assigning arbitrary values to the statements non-provable within that system, while the physical basis is the quantum uncertainty arising in quantum measurement. A new statement can arise from existing elements by acquiring the double function, however, for fixation of this new statement via expansion of existing formal system, some informational redundancy of the system is needed, which can be achieved by multiplication of some of its elements. Genome is a system which possesses an internal complementarity between the linear texts and their superposition. Relevantly to this, complementarity means that text and hypertext cannot be viewed at the same moment: they should be separated by a time interval. It is an example of uncertainty between the system and its embedding. Overlapping genes, alternatively splicing sequences, RNA and DNA editing, introns, and recombination according to molecular addresses are the features of this hypertext generating a potentially infinite number of language games. Genome as a complete language exists as a complementary set of its alternative combinations resulting in logical paradoxes which determine its temporal dynamics (Isalan, 2009). This superposition is a basis for ontogenesis, adaptation and evolution. Thus, the total “true” genome is a superposition of contradictory arrangements, which generate one single arrangement at a concrete moment of time. The pool of mobile genetic elements expands the combinatorial capacity of the genome by many times. An ambiguity in meaning is analogous to the quantum uncertainty principle in which it is impossible to define strictly the position and impulse of a particle simultaneously, or to fix certain energy in a very short period of time necessary for its registration. The question of a minimal size of the autocatalytic self-reproducing system and its composition has been discussed in several works (Sharov, 2009; Steel et al., 2013). Self-reproduction itself is a creative process of placing text in text with following self-growing of this joint structure. Any evolutionary change also begins from the placing of “text into text”. This is possible because genome is structurally adapted for realization of such a non-trivial function. Moreover, even a point mutation or deletion may be considered as generative if it is placed in the repeated (e.g., diploid) structure. The doubling is a premise of metasystem transition, which includes duplication of the original system and the establishment of control over multiple copies (Turchin, 1977). The evolutionary significance of gene duplication was considered by Ohno (1970) as a premise of neofunctionalization. The advantage of sexual reproduction is in the casual combinatorial generating of new statements from two separate texts that can acquire meanings, thus it resists evolutionary degradation. It becomes a prerequisite for growing of information and complexity (Igamberdiev, 2014). The combinatorial interaction of heterochronic texts generates a new system in which the internal time is rescaled in a new way that generally cannot be forecasted. The heterochronic duplication (via hybridization of temporally different organisms) generates more possibilities for the metasystem transition. Thus, the incompleteness of embedded set of symbols is the formal cause of evolution. The physical representation of this incompleteness is a quantum uncertainty in the course of measurement (Matsuno, 1992). It spans from the level of elementary particles to biological evolution and to the phenomenon of free will and consciousness. Growth of Information in the Expanding Universe The growth of information that we discuss here mainly in relation to biological evolution is relevant also to the physical space-time scales. The self-growing principle of quantum measurement has a property of intrinsic expansion of the informational field. The relationship between observable nature and a hidden “potential” nature is modeled, according to Kineman (2010), as an imaginary space-time domain geometrically represented as radial “Minkowski-space”. Despite of the fact that local space and time are normally represented as real numbers, the general relationship in this geometry is hyperbolic in accordance with the special theory of relativity. When mapped as a radial geometry, the space-time is seen to be intrinsically dynamic (expanding) and self-similar across all scales. The geometry has the properties of early and present acceleration. This representation eliminates the “light cone” and thus all regions in this model are the domains of existence and are observable over time. Nevertheless a domain of general, non-local reality is represented in the imaginary axes that exist simultaneously with measurable, local domains. The Universe in the concept of Kineman (2010) consists of the units called “holons”, which vaguely correspond to Leibniz’s monads. They possess simultaneous properties of location and non-location, as a point of non-differentiated whole appearing in a subject-object relation. The Everett’s interpretation of quantum mechanics works in these isolated domains but not between the domains, the same idea has been suggested by Matsuno (2012) for the individual biological systems taken as separate domains. The reality of superposition of the wave function is limited by the single monad and does not expand outside it, and in this sense monads do not have windows as originally proposed by Leibniz. Conclusion The growth of information is the basic property of evolving systems and it follows from the interaction between non-local and local domains in the course of internal quantum measurements. The internal measurement leads to an iterative recursive process which appears as evolution of the combined system containing the measuring device and the measured object. The system through measurement acquires the property of expansion, which is seen in biological evolution, social development, and at cosmic scales as expansion of the Universe. References Briegel, H.J.; Browne, D.E.; Dur, W.; Raussendorf, R.; Van den Nest, M. Measurement-based quantum computation. Nature Physics 2009, 5, 19-26. Eigen, M.; Schuster, P. The Hypercycle: A Principle of Natural Self-Organization. Springer, Berlin, 1979. Igamberdiev, A.U. Quantum mechanical properties of biosystems: A framework for complexity, structural stability and transformations. Biosystems 1993, 31, 65‐ Igamberdiev, A.U. Foundations of metabolic organization: coherence as a basis of computational properties in metabolic networks. Biosystems 1999, 50, 1-16. Igamberdiev, A.U. Quantum computation, non-demolition measurements, and reflective control in living systems. Biosystems 2004, 77, 47–56. Igamberdiev, A.U. Physical limits of computation and emergence of life. Biosystems 2007, 90, 340–349. Igamberdiev, A.U. Time rescaling and pattern formation in biological evolution. Biosystems 2014, 123, 19-26. Isalan, M. Gene networks and liar paradoxes. Bioessays 2009, 31, 1110-1115. Letelier, J.C.; Cárdenas, M.L.; Cornish-Bowden, A. From L'Homme Machine to metabolic closure: steps towards understanding life. Journal of Theoretical Biology 2011, 286, 100-113. Matsuno, K. The uncertainty principle as an evolutionary engine. Biosystems 1991, 27, 63-76. Matsuno, K. Quantum and biological computation. Biosystems 1995, 35, 209-212. Matsuno, K. Chemical evolution as a concrete scheme for naturalizing the relative-state of quantum mechanics. Biosystems 2012, 109, 159-168. Kineman, J.J. Relational self-similar space-time cosmology revisited. Proceedings of the 54th Meeting of the International Society for System Sciences. Waterloo, Canada, 2010. Ohno, S. Evolution by Gene Duplication. Springer, New York, 1970. Pattee, H.H. The physics of symbols: bridging the epistemic cut. Biosystems 2001, 60, 5-21. Sharov, A.A., 2009. Coenzyme autocatalytic network on the surface of oil microspheres as a model for the origin of life. International Journal of Molecular Sciences 2009, 10, 1838-1852. Steel, M.; Hordijk, W.; Smith, J. Minimal autocatalytic networks. Journal of Theoretical Biology 2013, 332, 96-107. Turchin, V. Phenomenon of Science. Columbia University Press, New York, 1977.
The file on this site provides the slides for a lecture given in Hangzhou in May 2018, and the lecture itself is available at the URL beginning 'sms' in the set of links provided in connection with this item. It is commonly assumed that regular physics underpins biology. Here it is proposed, in a synthesis of ideas by various authors, that in reality structures and mechanisms of a biological character underpin the world studied by physicists, in principle supplying detail in the domain that according to regular physics is of an indeterminate character. In regular physics mathematical equations are primary, but this constraint leads to problems with reconciling theory and reality. Biology on the other hand typically does not characterise nature in quantitative terms, instead investigating in detail important complex interrelationships between parts, leading to an understanding of the systems concerned that is in some respects beyond that which prevails in regular physics. It makes contact with quantum physics in various ways, for example in that both involve interactions between observer and observed, an insight that explains what is special about processes involving observation, justifying in the quantum physics context the replacement of the unphysical many-worlds picture by one involving collapse. The link with biology furthermore clarifies Wheeler’s suggestion that a multiplicity of observations can lead to the ‘fabrication of form’, including the insight that this process depends on very specific ‘structures with power’ related to the 'semiotic scaffolding' of the application of sign theory to biology known as biosemiotics. The observer-observed 'circle' of Wheeler and Yardley is a special case of a more general phenomenon, oppositional dynamics, related to the 'intra-action' of Barad's Agential Realism, involving cooperating systems such as mind and matter, abstract and concrete, observer and observed, that preserve their identities while interacting with one another in such a way as to act as a unit. A third system may also be involved, the mediating system of Peirce linking the two together. Such a situation of changing connections and separations may plausibly lead in the future to an understanding of how complex systems are able to evolve to produce 'life, the universe and everything'. (Added 1 July 2018) The general structure proposed here as an alternative to a mathematics-based physics can be usefully characterised by relating it to different disciplines and the specialised concepts utilised therein. In theoretical physics, the test for the correctness of a theory typically involves numerical predictions, corresponding to which theories are expressed in terms of equations, that is to say assertions that two quantities have identical values. Equations have a lesser significance in biology which typically talks in terms of functional mechanisms, dependent for example on details of chemistry and concepts such as genes, natural selection, signals and geometrical or topologically motivated concepts such as the interconnections between systems and the unfolding of DNA. Biosemiotics adds to this the concept of signs and their interpretation, implying novel concepts such as semiotic scaffolding and the semiosphere, code duality, and appreciation of the different types of signs, including symbols and their capacity for abstraction and use in language systems. Circular Theory adds to this picture, as do the ideas of Barad, considerations such as the idea of oppositional dynamics. The proposals in this lecture can be regarded as the idea that concepts such as those deriving from biosemiotics have more general applicability than just conventional biology and may apply, in some circumstances, to nonlinear systems generally, including the domain new to science hypothesised to underlie the phenomena of present-day physics. The task then has to be to restore the mathematical aspect presumed, in this picture, not to be fundamental as it is in conventional theory. Deacon has invoked a complex sequence of evolutionary steps to account for the emergence over time of human language systems, and correspondingly mathematical behaviour can be subsumed under the general evolutionary mechanisms of biosemiotics (cf. also the proposals of Davis and Hersh regarding the nature of mathematics), so that the mathematical behaviour of physical systems is consistent with the proposed scheme. In conclusion, it is suggested that theoretical physicists should cease expecting to find some universal mathematical ‘theory of everything’, and focus instead on understanding in more detail complex systems exhibiting behaviour of a biological character, extending existing understanding. This may in time provide a more fruitful understanding of the natural world than does the regular approach. The essential concepts have an observational basis from both biology and the little-known discipline of cymatics (a discipline concerned with the remarkable patterns that specific waveforms can give rise to), while again computer simulations also offer promise in providing insight into the complex behaviours involved in the above proposals. References Jesper Hoffmeyer, Semiotic Scaffolding of Living Systems. Commens, a Digital Companion to C. S. Peirce (on Commens web site). Terrence Deacon, The Symbolic Species, W.W. Norton & Co. Karen Barad, Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning, Duke University Press. Philip Davis and Reuben Hersh, The Mathematical Experience, Penguin. Ilexa Yardley, Circular Theory.