Elements of Mathematical Connections theory, Mathematics of format-numbers, Some format-numbers for s- morphology, Fundamentally New approach to elementary particles by format-numbers
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) 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.
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.
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.
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.
Abstract The new quantum mechanics consists of a scheme of equations which are very closely analogous to the equations of classical mechanics, with the fundamental difference that the dynamical variables do not obey the commutative law of multiplication, but satisfy instead the well-known quantum conditions. It follows that one cannot suppose the dynamical variables to be ordinary numbers (c-numbers), but may call them numbers of a special type (q-numbers). The theory shows that these q-numbers can in general be represented by matrices whose elements are c-numbers (functions of a time parameter). When one has performed the calculations with the q-numbers and obtained all the matrices one wants, the question arises how one is to get physical results from the theory, i. e., how can one obtain c-numbers from the theory that one can compare with experimental values ? Hitherto this has been done with the help of a number of special assumptions. In Heisenberg’s original matrix mechanics it was assumed that the elements of the diagonal matrix that represents the energy are the energy levels of the system, and the elements of the matrix that represents the total polarisation, which are periodic functions of the time, determine the frequencies and intensities of the spectral lines in analogy to the classical theory. Schrodinger’s wave representation of the quantum mechanics has provided new ways of obtaining physical results from the theory, based on the assumption that the square of the amplitude of the wave function can in certain cases be interpreted as a probability. From this assumption one can, for instance, work out the probability of a transition being produced in a system (or the number of transitions produced in an assembly of like systems) by an arbitrary external perturbing force, and can thus, by supposing the perturbation to consist of incident radiation, obtain directly Einstein’s B coefficients. Again in Born’s treatment of collision problems it is assumed that the square of the amplitude of the wave function scattered in any direction determines the probability of the colliding electron (or other body) being scattered in that direction.
Quantum field theory has emerged from the background of fluctuating non-zero vacuum energy states. Through entanglement it appears energy can be removed from these fluctuations producing negative energy states. To accommodate these phenomena, a theoretical framework of Hilbert Spaces, nth order differential equations, group theory, complex numbers, topology, CPT Theorems, CP symmetry breaking and operators is developing. The theoretical constructs can be epitomised in part by De Broglie’s formula n(n+1) Periodicity and n(n1) Compressibility – The Quantum Mechanical Table. The inverted form of the Periodic Table with mass number removed – known as The Roberts-Janet Nuclear Periodic Table – is a testament to the empirical work of chemists previously. The one-to-one mapping between these tables merges theoretical and empirical science. From individual elements via molecules to multi-disciplinary science a new era is beginning. Underlying mechanisms of quantum tunnelling, superposition, entanglement, vibronic mixing and decoherence abound. In time such processes could extend to cosmology at the top end of the energy scale down to catalytic and reversible reactions, solubility, electrolysis, biochemical pathways, evolution, bioluminescence, medical and psychological ruminations at the lower end of the energy scale including low temperature physics. Quantum biology and neuroscience in Nature appear fertile ground to consolidate further applications of quantum field theory as it matures while entropy changes, information theory, oscillations between self-assembly and chaos coupled with phase changes overlay multiple layers within the universe at all orders of magnitude. Enter entropic gravity that derives gravity from treating the metric of spacetime as a quantum operator. This uses quantum relative entropy from quantum information theory to link spacetime geometry and matter.
Time and reality are central concepts in both philosophy and physics. While classical mechanics describes the universe as deterministic, where the present emerges from past conditions, quantum theory introduces probabilistic interpretations suggesting inherent uncertainty at microscopic scales. These two perspectives have led to an ongoing debate regarding whether reality is fundamentally deterministic, probabilistic, or a combination of both. The Zia Theory of Temporal Reality (ZTTR) integrates these frameworks by proposing that the present state of reality is determined by accumulated past causes, while the future evolves probabilistically under uncertainty. To formalize this concept, the Zia Unified Continuity Equation (ZUCE) is expressed as a stochastic model where the state of reality represents a combination of initial conditions, integrated causal influences, and stochastic fluctuations represented by a Wiener process. To enhance generality and address limitations of fixed functional assumptions, the uncertainty term is further extended as a generalized function, allowing different forms such as diffusion-like, logarithmic, or nonlinear growth depending on system dynamics. In this framework, deterministic causal accumulation represents the structured continuity of past influences, while the stochastic component reflects uncertainty arising from complexity, interaction, and incomplete knowledge of system variables. This interpretation aligns with developments in statistical mechanics, information theory, and complex systems research. The applicability of the model is illustrated through conceptual and numerical examples drawn from physical processes, biological systems, and learning dynamics. These examples demonstrate that deterministic historical structures and stochastic variations can coexist within a single temporal framework. The Zia Theory of Temporal Reality thus provides a generalized and mathematically consistent perspective on temporal evolution and contributes to interdisciplinary research in physics, complexity science, and artificial intelligence.