The paper discusses this year’s Nobel Prize in physics for experiments of entanglement “establishing the violation of Bell inequalities and pioneering quantum information science” in a much wider, including philosophical context legitimizing by the authority of the Nobel Prize a new scientific area out of “classical” quantum mechanics relevant to Pauli’s “particle” paradigm of energy conservation and thus to the Standard model obeying it. One justifies the eventual future theory of quantum gravitation as belonging to (...) the newly established quantum information science. Entanglement, involving non-Hermitian operators for its rigorous description, non-unitarity as well as nonlocal and superluminal physical signals “spookily” (by Einstein’s flowery epithet) synchronizing and transferring some nonzero action at a distance, can be considered to be quantum gravity so that its local counterpart to be Einstein’s gravitation according to general relativity therefore pioneering an alternative pathway to quantum gravitation different from the “secondary quantization” of the Standard model. So, the experiments of entanglement once they have been awarded by the Nobel Prize launch particularly the relevant theory of quantum gravitation grounded on “quantum information science” thus granted to be nonclassical quantum mechanics in the shared framework of the generalized quantum mechanics obeying rather quantum-information conservation than only energy conservation. The concept of “dark phase” of the universe naturally linked to the very well confirmed “dark matter” and “dark energy” and opposed to its “light phase” inherent to classical quantum mechanics and the Standard model obeys quantum-information conservation, after which reversible causality or the mutual transformation of energy and information are valid. The mythical Big Bang after which energy conservation holds universally is to be replaced by an omnipresent and omnitemporal medium of decoherence of the dark and nonlocal phase into the light and local phase. The former is only an integral image of the latter and borrowed in fact rather from religion than from science. Physical, methodological and proper philosophical conclusions follow from that paradigm shift heralded by this year’s Nobel Prize in physics. For example, the scientific theory of thinking should originate from the dark phase of the universe, as well: probably only approximately modeled by neural networks physically belonging to the light phase thoroughly. A few crucial philosophical sequences follow from the break of Pauli’s paradigm: (1) the establishment of the “dark” phase of the universe as opposed to its “light” phase, only to which the Cartesian dichotomy of “body” and “mind” is valid; (2) quantum information conservation as relevant to the dark phase, furthermore generalizing energy conservation as to its light phase, productively allowing for physical entities to appear “ex nihilo”, i.e., from the dark phase, in which energy and time are yet inseparable from each other; (3) reversible causality as inherent to the dark phase; (4) the interpretation of gravitation only mathematically: as an interpretation of the incompleteness of finiteness to infinity, for example, following the Gödel dichotomy (“either contradiction or incompleteness”) about the relation of arithmetic to set theory; (5) the restriction of the concept of hierarchy only to the light phase; (6) the commensurability of both physical extremes of a quantum and the universe as a whole in the dark phase obeying quantum information conservation and akin to Nicholas of Cusa’s philosophical and theological worldview. (shrink)

This is Part 1 of a four part paper, intended to redress some of the most fundamental confusions in the subject of physical time directionality, and represent the concepts accurately. There are widespread fallacies in the subject that need to be corrected in introductory courses for physics students and philosophers. We start in Part 1 by analysing the time reversal symmetry of quantum probability laws. Time reversal symmetry is defined as the property of invariance under the time reversal (...) transformation, T: t --> -t. It is shown that quantum mechanics (classical or relativistic) is strongly time asymmetric in its probability laws. This contradicts the orthodox analysis, found throughout the conventional literature on physical time, which claims that quantum mechanics is time symmetric or reversible. This is widely claimed as settled scientific fact, and large philosophical and scientific conclusions are drawn from it. But it is an error. The fact is that while quantum mechanics is widely claimed to be reversible on the basis of two formal mathematical properties (that it does have), these properties do not represent invariance under the time reversal transformation. A recent experiment (Batalhão at alia, 2015) showing irreversibility of quantum thermodynamics is discussed as an illustration of this result. Most physicists remain unaware of the errors, decades after they were first demonstrated. Orthodox specialists in the philosophy of time who are aware of the error continue to refer to the ‘time symmetry’ or ‘reversibility’ of quantum mechanics anyway – and exploit the ambiguity to claim false implications about physical time reversal symmetry in nature. The excuse for perpetrating the confusion is that, since it is has now become customary to refer to the formal properties of quantum mechanics as ‘reversibility’ or ‘time reversal symmetry’, we should just keep referring to them by this name, even though they are not time reversal symmetry. This causes endless confusion, in attempts to explain the physical irreversibility of our universe, and in philosophical discussions of implications of physics for the nature of time. The failure of genuine time reversal symmetry in quantum mechanics changes the interpretation of modern physics in a deep way. It changes the problem of explaining the real irreversibility found throughout nature. (shrink)

We start from previous studies of G.N. Ord and A.S. Deakin showing that both the classical diffusion equation and Schrödinger equation of quantum mechanics have a common stump. Such result is obtained in rigorous terms since it is demonstrated that both diffusion and Schrödinger equations are manifestation of the same mathematical axiomatic set of the Clifford algebra. By using both such ( ) i A S and the i,±1 N algebra, it is evidenced, however, that possibly the (...) two basic equations of the physics cannot be reconciled. 1. (shrink)

Foundations of Relational Realism presents an intuitive interpretation of quantum mechanics, based on a revised decoherent histories interpretation, structured within a category theoretic topological formalism. -/- If there is a central conceptual framework that has reliably borne the weight of modern physics as it ascends into the twenty-first century, it is the framework of quantum mechanics. Because of its enduring stability in experimental application, physics has today reached heights that not only inspire wonder, but (...) arguably exceed the limits of intuitive vision, if not intuitive comprehension. For many physicists and philosophers, however, the currently fashionable tendency toward exotic interpretation of the theoretical formalism is recognized not as a mark of ascent for the tower of physics, but rather an indicator of sway—one that must be dampened rather than encouraged if practical progress is to continue. -/- In this unique two-part volume, designed to be comprehensible to both specialists and non-specialists, the authors chart out a pathway forward by identifying the central deficiency in most interpretations of quantum mechanics: That in its conventional, metrical depiction of extension, inherited from the Enlightenment, objects are characterized as fundamental to relations—i.e., such that relations presuppose objects but objects do not presuppose relations. The authors, by contrast, argue that quantum mechanics exemplifies the fact that physical extensiveness is fundamentally topological rather than metrical, with its proper logico-mathematical framework being category theoretic rather than set theoretic. -/- By this thesis, extensiveness fundamentally entails not only relations of objects, but also relations of relations. Thus, the fundamental quanta of quantum physics are properly defined as units of logico-physical relation rather than merely units of physical relata as is the current convention. Objects are always understood as relata, and likewise relations are always understood objectively. In this way, objects and relations are coherently defined as mutually implicative. The conventional notion of a history as “a story about fundamental objects” is thereby reversed, such that the classical “objects” become the story by which we understand physical systems that are fundamentally histories of quantum events. -/- These are just a few of the novel critical claims explored in this volume—claims whose exemplification in quantum mechanics will, the authors argue, serve more broadly as foundational principles for the philosophy of nature as it evolves through the twenty-first century and beyond. (shrink)

Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation (...) can be also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators on it. One can interpret special Minkowski space involved by special relativity and the qubit Hilbert space of quantum information as Fourier counterparts immediately noticing that general relativity means gravitation as the Fourier counterpart of non-Hermitian operators implying non-unitarity and the violation of energy conservation and thus destroying Pauli’s particle paradigm. Since the Standard model obeys it, this explains the impossibility of “quantum gravitation” in any framework conservatively generalizing the Standard model so that it would include gravitation along with electromagnetic, weak, and strong interactions. Einstein’s geometrization of gravitation can be continued into a purely mathematical theory of it following Euclid’s realization for geometry to be exhaustively built in a deductive and axiomatic way as well as Riemann’s parametrization of all the class of Euclidean and non-Euclidean geometries by “space curvature”, then being generalized to Minkowski space as the operators on pseudo-Riemannian space as the Einstein field equation means gravitation. The transition from mathematical gravitation to logical one can rely on the historical lesson of the pair of Lobachevski’s and Riemann’s approaches now “reversely”, i.e., from the latter to the former. Logical gravitation is linkable to Hegel’s dialectical logic and ontological dialectics abandoning their interpretations as a new zero logic substituting classical propionyl logic. The approach of ontomathematics generalizing that of ontology, traceable even to Aristotle’s reformation of Plato’s doctrine, needs Hegel’s doctrine to be formalized as a first-order logic naturally containing Boolean algebra, isomorphic to both classical propositional logic and set theory being the class of all first-order logics, as a sub-logic along with Peano arithmetic as another sub-logic. The first-order logic at issue is called Hilbert arithmetic and elaborated in detail in other papers. It allows for both self-foundation of mathematics to be internally proved as complete and furthermore, quantum mechanics reinterpreted as quantum information to be included by the qubit Hilbert space interpretable in turn as a dual and physical counterpart of Hilbert arithmetic in a narrow sense, that is, both counterparts constitute Hilbert arithmetic in a wide sense, being mathematical and physical simultaneously and thus overcoming the Cartesian dualism of “body” gapped from “mind” by an abyss. Then, the proper philosophical interpretation of gravitation to be the fundamental ontomathematical force or interaction overcomes the ridiculous belief of the Big Bang wrongly alleged to be a scientific theory. Ontomathematical gravitation suggests an omnipresent and omnitemporal medium of “God’s” creation “ex nihilo” following only the natural necessity of quantum-information conservation particularly and locally manifested as energy conservation. (shrink)

The persistent interpretation problem for quantum mechanics may indicate an unwillingness to consider unpalatable assumptions that could open the way toward progress. With this in mind, I focus on the work of David Bohm, whose earlier work has been more influential than that of his later. As I’ll discuss, I believe two assumptions play a strong role in explaining the disparity: 1) that theories in physics must be grounded in mathematical structure and 2) that consciousness must (...) supervene on material processes. I’ll argue that the first assumption appears to lead us toward Everett’s many worlds interpretation, which suggests a red flag. I’ll also argue that the second assumption is suspect due to the persistent explanatory gap for consciousness. Later, I explore ways that Bohm’s later work holds some promise in providing a better fit with our world, both phenomenologically and empirically. Also, I’ll address the possible problem of realism. (shrink)

The limitations and unsuitability of the twentieth century intellectual marvel, the quantum mechanics for the task of unraveling working of human consciousness is critically analyzed. The inbuilt traits of the probabilistic, approximate and imprecise nature of quantum mechanical approach are brought out. -/- The limitations and the unsuitability of using such knowledge for the understanding of precise, correct, finite and definite happenings of activities relating to human consciousness and mind, which are not quantum in nature, are (...) pointed out. -/- Analytical methods interpreting philosophical and Indian spiritual analyses suiting the unraveling of working of human consciousness and mind over the deductive approach of quantum physics and advanced mathematics are highlighted. A model of human consciousness and mental functions is presented taking ideas from the Upanishads and related texts. -/- Comparisons with theological interpretations of Upanishadic insight are dealt with to have an idea of working of human consciousness and mind in relation to spirituality. (shrink)

One of the key episodes of history of modern physics – Paul Dirac’s startling contrivance of the relativistic theory of the electron – is elicited in the context of lucid epistemological model of mature theory change. The peculiar character of Dirac’s synthesis of special relativity and quantum mechanics is revealed by comparison with Einstein’s sophisticated methodology of the General Relativity contrivance. The subtle structure of Dirac’s scientific research program and first and foremost the odd principles that put (...) up its powerful heuristics is scrutinized with special emphasis on the highly controversial tenet of “mathematical beauty.” It is contended that despite the relentless Dirac’s remarks denigrating the controversial role of philosophy one can trace its indirect influence through Arthur Eddington’s and Hermann Weyl’s whimsical mathematical models. Accordingly, the milestones of Dirac’s research programme realization in the distinctive context of the applied epistemological doctrine are indicated. (shrink)

We look into the ontology of quantum theory as distinct from that of the classical theory in the sciences. Theories carry with them their own ontology while the metaphysics may remain the same in the background. We follow a broadly Kantian tradition, distinguishing between the noumenal and phenomenal realities where the former is independent of our perception while the latter is assembled from the former by means of fragmentary bits of interpretation. Theories do not tell us how the noumenal (...) world is constituted but are conceptual constructs applying to models generated in the phenomenal world within limited contexts. -/- The ontology of quantum theory principally rests on the view that entities in the world are pervasively correlated with one another not by means of probabilities as in the case of the classical theory, but by means of probability amplitudes involving finely tuned phases characterising the oscillatory behaviour of quantum mechanical states. -/- The amplitude-dependent correlations (quantum entanglement) exist over and above the classical ones expressed in terms of probabilities. While the classical correlations are essentially local in nature, quantum correlations are shared globally in the process of environment-induced decoherence. The decoherence is an effectively random process that removes local correlations in the course of global sharing of entanglement—the removal being especially manifest in the case of systems that appear as classical ones. It is this aspect of the decoherence process that makes the so-called measurement postulate (one relating to wave function collapse) cohere with the rest of the principles of quantum theory where the latter implies a Schrodinger type time evolution of quantum mechanical systems. -/- The mathematical basis of the quantum correlations consists of the description of pure states of a system in terms of vectors in a linear vector space (a mixed state appears as an admixture of pure states with some probability distribution associated with it) and, in addition, the description of (pure) states of composite systems as vectors in the product space arising from the component sub-systems. -/- The crucial aspect of the decoherence process, of significance in the context of the apparent incompatibility of the measurement postulate with the unitary Schrodinger evolution, relates to the fact that it is almost instantaneous in the case of a classical object (one that is nevertheless amenable to a quantum description). Indeed, the decoherence time is, in all likelihood, of the order of the Planck scale, being driven by field fluctuations in the Planck regime. This points to factors of an unknown nature determining the finest details of the decoherence process since Planck scale physics remains an obscure terrain. -/- In other words, quantum theory is, to all intents and purposes, in the need of a radical revision, in keeping with the fact that all theories are defeasible and need revision as our domains of experience expand and get realigned in a complex manner. The context within which quantum theory (and quantum field theory too) is defined is set precisely by the Planck scale, across which a novel theoretical framework is likely to emerge. However, as in the case of theory revisions in general, that emerging theory will stand in an asymmetric relation of incommensurability with the present-day quantum theory, where the concepts of the latter will be comprehensible in terms of those of the former, but the converse will not hold. (shrink)

The biochemistry of geotropism in plants and gravisensing in e.g. cyanobacteria or paramacia is still not well understood today [1]. Perhaps there are more ways than one for organisms to sense gravity. The two best known relatively old explanations for gravity sensing are sensing through the redistribution of cellular starch statoliths and sensing through redistribution of auxin. The starch containing statoliths in a gravity field produce pressure on the endoplasmic reticulum of the cell. This enables the cell to sense direction. (...) Alternatively, there is the redistribution of auxin under the action of gravity. This is known as the Cholodny-Went hypothesis [2], [3]. The latter redistribution coincides with a redistribution of electrical charge in the cell. With the present study the aim is to add a mathematical unified field explanation to gravisensing. (shrink)

The paper addresses the problem, which quantum mechanics resolves in fact. Its viewpoint suggests that the crucial link of time and its course is omitted in understanding the problem. The common interpretation underlain by the history of quantum mechanics sees discreteness only on the Plank scale, which is transformed into continuity and even smoothness on the macroscopic scale. That approach is fraught with a series of seeming paradoxes. It suggests that the present mathematical formalism of (...) quantum mechanics is only partly relevant to its problem, which is ostensibly known. The paper accepts just the opposite: The mathematical solution is absolute relevant and serves as an axiomatic base, from which the real and yet hidden problem is deduced. Wave-particle duality, Hilbert space, both probabilistic and many-worlds interpretations of quantum mechanics, quantum information, and the Schrödinger equation are included in that base. The Schrödinger equation is understood as a generalization of the law of energy conservation to past, present, and future moments of time. The deduced real problem of quantum mechanics is: “What is the universal law describing the course of time in any physical change therefore including any mechanical motion?”. (shrink)

The problem of indeterminism in quantum mechanics usually being considered as a generalization determinism of classical mechanics and physics for the case of discrete (quantum) changes is interpreted as an only mathematical problem referring to the relation of a set of independent choices to a well-ordered series therefore regulated by the equivalence of the axiom of choice and the well-ordering “theorem”. The former corresponds to quantum indeterminism, and the latter, to classical determinism. No (...) other premises (besides the above only mathematical equivalence) are necessary to explain how the probabilistic causation of quantum mechanics refers to the unambiguous determinism of classical physics. The same equivalence underlies the mathematical formalism of quantum mechanics. It merged the well-ordered components of the vectors of Heisenberg’s matrix mechanics and the non-ordered members of the wave functions of Schrödinger’s undulatory mechanics. The mathematical condition of that merging is just the equivalence of the axiom of choice and the well-ordering theorem implying in turn Max Born’s probabilistic interpretation of quantum mechanics. Particularly, energy conservation is justified differently than classical physics. It is due to the equivalence at issue rather than to the principle of least action. One may involve two forms of energy conservation corresponding whether to the smooth changes of classical physics or to the discrete changes of quantum mechanics. Further both kinds of changes can be equated to each other under the unified energy conservation as well as the conditions for the violation of energy conservation to be investigated therefore directing to a certain generalization of energy conservation. (shrink)

In this paper I investigate, within the framework of realistic interpretations of the wave function in nonrelativistic quantum mechanics, the mathematical and physical nature of the wave function. I argue against the view that mathematically the wave function is a two-component scalar field on configuration space. First, I review how this view makes quantum mechanics non- Galilei invariant and yields the wrong classical limit. Moreover, I argue that interpreting the wave function as a ray, in (...) agreement many physicists, Galilei invariance is preserved. In addition, I discuss how the wave function behaves more similarly to a gauge potential than to a field. Finally I show how this favors a nomological rather than an ontological view of the wave function. (shrink)

Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change this picture and show why it is helpful to consider (...) the instants of time as Fuzzy numbers. In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it. Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Para-consistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time. (shrink)

The purpose of this paper is to show that the mathematics of quantum mechanics is the mathematics of set partitions linearized to vector spaces, particularly in Hilbert spaces. That is, the math of QM is the Hilbert space version of the math to describe objective indefiniteness that at the set level is the math of partitions. The key analytical concepts are definiteness versus indefiniteness, distinctions versus indistinctions, and distinguishability versus indistinguishability. The key machinery to go from indefinite to (...) more definite states is the partition join operation at the set level that prefigures at the quantum level projective measurement as well as the formation of maximally-definite state descriptions by Dirac’s Complete Sets of Commuting Operators. This development is measured quantitatively by logical entropy at the set level and by quantum logical entropy at the quantum level. This follow-the-math approach supports the Literal Interpretation of QM—as advocated by Abner Shimony among others which sees a reality of objective indefiniteness that is quite different from the common sense and classical view of reality as being “definite all the way down”. (shrink)

Quantum Mechanics is a fundamental physical theory about atomic-scale processes. It was built between 1920 and 1940 by the most distinguished physicists of that time. The accordance between the predictions of the theory and experimental results is remarkable. The physical interpretation of its mathematical constructs, however, raised unprecedented controversies. Ontological, semantic, and epistemic vagueness abound in the orthodox interpretations and have resulted in serious misunderstandings that are often repeated in textbooks and elsewhere. In this work, we identify, (...) criticize, and clarify the most spread ones. (shrink)

Non-commuting quantities and hidden parameters – Wave-corpuscular dualism and hidden parameters – Local or nonlocal hidden parameters – Phase space in quantum mechanics – Weyl, Wigner, and Moyal – Von Neumann’s theorem about the absence of hidden parameters in quantum mechanics and Hermann – Bell’s objection – Quantum-mechanical and mathematical incommeasurability – Kochen – Specker’s idea about their equivalence – The notion of partial algebra – Embeddability of a qubit into a bit – (...) class='Hi'>Quantum computer is not Turing machine – Is continuality universal? – Diffeomorphism and velocity – Einstein’s general principle of relativity – „Mach’s principle“ – The Skolemian relativity of the discrete and the continuous – The counterexample in § 6 of their paper – About the classical tautology which is untrue being replaced by the statements about commeasurable quantum-mechanical quantities – Logical hidden parameters – The undecidability of the hypothesis about hidden parameters – Wigner’s work and и Weyl’s previous one – Lie groups, representations, and psi-function – From a qualitative to a quantitative expression of relativity − psi-function, or the discrete by the random – Bartlett’s approach − psi-function as the characteristic function of random quantity – Discrete and/ or continual description – Quantity and its “digitalized projection“ – The idea of „velocity−probability“ – The notion of probability and the light speed postulate – Generalized probability and its physical interpretation – A quantum description of macro-world – The period of the as-sociated de Broglie wave and the length of now – Causality equivalently replaced by chance – The philosophy of quantum information and religion – Einstein’s thesis about “the consubstantiality of inertia ant weight“ – Again about the interpretation of complex velocity – The speed of time – Newton’s law of inertia and Lagrange’s formulation of mechanics – Force and effect – The theory of tachyons and general relativity – Riesz’s representation theorem – The notion of covariant world line – Encoding a world line by psi-function – Spacetime and qubit − psi-function by qubits – About the physical interpretation of both the complex axes of a qubit – The interpretation of the self-adjoint operators components – The world line of an arbitrary quantity – The invariance of the physical laws towards quantum object and apparatus – Hilbert space and that of Minkowski – The relationship between the coefficients of -function and the qubits – World line = psi-function + self-adjoint operator – Reality and description – Does a „curved“ Hilbert space exist? – The axiom of choice, or when is possible a flattening of Hilbert space? – But why not to flatten also pseudo-Riemannian space? – The commutator of conjugate quantities – Relative mass – The strokes of self-movement and its philosophical interpretation – The self-perfection of the universe – The generalization of quantity in quantum physics – An analogy of the Feynman formalism – Feynman and many-world interpretation – The psi-function of various objects – Countable and uncountable basis – Generalized continuum and arithmetization – Field and entanglement – Function as coding – The idea of „curved“ Descartes product – The environment of a function – Another view to the notion of velocity-probability – Reality and description – Hilbert space as a model both of object and description – The notion of holistic logic – Physical quantity as the information about it – Cross-temporal correlations – The forecasting of future – Description in separable and inseparable Hilbert space – „Forces“ or „miracles“ – Velocity or time – The notion of non-finite set – Dasein or Dazeit – The trajectory of the whole – Ontological and onto-theological difference – An analogy of the Feynman and many-world interpretation − psi-function as physical quantity – Things in the world and instances in time – The generation of the physi-cal by mathematical – The generalized notion of observer – Subjective or objective probability – Energy as the change of probability per the unite of time – The generalized principle of least action from a new view-point – The exception of two dimensions and Fermat’s last theorem. (shrink)

The new logic of partitions is dual to the usual Boolean logic of subsets (usually presented only in the special case of the logic of propositions) in the sense that partitions and subsets are category-theoretic duals. The new information measure of logical entropy is the normalized quantitative version of partitions. The new approach to interpreting quantum mechanics (QM) is showing that the mathematics (not the physics) of QM is the linearized Hilbert space version of the mathematics of (...) partitions. Or, putting it the other way around, the math of partitions is a skeletal version of the math of QM. The key concepts throughout this progression from logic, to logical information, to quantum theory are distinctions versus indistinctions, definiteness versus indefiniteness, or distinguishability versus indistinguishability. The distinctions of a partition are the ordered pairs of elements from the underlying set that are in different blocks of the partition and logical entropy is defined (initially) as the normalized number of distinctions. The cognate notions of definiteness and distinguishability run throughout the math of QM, e.g., in the key non-classical notion of superposition (= ontic indefiniteness) and in the Feynman rules for adding amplitudes (indistinguishable alternatives) versus adding probabilities (distinguishable alternatives). (shrink)

Gravity remains the most elusive field. Its relationship with the electromagnetic field is poorly understood. Relativity and quantum mechanics describe the aforementioned fields, respectively. Bosons and fermions are often credited with responsibility for the interactions of force and matter. It is shown here that fermions factually determine the gravitational structure of the universe, while bosons are responsible for the three established and described forces. Underlying the relationships of the gravitational and electromagnetic fields is a symmetrical probability distribution of (...) fermions and bosons. Werner Heisenberg's assertion that the Schr\'f6dinger wave function and Heisenberg matrices do not describe one thing is confirmed. It is asserted that the conscious observation of Schr\'f6dinger's wave function never causes its collapse, but invariably produces the classical space described by the Heisenberg picture. As a result, the Heisenberg picture can be explained and substantiated only in terms of conscious observation of the Schr\'f6dinger wave function. Schr\'f6dinger\'92s picture is defined as information space, while Heisenberg\'92s picture is defined as classical space. B-theory postulates that although the Schr\'f6dinger picture and the Heisenberg picture are mathematically connected, the former is eternal while the latter is discrete, existing only as the sequence of discrete conscious moments. Inferences related to information-based congruence between physical and mental phenomena have long been discussed in the literature. Moreover, John Wheeler suggested that information is fundamental to the physics of the universe. However, there is a great deal of uncertainty about how the physical and the mental complement each other. Bishop Berkeley and Ernst Mach, to name two who have addressed the subject, simply reject the concept of the material world altogether. Professor Hardy defined physical reality as 'dubious and elusive'. It is proposed in this paper that physical reality, or physical instantiation in the classical space as described by Heisenberg picture is one thing with the consciousness. (shrink)

If you have enjoyed any of the 7 (seven) other books I have published over 20 years, including literally thousands of pages of mathematical and topological concepts, Python programs and conceptually expanding papers, please consider buying this book for $20.00 on google play books. -/- Introduction: -/- Though the following pages provide extensive exposition and dedicated descriptions of the phenomenological velocity formulas, theory and mystery, I thought it appropriate to write this introduction as a partial explanation for what phenomenal (...) velocity is, and describe, briefly its theory and applications. Phenomenological Velocity is a method for solving for something that ought cancel out with itself, but there are specific implicit forms for this thing that, “ought cancel out with itself,” namely the Lorentz coefficient ought cancel out with itself when applied to the height of a cone derived from the difference between the circumferences of two circles applied to the Pythagorean Theorem, or, more generally, the height implied by application of the Pythagorean theorem to the difference between two arc lengths’ equaling a third arc length. These difference equations are essential to conceptualizing differentiation, and in these further chapters, I demonstrate that the phenomenological velocity is, indeed the conditional derivative in the chapter, “Conditional Integral of Phenomenological Velocity.” The phenomenological velocity algebraic solution to the velocity within the Lorentz coefficient when applied to the height function in such a way that it ought cancel out with itself is both constructive mathematics and it employs the concept of, “bracketing,” - first introduced by Edmund Husserl in his writings on the phenomenological reduction. Phenomenological Velocity’s algebraic solution from the difference between two arc lengths applied to the Pythagorean Theorem to solve for a theoretical height (which is a projected distance in space), employs bracketing, because we, “set aside,” the existence of an undefined solution, namely due to the presence of necessitated complex analytical forms by the architecture of the equation, or the “mathetecture,” of the algebraic form. -/- With respect to theology, the phenomenological velocity is somehow symbolic of the creation itself; symbolic of creation due to the fact that we find the canceling out of the Lorentz coefficient as, “impotent,” non-existent or non-effecting to the mathetecture of the height function. However, via the modus-ponens work around to phenomenological velocity, which in itself does not require the complex field, but embeds implied complex field solutions to the equation while maintaining logical consistency, we find existence from non-existence. This is directly linguistically applicable to the concept of the big-bang, the resurrection of Yeshua the Messiah, and opens analogies for us to draw relationships between the, “fall,” of Adam and Eve as the generation of error, or the introduction of paradox, as we see the phallus representing paradox topologically. -/- The phenomenological velocity is a gestalt concept, relevant to cosmology, because we find that it is the perfect language-form for discussing dark matter. It does, however, require the reader to re-conceive or re-frame rather, some of the fundamental aspects of assumed physical reality like time, experience, solidity of dark matter, etc. We find the hidden dimension of phenomenological velocity to have been an overlooked aspect of mathematical physics by the researchers of Bell’s theorem and undoubtedly a host of other theorems. Thus, raising awareness about the real existence and necessitated reality of phenomenological velocity is in no way an endeavor deserving further procrastination by the scientific community, for doing so would be intellectually dishonest and further the propagation of incomplete or misleading theories on reality. -/- This work details how the Lorentz coefficient, when applied to the height of a cone in such a way as to cancel out with itself, permits the velocity variable to have a solution to it anyway, even though it ought cancel out with itself. This mathe-tecture, so to speak has consequences for complex analysis, and pave the way for, "transcendental relativity," building an adaptive framework for consciousness and physical reality. (shrink)

The text is a continuation of the article of the same name published in the previous issue of Philosophical Alternatives. The philosophical interpretations of the Kochen- Specker theorem (1967) are considered. Einstein's principle regarding the,consubstantiality of inertia and gravity" (1918) allows of a parallel between descriptions of a physical micro-entity in relation to the macro-apparatus on the one hand, and of physical macro-entities in relation to the astronomical mega-entities on the other. The Bohmian interpretation ( 1952) of quantum (...) class='Hi'>mechanics proposes that all quantum systems be interpreted as dissipative ones and that the theorem be thus derstood. The conclusion is that the continual representation, by force or (gravitational) field between parts interacting by means of it, of a system is equivalent to their mutual entanglement if representation is discrete. Gravity (force field) and entanglement are two different, correspondingly continual and discrete, images of a single common essence. General relativity can be interpreted as a superluminal generalization of special relativity. The postulate exists of an alleged obligatory difference between a model and reality in science and philosophy. It can also be deduced by interpreting a corollary of the heorem. On the other hand, quantum mechanics, on the basis of this theorem and of V on Neumann's (1932), introduces the option that a model be entirely identified as the modeled reality and, therefore, that absolutely reality be recognized: this is a non-standard hypothesis in the epistemology of science. Thus, the true reality begins to be understood mathematically, i.e. in a Pythagorean manner, for its identification with its mathematical model. A few linked problems are highlighted: the role of the axiom of choice forcorrectly interpreting the theorem; whether the theorem can be considered an axiom; whether the theorem can be considered equivalent to the negation of the axiom. (shrink)

In his entry on "Quantum Logic and Probability Theory" in the Stanford Encyclopedia of Philosophy, Alexander Wilce (2012) writes that "it is uncontroversial (though remarkable) the formal apparatus quantum mechanics reduces neatly to a generalization of classical probability in which the role played by a Boolean algebra of events in the latter is taken over the 'quantum logic' of projection operators on a Hilbert space." For a long time, Patrick Suppes has opposed this view (see, for (...) example, the paper collected in Suppes and Zanotti (1996). Instead of changing the logic and moving from a Boolean algebra to a non-Boolean algebra, one can also 'save the phenomena' by weakening the axioms of probability theory and work instead with upper and lower probabilities. However, it is fair to say that despite Suppes' efforts upper and lower probabilities are not particularly popular in physics as well as in the foundations of physics, at least so far. Instead, quantum logic is booming again, especially since quantum information and computation became hot topics. Interestingly, however, imprecise probabilities are becoming more and more popular in formal epistemology as recent work by authors such as James Joye (2010) and Roger White (2010) demonstrates. (shrink)

What is the proper metaphysics of quantum mechanics? In this dissertation, I approach the question from three different but related angles. First, I suggest that the quantum state can be understood intrinsically as relations holding among regions in ordinary space-time, from which we can recover the wave function uniquely up to an equivalence class (by representation and uniqueness theorems). The intrinsic account eliminates certain conventional elements (e.g. overall phase) in the representation of the quantum state. It (...) also dispenses with first-order quantification over mathematical objects, which goes some way towards making the quantum world safe for a nominalistic metaphysics suggested in Field (1980, 2016). Second, I argue that the fundamental space of the quantum world is the low-dimensional physical space and not the high-dimensional space isomorphic to the ``configuration space.'' My arguments are based on considerations about dynamics, empirical adequacy, and symmetries of the quantum mechanics. Third, I show that, when we consider quantum mechanics in a time-asymmetric universe (with a large entropy gradient), we obtain new theoretical and conceptual possibilities. In such a model, we can use the low-entropy boundary condition known as the Past Hypothesis (Albert, 2000) to pin down a natural initial quantum state of the universe. However, the universal quantum state is not a pure state but a mixed state, represented by a density matrix that is the normalized projection onto the Past Hypothesis subspace. This particular choice has interesting consequences for Humean supervenience, statistical mechanical probabilities, and theoretical unity. (shrink)

Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change this picture and show why it is helpful to consider (...) the instants of time as Fuzzy numbers. In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it. Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Para-consistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time. These, provides a new interpretation of Quantum Mechanics.More exactly what we see here is "Particle-Fuzzy time" interpretation of quantum Mechanics, in contrast to some other interpretations of Quantum Mechanics like " Wave-Particle" interpretation. At the end, we propound a question about the possible solution of a paradox in Physics, the contradiction between General Relativity and Quantum Mechanics. (shrink)

The mathematical formalism of quantum theory has been established for nearly a century, yet its physical foundations remain elusive. In recent decades, connections between quantum theory and information theory have garnered increasing attention. This study presents a physical derivation of the mathematical formalism quantum theory based on information-theoretic considerations in physical systems. We postulate that quantum systems are characterized by single independent adjustable variables. Utilizing this physical postulate along with the conservation of total probability, (...) we derive the standard Hilbert space formalism of quantum theory, including the Born probability rule. This comprehensive derivation of quantum theory offers a clear and concise physical foundation for the mathematical formalism of quantum mechanics. (shrink)

Quantum mechanics was reformulated as an information theory involving a generalized kind of information, namely quantum information, in the end of the last century. Quantum mechanics is the most fundamental physical theory referring to all claiming to be physical. Any physical entity turns out to be quantum information in the final analysis. A quantum bit is the unit of quantum information, and it is a generalization of the unit of classical information, a (...) bit, as well as the quantum information itself is a generalization of classical information. Classical information refers to finite series or sets while quantum information, to infinite ones. Quantum information as well as classical information is a dimensionless quantity. Quantum information can be considered as a “bridge” between the mathematical and physical. The standard and common scientific epistemology grants the gap between the mathematical models and physical reality. The conception of truth as adequacy is what is able to transfer “over” that gap. One should explain how quantum information being a continuous transition between the physical and mathematical may refer to truth as adequacy and thus to the usual scientific epistemology and methodology. If it is the overall substance of anything claiming to be physical, one can question how different and dimensional physical quantities appear. Quantum information can be discussed as the counterpart of action. Quantum information is what is conserved, action is what is changed in virtue of the fundamental theorems of Emmy Noether (1918). The gap between mathematical models and physical reality, needing truth as adequacy to be overcome, is substituted by the openness of choice. That openness in turn can be interpreted as the openness of the present as a different concept of truth recollecting Heidegger’s one as “unconcealment” (ἀλήθεια). Quantum information as what is conserved can be thought as the conservation of that openness. (shrink)

The paper follows the track of a previous paper “Natural cybernetics of time” in relation to history in a research of the ways to be mathematized regardless of being a descriptive humanitarian science withal investigating unique events and thus rejecting any repeatability. The pathway of classical experimental science to be mathematized gradually and smoothly by more and more relevant mathematical models seems to be inapplicable. Anyway quantum mechanics suggests another pathway for mathematization; considering the historical reality as (...) dual or “complimentary” to its model. The historical reality by itself can be seen as mathematical if one considers it in Hegel’s manner as a specific interpretation of the totality being in a permanent self-movement due to being just the totality, i.e. by means of the “speculative dialectics” of history, however realized as a theory both mathematical and empirical and thus falsifiable as by logical contradictions within itself as emprical discrepancies to facts. Not less, a Husserlian kind of “historical phenomenology” is possible along with Hegel’s historical dialectics sharing the postulate of the totality (and thus, that of transcendentalism). One would be to suggest the transcendental counterpart: an “eternal”, i.e. atemporal and aspatial history to the usual, descriptive temporal history, and equating the real course of history as with its alternative, actually happened branches of the regions of the world as with only imaginable, counterfactual histories. That universal and transcendental history is properly mathematical by itself, even in a neo-Pythagorean model. It is only represented on the temporal screen of the standard historiography as a discrete series of unique events. An analogy to the readings of the apparatus in quantum mechanics can be useful. Even more, that analogy is considered rigorously and logically as implied by the mathematical transcendental history and sharing with it the same quantity of information as an invariant to all possible alternative or counterfactual histories. One can involve the hypothetical external viewpoint to history (as if outside of history or from “God’s viewpoint to it), to which all alternative or counterfactual histories can be granted as a class of equivalence sharing the same information (i.e. the number choices, but realized in different sequence or adding redundant ones in each branch) being similar and even mathematically isomorphic to Feynman trajectories in quantum mechanics. Particularly, a fundamental law of mathematical history, the law of least choice of the real historical pathway is deducible from the same approach. Its counterpart in physics is the well-known and confirmed law of least action as far as the quantity of action corresponds equivocally to the quantity of information or that of number elementary historical choices. (shrink)

This is the first book in a two-volume series. The present volume introduces the basics of the conceptual foundations of quantum physics. It appeared first as a series of video lectures on the online learning platform Udemy.]There is probably no science that is as confusing as quantum theory. There's so much misleading information on the subject that for most people it is very difficult to separate science facts from pseudoscience. The goal of this book is to make (...) you able to separate facts from fiction with a comprehensive introduction to the scientific principles of a complex topic in which meaning and interpretation never cease to puzzle and surprise. An A-Z guide which is neither too advanced nor oversimplified to the weirdness and paradoxes of quantum physics explained from the first principles to modern state-of-the-art experiments and which is complete with figures and graphs that illustrate the deeper meaning of the concepts you are unlikely to find elsewhere. A guide for the autodidact or philosopher of science who is looking for general knowledge about quantum physics at intermediate level furnishing the most rigorous account that an exposition can provide and which only occasionally, in few special chapters, resorts to a mathematical level that goes no further than that of high school. It will save you a ton of time that you would have spent searching elsewhere, trying to piece together a variety of information. The author tried to span an 'arch of knowledge' without giving in to the temptation of taking an excessively one-sided account of the subject. What is this strange thing called quantum physics? What is its impact on our understanding of the world? What is ‘reality’ according to quantum physics? This book addresses these and many other questions through a step-by-step journey. The central mystery of the double-slit experiment and the wave-particle duality, the fuzzy world of Heisenberg's uncertainty principle, the weird Schrödinger's cat paradox, the 'spooky action at a distance' of quantum entanglement, the EPR paradox and much more are explained, without neglecting such main contributors as Planck, Einstein, Bohr, Feynman and others who struggled themselves to come up with the mysterious quantum realm. We also take a look at the experiments conducted in recent decades, such as the surprising "which-way" and "quantum-erasure" experiments. Some considerations on why and how quantum physics suggests a worldview based on philosophical idealism conclude this first volume. This treatise goes, at times, into technical details that demand some effort and therefore requires some basics of high school math (calculus, algebra, trigonometry, elementary statistics). However, the final payoff will be invaluable: Your knowledge of, and grasp on, the subject of the conceptual foundations of quantum physics will be deep, wide, and outstanding. Additionally, because schools, colleges, and universities teach quantum physics using a dry, mostly technical approach which furnishes only superficial insight into its foundations, this manual is recommended for all those students, physicists or philosophers of science who would like to look beyond the mere formal aspect and delve deeper into the meaning and essence of quantum mechanics. The manual is a primer that the public deserves. (shrink)

In this paper, the issues of computability and constructivity in the mathematics of physics are discussed. The sorts of questions to be addressed are those which might be expressed, roughly, as: Are the mathematical foundations of our current theories unavoidably non-constructive: or, Are the laws of physics computable?

Any computer can create a model of reality. The hypothesis that quantum computer can generate such a model designated as quantum, which coincides with the modeled reality, is discussed. Its reasons are the theorems about the absence of “hidden variables” in quantum mechanics. The quantum modeling requires the axiom of choice. The following conclusions are deduced from the hypothesis. A quantum model unlike a classical model can coincide with reality. Reality can be interpreted as (...) a quantum computer. The physical processes represent computations of the quantum computer. Quantum information is the real fundament of the world. The conception of quantum computer unifies physics and mathematics and thus the material and the ideal world. Quantum computer is a non-Turing machine in principle. Any quantum computing can be interpreted as an infinite classical computational process of a Turing machine. Quantum computer introduces the notion of “actually infinite computational process”. The discussed hypothesis is consistent with all quantum mechanics. The conclusions address a form of neo-Pythagoreanism: Unifying the mathematical and physical, quantum computer is situated in an intermediate domain of their mutual transformation. (shrink)

The quantum information introduced by quantum mechanics is equivalent to that generalization of the classical information from finite to infinite series or collections. The quantity of information is the quantity of choices measured in the units of elementary choice. The qubit can be interpreted as that generalization of bit, which is a choice among a continuum of alternatives. The axiom of choice is necessary for quantum information. The coherent state is transformed into a well-ordered series of (...) results in time after measurement. The quantity of quantum information is the ordinal corresponding to the infinity series in question. Number and being (by the meditation of time), the natural and artificial turn out to be not more than different hypostases of a single common essence. This implies some kind of neo-Pythagorean ontology making related mathematics, physics, and technics immediately, by an explicit mathematical structure. (shrink)

This work is a conceptual analysis of certain recent developments in the mathematical foundations of Classical and Quantum Mechanics which have allowed to formulate both theories in a common language. From the algebraic point of view, the set of observables of a physical system, be it classical or quantum, is described by a Jordan-Lie algebra. From the geometric point of view, the space of states of any system is described by a uniform Poisson space with transition (...) probability. Both these structures are here perceived as formal translations of the fundamental twofold role of properties in Mechanics: they are at the same time quantities and transformations. The question becomes then to understand the precise articulation between these two roles. The analysis will show that Quantum Mechanics can be thought as distinguishing itself from Classical Mechanics by a compatibility condition between properties-as-quantities and properties-as-transformations. -/- Moreover, this dissertation shows the existence of a tension between a certain "abstract way" of conceiving mathematical structures, used in the practice of mathematical physics, and the necessary capacity to specify particular states or observables. It then becomes important to understand how, within the formalism, one can construct a labelling scheme. The “Chase for Individuation” is the analysis of different mathematical techniques which attempt to overcome this tension. In particular, we discuss how group theory furnishes a partial solution. (shrink)

Most physics theories are deterministic, with the notable exception of quantum mechanics which, however, comes plagued by the so-called measurement problem. This state of affairs might well be due to the inability of standard mathematics to “speak” of indeterminism, its inability to present us a worldview in which new information is created as time passes. In such a case, scientific determinism would only be an illusion due to the timeless mathematical language scientists use. To investigate this (...) possibility it is necessary to develop an alternative mathematical language that is both powerful enough to allow scientists to compute predictions and compatible with indeterminism and the passage of time. We suggest that intuitionistic mathematics provides such a language and we illustrate it in simple terms. (shrink)

We discuss the mathematical structures that underlie quantum probabilities. More specifically, we explore possible connections between logic, geometry and probability theory. We propose an interpretation that generalizes the method developed by R. T. Cox to the quantum logical approach to physical theories. We stress the relevance of developing a geometrical interpretation of quantum mechanics.

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

I maintain that quantum mechanics is fundamentally about a system of N particles evolving in three-dimensional space, not the wave function evolving in 3N-dimensional space.

An isomorphism is built between the separable complex Hilbert space (quantum mechanics) and Minkowski space (special relativity) by meditation of quantum information (i.e. qubit by qubit). That isomorphism can be interpreted physically as the invariance between a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting another way for proving it, more concise and meaningful physically. Mathematically, the isomorphism means (...) the invariance to choice, the axiom of choice, well-ordering, and well-ordering “theorem” (or “principle”) and can be defined generally as “information invariance”. (shrink)

The paper portrays the influence of major philosophical ideas on the 1935 debates on quantum theory that reached their climax in the paper by Einstein, Podosky and Rosen, and describes the relevance of these ideas to the vast impact of the paper. I claim that the focus on realism in many common descriptions of the debate misses important aspects both of Einstein's and Bohr's thinking. I suggest an alternative understanding of Einstein's criticism of quantum mechanics as a (...) manifestation of the same methodological principles that served him in the construction of the special and the general theories of relativity. These principles address, in a very specific way, the relation of the theoretical mathematical representations to the represented physical systems. These ideas, I claim, played a key role in the influence of the paper on later works that changed our understanding of quantum theory despite the rejection of EPR's central conclusion. (shrink)

A homeomorphism is built between the separable complex Hilbert space (quantum mechanics) and Minkowski space (special relativity) by meditation of quantum information (i.e. qubit by qubit). That homeomorphism can be interpreted physically as the invariance to a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting at another way for proving it, more concise and meaningful physically. Furthermore, the conjecture (...) can be generalized and interpreted in relation to the pseudo-Riemannian space of general relativity therefore allowing for both mathematical and philosophical interpretations of the force of gravitation due to the mismatch of choice and ordering and resulting into the “curving of information” (e.g. entanglement). Mathematically, that homeomorphism means the invariance to choice, the axiom of choice, well-ordering, and well-ordering “theorem” (or “principle”) and can be defined generally as “information invariance”. Philosophically, the same homeomorphism implies transcendentalism once the philosophical category of the totality is defined formally. The fundamental concepts of “choice”, “ordering” and “information” unify physics, mathematics, and philosophy and should be related to their shared foundations. (shrink)

In their seeking of simplicity, scientists fall into the error of Whitehead's "fallacy of misplaced concreteness." They mistake their abstract concepts describing reality for reality itself--the map for the territory. This leads to dogmatic overstatements, paradoxes, and mysteries such as the deep incompatibility of our two most fundamental physical theories--quantum mechanics and general relativity. To avoid such errors, we should evoke Whitehead's conception of the universe as a universe-in-process, where physical relations perpetually beget new physical relations. Today, the (...) most promising interpretations of quantum mechanics exemplify this Whiteheadian idea, formalizing physical systems, and the universe itself, as ongoing histories of actualizations of potential states, where actual states and potential states exist in mutually implicative relation as two separate categories of reality—an idea first proposed by Aristotle and rehabilitated by Heisenberg. In these interpretations, the classical conception of a history as a derivative story about fundamental physical objects is reversed: the classical physical object becomes the derivative story about fundamental histories of quantum states. The consistent histories interpretation of Robert Griffiths and the decoherent histories interpretation of Roland Omnès are cardinal examples of this approach to quantum mechanics. Another example, the relational realist interpretation, begins with the decoherent histories approach and formalizes it explicitly as a Whiteheadian interpretation, taking his “algebraic method” and applying it to quantum mechanics via algebraic topology. This branch of mathematics can be thought of as a “de-concretized” geometry in that it focuses only on the logical relations among objects and regions (and relations of these relations) rather than the fixed magnitudes of lines, planes, and other such rigid intervals. It has all the robust logical structure of geometry yet allows for an elasticity of relations that makes topological mathematical structures inherently immune misplaced concretization. (shrink)

The main idea consists in researching the existence of certain characteristics of nature similar to human reasonability and purposeful actions, originating and rigorously inferable from the postulates of quantum mechanics as well as from those of special and general relativity. The pathway of the “free-will theorems” proved by Conway and Kochen in 2006 and 2009 is followed and pioneered further. Those natural reasonability and teleology are identified as a special subject called “God” and studyable by “quantum theology”, (...) a scientific counterpart of classical theology as far as the latter endeavors to justify rationally God (without quotation marks) postulated by religion, but meaning in the present study, first of all, Christianity. The suggested “quantum theology” is situated in the historical opposition and conflict of science and religion in Modernity and its reflection in Heidegger’s conception of “ontotheology”. The conception of “ontomathematics” introduced in previous papers to unite and unify physics, mathematics, and philosophy is reinterpreted in the present context to be conservatively generalized in a way to include “quantum theology”. Two conceptions, “locality” and “nonlocality”, originating initially from physics and especially, from theory of entanglement and quantum information, are also generalized ontomathematically, and thus in relation to the newly introduced “quantum theology”. The “quantum theology” subject of “God” is juxtaposed with God of religion and billions of believers all over the world. Husserl’s conception of “philosophy as a rigorous science” is considered to be generalized now to theology as quantum theology, particularly by the phenomenon (in the sense of his “phenomenology”) of “God”, or by an “epoché” to whether God exists or not. The research of the phenomenon of “God” is extended to the conception of the “totality” being inherent for philosophy, especially for classical German philosophy preceding Husserl’s phenomenology. Those sequences for philosophy implied by the introduction of quantum theology are investigated further, on the pathway of ontomathematics, also in relation to what “God” should mean for today’s physics and mathematics. The option and research field of “experimental quantum theology” is discussed as a direct corollary from quantum theology though being sacrilegious as for classical theology. The concluding section reflects in a more loose way on the relation of “God” for quantum theology to God for religion and billions of believers all over the world. (shrink)

The main algebraic foundations of quantum mechanics are quickly reviewed. They have been suggested since the birth of this theory till up to last years. They are the following ones: Heisenberg-Born- Jordan’s (1925), Weyl’s (1928), Dirac’s (1930), von Neumann’s (1936), Segal’s (1947), T.F. Jordan’s (1986), Morchio and Strocchi’s (2009) and Buchholz and Fregenhagen’s (2019). Four cases are stressed: 1) the misinterpretation of Dirac’s algebraic foundation; 2) von Neumann’s ‘conversion’ from the analytic approach of Hilbert space to the algebraic (...) approach of the rings of operators; 3) Morchio and Strocchi’s improving Dirac’s analogy between commutators and Poisson Brackets into an exact equivalence; 4) the recent foundation of quantum mechanics upon the algebra of perturbations. Some considerations on alternating theoretical importance of the algebraic approach in the history of QM are offered. The level of formalism has increased from the mere introduction of matrices to group theory and C*-algebras but has not led to a definition of the foundations of physics; in particular, an algebraic formulation of QM organized as a problem-based theory and an exclusive use of constructive mathematics is still to be discovered. (shrink)

The concept of quantum information is introduced as both normed superposition of two orthogonal sub-spaces of the separable complex Hilbert space and in-variance of Hamilton and Lagrange representation of any mechanical system. The base is the isomorphism of the standard introduction and the representation of a qubit to a 3D unit ball, in which two points are chosen. The separable complex Hilbert space is considered as the free variable of quantum information and any point in it (a wave (...) function describing a state of a quantum system) as its value as the bound variable. A qubit is equivalent to the generalization of ‘bit’ from the set of two equally probable alternatives to an infinite set of alternatives. Then, that Hilbert space is considered as a generalization of Peano arithmetic where any unit is substituted by a qubit and thus the set of natural number is mappable within any qubit as the complex internal structure of the unit or a different state of it. Thus, any mathematical structure being reducible to set theory is re-presentable as a set of wave functions and a subspace of the separable complex Hilbert space, and it can be identified as the category of all categories for any functor represents an operator transforming a set (or subspace) of the separable complex Hilbert space into another. Thus, category theory is isomorphic to the Hilbert-space representation of set theory & Peano arithmetic as above. Given any value of quantum information, i.e. a point in the separable complex Hilbert space, it always admits two equally acceptable interpretations: the one is physical, the other is mathematical. The former is a wave function as the exhausted description of a certain state of a certain quantum system. The latter chooses a certain mathematical structure among a certain category. Thus there is no way to be distinguished a mathematical structure from a physical state for both are described exhaustedly as a value of quantum information. This statement in turn can be utilized to be defined quantum information by the identity of any mathematical structure to a physical state, and also vice versa. Further, that definition is equivalent to both standard definition as the normed superposition and in-variance of Hamilton and Lagrange interpretation of mechanical motion introduced in the beginning of the paper. Then, the concept of information symmetry can be involved as the symmetry between three elements or two pairs of elements: Lagrange representation and each counterpart of the pair of Hamilton representation. The sense and meaning of information symmetry may be visualized by a single (quantum) bit and its interpretation as both (privileged) reference frame and the symmetries of the Standard model. (shrink)

In this paper I argue that we can solve the interpretation problem of quantum mechanics and the question of ontology of Quantum Field Theory on the basis of simple metaphysical position: The connection of the phase space with the ancient Theory of Logi of Beings, which is, by giving ontological meaning to the entities which "live" at the phase space, the Hamiltonian or Lagrangian formalism. There is a physical subject of such functions and it is the logos (...) of a being. Therefore we can refer to the logical space as the total sum of logi of being. The result of this position is that we can attribute to the wave function a physical meaning, a special case of logos of a being and also give an ontological meaning at a quantum field. The developed metaphysical scheme can interpret the quantum paradoxes, by using the commonly accepted mathematical formalism. It can also interpret certain issues of Quantum Field Theory, although further study of this topic is necessary. (shrink)

By the relational realist interpretation of wave function collapse, the quantum mechanical actualization of potentia is defined as a decoherence-driven process by which each actualization (in “orthodox” terms, each measurement outcome) is conditioned both by physical and logical relations with the actualities conventionally demarked as “environmental” or external to that particular outcome. But by the relational realist interpretation, the actualization-in-process is understood as internally related to these “enironmental” data per the formalism of quantum decoherence. The concept of “actualization (...) via wave function collapse” is accounted for solely by virtue of these presupposed logical relations—the same logical relations otherwise presupposed by the scientific method itself—and thus requires no “external” physical-dynamical trigger: e.g., the Gaussian hits of GRW, acts of conscious observation, etc. By the relational realist interpretation, it is the physical and logical relations among quantum actualities (quantum “final real things”) that drives the process of decoherence and, via the latter, the logically conditioned actualization of potentia. In this regard, the relational realist interpretation of quantum mechanics is a praxiological interpretation; that is, these physical and logical relations are ontologically active relations, contributing not just to the epistemic coordination of quantum actualizations, but to the process of actualization itself. (shrink)

The paper discusses the philosophical conclusions, which the interrelation between quantum mechanics and general relativity implies by quantum measure. Quantum measure is three-dimensional, both universal as the Borel measure and complete as the Lebesgue one. Its unit is a quantum bit (qubit) and can be considered as a generalization of the unit of classical information, a bit. It allows quantum mechanics to be interpreted in terms of quantum information, and all physical processes (...) to be seen as informational in a generalized sense. This implies a fundamental connection between the physical and material, on the one hand, and the mathematical and ideal, on the other hand. Quantum measure unifies them by a common and joint informational unit. Quantum mechanics and general relativity can be understood correspondingly as the holistic and temporal aspect of one and the same, the state of a quantum system, e.g. that of the universe as a whole. (shrink)

An essay on the connection between the mind-body-problem and quantum mechanics.

The paper justifies the following theses: The totality can found time if the latter is axiomatically represented by its “arrow” as a well-ordering. Time can found choice and thus information in turn. Quantum information and its units, the quantum bits, can be interpreted as their generalization as to infinity and underlying the physical world as well as the ultimate substance of the world both subjective and objective. Thus a pathway of interpretation between the totality via time, order, choice, (...) and information to the substance of the world is constructed. The article is based only on the well-known facts and definitions and is with no premises in this sense. Nevertheless it is naturally situated among works and ideas of Husserl and Heidegger, linked to the foundation of mathematics by the axiom of choice, to the philosophy of quantum mechanics and information. (shrink)

Look! Up in the bookshelf! Is it science? Is it science-fiction? No, it's Super Science: strange visitor from the future who can be everywhere in the universe and everywhen in time, can change the world in a single bound and who - disguised as a mild mannered author - fights for truth, justice and the super-scientific way. -/- Though I put a lot of hard work into this book, I can't take all the credit. I believe that the whole universe (...) - everything on Earth and in space plus everything in the past, present, and future - is entangled and unified. Everybody is part of this unity, so anybody could have written the ideas in this book. It turned out to be me simply because I've got intense curiosity about the book's contents, enough persistence and imagination to combine science with topics like religion and philosophy, and enough spare time to assemble all the pre-existing pieces in space and time (my contribution to the book is like putting together the pieces of a big jigsaw puzzle). -/- This book, with its vast collection of scientific fact and study results, presents some fascinating theories and is an expansive journey through my research. The topic will appeal to the science-minded reader who is open to speculating on how conditions may evolve in the future, perhaps questioning the very foundations of our place in the universe. This book is not written as a single story but is a collection of 9 articles written in the first half of 2022. Each chapter of this book is presented as a research paper. There's the abstract, the introduction, the keywords, the body of the work divided into sections, and a reference section. Though this might turn some readers off, I'm a member of ResearchGate, a community of researchers. So it isn't surprising that I've presented this book this way. Each article is meant to be self-contained and well explained in plain English. As a result, some explanations appear in several of the articles. -/- Please be patient when you encounter jargon and mathematics - I've tried to keep these to a minimum but they're bound to put in an appearance in a book that's largely about science (and I have compiled an enormous amount of intricate research for this project, hopefully impressing with the organization). Quotes from a range of scientists and icons in the industry should add further fascination to the descriptions, inspiring the reader into more of an openness to speculating on the distant future. There's a lot to absorb here but understanding the future . . . It Don't Come Easy (just ask Ringo Starr who once dreamed he was an alien living on another planet in the future. -/- Contents -/- Special Relativity's Consequences For General Relativity, Quantum Mechanics And Quantum Gravity (Can Science And The Paranormal Coexist?) -/- Intergalactic Travel and Riemann Hypothesis - featuring Dark Matter, Dark Energy, Higgs Boson, Higgs Field, Electroweak Interaction, No Big Bang, Other Dimensions, Plus Other Physics and Mathematics -/- New Perspectives On Life, Death, Cancer and Covid-19 Arising From An Artificially Intelligent, Non-probabilistic Universe -/- Unipositional Interpretation Of Quantum Mechanics Means Entanglement Occurring Simultaneously With Gravitational Slingshots Reduces Problems Associated With Spaceflight -/- Unipositional Interpretation Of Quantum Mechanics Explains Time Dilation, Updates Cosmology -/- WHERE DID EVERYTHING COME FROM – Combining Science, Mathematics, Computers, Religion, Philosophy, Relativity, Quantum Physics, Darwinism, and a Podcast to Reach One Person’s Plausible Ideas -/- Thoughts on Artificial Intelligence and the Origin of Life Resulting from General Relativity, with Neo-Darwinist Reference to Human Evolution and Mathematical Reference to Cosmology -/- Planet 9 and Black Hole Versus Relativity’s Precession and Dark Matter -/- THE WORLD’S REAL-LIFE EXPERIMENTS WITH COVID-19 AND PHYSICS ALTER SOCIETY AND GLOBAL ECONOMICS . (shrink)

Our conscious minds exist in the Universe, therefore they should be identified with physical states that are subject to physical laws. In classical theories of mind, the mental states are identified with brain states that satisfy the deterministic laws of classical mechanics. This approach, however, leads to insurmountable paradoxes such as epiphenomenal minds and illusionary free will. Alternatively, one may identify mental states with quantum states realized within the brain and try to resolve the above paradoxes using the (...) standard Hilbert space formalism of quantum mechanics. In this essay, we first show that identification of mind states with quantum states within the brain is biologically feasible, and then elaborating on the mathematical proofs of two quantum mechanical no-go theorems, we explain why quantum theory might have profound implications for the scientific understanding of one's mental states, self identity, beliefs and free will. (shrink)