The nature of time is perceived by intellectuals variedly. An attempt is made in this paper to reconcile such varied views in the light of the Upanishads and related Indian spiritual and philosophical texts. The complex analysis of modern mathematics is used to represent the nature and presentation physical and psychological times so differentiated. Also the relation between time and energy is probed using uncertainty relations, forms of energy and phases of matter.

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 – 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)

This paper presents an analysis of the sorites paradox for collective nouns and gradable adjectives within the framework of classical logic. The paradox is explained by distinguishing between qualitative and quantitative representations. This distinction is formally represented by the use of a different mathematical model for each type of representation. Quantitative representations induce Archimedean models, but qualitative representations induce non-Archimedean models. By using a non-standard model of \ called \, which contains infinite and infinitesimal numbers, the (...) two paradoxes are shown to have distinct structures. The sorites paradox for collective nouns arises from the use of infinite numbers, whereas the sorites paradox for gradable adjectives arises from the use of infinitesimal numbers. Each paradox can be traced to a different source of vagueness. The sorites paradox for collective nouns is caused by \, and the sorites paradox for gradable adjectives is caused by \ \. If correct, this analysis implies that infinite and infinitesimal numbers are cognitively real, and that they play a role in the semantic interpretation of natural language. (shrink)

Information can be considered as the most fundamental, philosophical, physical and mathematical concept originating from the totality by means of physical and mathematical transcendentalism (the counterpart of philosophical transcendentalism). Classical and quantum information, particularly by their units, bit and qubit, correspond and unify the finite and infinite. As classical information is relevant to finite series and sets, as quantum information, to infinite ones. A fundamental joint relativity of the finite and infinite, of the external and internal is to be investigated. (...) The corresponding invariance is able to define physical action and its quantity only on the basis of information and especially: on the relativity of classical and quantum information. The concept of transcendental time, an epoché in relation to the direction of time arrow can be defined. Its correlate is that information invariant to the finite and infinite, therefore unifying both classical and quantum information. (shrink)

The usual representation of quantum algorithms, limited to the process of solving the problem, is physically incomplete. We complete it in three steps: extending the representation to the process of setting the problem, relativizing the extended representation to the problem solver to whom the problem setting must be concealed, and symmetrizing the relativized representation for time reversal to represent the reversibility of the underlying physical process. The third steps projects the input state of the representation, where the problem solver is (...) completely ignorant of the setting and thus the solution of the problem, on one where she knows half solution. Completing the physical representation shows that the number of computation steps required to solve any oracle problem in an optimal quantum way should be that of a classical algorithm endowed with the advanced knowledge of half solution. (shrink)

The basic dynamical quantities of classical mechanics, such as position, linear momentum, angular momentum and energy, obtain their fundamental epistomological content by means of their intimate relationship to the symmetries of the space-time manifold which is the arena of physics. The program of canonical quantization can be understood as a two stage process. The first stage is Bohr's Correspondence Principle, whereby the basic dynamical quantities of the quantum theory are required to retain precisely the same relationship to the symmetries of (...) the space-time manifold as do their classical counterparts, thereby preserving their epistemological, as well as measurement-theoretic, significance. Having so identified the basic dynamical variables, functions of these may now be used to identify the subtler symmetries of the proper canonical group. The second and determining stage of the quantization program requires the establishment of a correspondence between some of these subtler symmetries of the classical theory and related symmetries of the quantum theory, the relationship being determined by a common algebraic form for their defining functions. (shrink)

This book brings together papers from a conference that took place in the city of L'Aquila, 4–6 April 2019, to commemorate the 10th anniversary of the earthquake that struck on 6 April 2009. Philosophers and scientists from diverse fields of research debated the problem that, on 6 April 1922, divided Einstein and Bergson: the nature of time. For Einstein, scientific time is the only time that matters and the only time we can rely on. Bergson, however, believes that scientific time (...) is derived by abstraction, even in the sense of extraction, from a more fundamental time. The plurality of times envisaged by the theory of Relativity does not, for him, contradict the philosophical intuition of the existence of a single time. But how do things stand today? What can we say about the relationship between the quantitative and qualitative dimensions of time in the light of contemporary science? What do quantum mechanics, biology and neuroscience teach us about the nature of time? The essays collected here take up the question that pitted Einstein against Bergson, science against philosophy, in an attempt to reverse the outcome of their monologue in two voices, with a multilogue in several voices. (shrink)

It is common for visitors to have rich and varied experiences in the limited space of a classical Chinese garden. This leads to the sense that the garden’s scale is much larger than it really is. A main reason for this perceptual bias is the gardener’s manipulation of visual information. Most studies have discussed this phenomenon in terms of qualitative description with fragmented perspectives taken from static points, without considering ambient visual information or continuously changing observation points. A general (...) question arises, then, on why depth perception can vary from one observation point to another along a garden path. To better understand the spatial experience in classical Chinese gardens, this study focused on variations in perceived depth among different observation points and aimed to identify influential visual information through psychophysical experimentation. As stimuli for the experiment, panoramic photos of Liu garden were taken from three positions at Lvyin Pavilion. Considering the effects of pictorial visual cues on depth perception, the photos were processed to create 18 kinds of stimuli. Two tasks were presented to the participants. In Task 1, 71 participants were asked to rate the depth value of the garden using the magnitude estimation method in a cave automatic virtual environment. Statistical analysis of Task 1 revealed that depth values differed significantly among different viewpoints. In Task 2, participants were asked to compare 18 stimuli and 3D images presented on three connected monitors and to judge the depth of the garden using the adjustment method. The results of Task 2 again showed that depth values differed significantly among different viewpoints. In both tasks, ambient information significantly influenced depth perception. (shrink)

Various understandings and definitions of time will be reviewed. The nature and structure of time will be reviewed and the concepts of time and passage of time will be refreshed. The fundamental role played by energy and four natural forces in the actions, reactions and interactions concerning matter, anti-matter, energy in space and time will be critically analyzed. The reality how time is constructed during the construction of materials will be presented and discussed. The classical and quantum ideas in this (...) regard will be comprehensively studied. How these ideas will give us a fresh insight about the nature, structure and role of time in the construction of materials through natural scientific and manmade processes will be highlighted. The relations among matter, anti-matter, energy and time will be freshly stated. The milli-, micro-, nano, pico-, femto-, atto-times will be qualitatively analyzed considering physical, inorganic, organic and bio-materials and their construction and structure. The physics of timelessness also will be put forward. -/- . (shrink)

Xiong was the originator and founder of Modern Confucianism (xin ruxue ) as well as one of the first Chinese philosophers, who developed his own system of thought, which was based upon classical Confucian concepts and, at the same time, adjusted to the conditions of the New Era. His contribution to the development of modern Chinese philosophy can also be demonstrated in a much broader, general sense. Xiong Shili, namely, also represents one of the first theoretically qualified intellectuals of his (...) age, who didn’t advocate the conservative elitist nationalism, but at the same time opposed the prevailing trends of iconoclastic negation of tradition. Even later on, during the predomination of the so-called communist ideologies, Xiong rather consequently persisted in his—for that time completely unacceptable— standpoints.Thus Xiong Shili, remaining a real Confucian scholar at a time, when Confucianism was everything else but the prevailing state doctrine, doubtless represents a real traditional sage. For him, Confucianism was not solely the predominating system of thought, to which he should formally conform in order to achieve the realization of some privileges and private interests. He was a Confucian scholar by following his own inner conviction, or, with other words, he was a Confucian “inner sage.” Hereby,we encounter an extremely rare kind of Confucian scholars, namely of those, who did not remain limited to a paper-wrapped reproduction of idealistic principles of Confucian thought, but who also tried to perform them in their own life. Xiong’s personal moral was the ethics of a Confucian scholar, who can be a gentle, subtle thinker and a steadfast, consequent rebel at the same time. (shrink)

We chart the ways in which closure properties of consequence relations for uncertain inference take on different forms according to whether the relations are generated in a quantitative or a qualitative manner. Among the main themes are: the identification of watershed conditions between probabilistically and qualitatively sound rules; failsafe and classicality transforms of qualitatively sound rules; non-Horn conditions satisfied by probabilistic consequence; representation and completeness problems; and threshold-sensitive conditions such as `preface' and `lottery' rules.

The concept of time-coarsened density matrix for open systems has frequently featured in equilibrium and non-equilibrium statistical mechanics, without being probed as to the detailed consequences of the time averaging procedure. In this work we introduce and prove the need for a selective and non-uniform time-sampling, whose form depends on the properties of the bath. It is also applicable when an open microscopic sub-system is coupled to another finite system. By use of a time-periodic minimal coupling model between these two (...) systems, we present detailed quantitative consequences of time coarsening, which include initial state independence of equilibration, deviations from long term averages, their environment size dependence and the approach to classicality, as measured by a Leggett–Garg type inequality. An interacting multiple qubit model affords comparison between the time integrating procedure and the more conventional environment tracing method. (shrink)

We present a description of the Stern–Gerlach type experiments using only the concepts of classical electrodynamics and the Newton’s equations of motion. The quantization of the projections of the spin (or the projections of the magnetic dipole) is not introduced in our calculations. The main characteristic of our approach is a quantitative analysis of the motion of the magnetic atoms at the entrance of the magnetic field region. This study reveals a mechanism which modifies continuously the orientation of the (...) magnetic dipole of the atom in a very short time interval, at the entrance of the magnetic field region. The mechanism is based on the conservation of the total energy associated with a magnetic dipole which moves in a non uniform magnetic field generated by an electromagnet. A detailed quantitative comparison with the (1922) Stern–Gerlach experiment and the didactical (1967) experiment by J.R. Zacharias is presented. We conclude, contrary to the original Stern–Gerlach statement, that the classical explanations are not ruled out by the experimental data. (shrink)

The paper discuss the application of qualitative and quantitative techniques in political studies. It describes the classical proposal of Johan Galtung, known as trilateral science, which invites to the permanent contrast to confirm, validate and accept facts and ideas; then it explores Grounded Theory as a mechanism to achieve and explore data in order to identify a possible dialogue with experimental methodology. Finally, it shows social capital as a case study to demonstrate the relevance of multi-methodological applications. El (...) propósito de este texto es discutir la aplicación de técnicas cualitativas y cuantitativas en los estudios políticos. Para ello, se describe la propuesta clásica de Johan Galtung, conocida como trilateralismo, que invita al contraste permanente con el fin de confirmar, validar y aceptar hechos e ideas; luego, se busca explorar la Grounded Theory como mecanismo de consecución y exploración de datos con el fin de identificar un posible diálogo con la metodología experimental. Por último, se aborda el capital social como objeto de estudio que demuestra la pertinencia de aplicaciones multimetodológicas. (shrink)

This paper investigates the behavior of conformal fluctuations of space-time geometry that are admissible under the quantized version of Einstein's general relativity. The approach to quantum gravity is via path integrals. It is shown that considerable simplification results when only the conformal degrees of freedom are considered under this scheme, so much so that it is possible to write down a formal kernel in the most general case where the space-time contains arbitrary distributions of particles with no other interaction except (...) gravity. The behavior of this kernel near the classical space-time singularity then shows that quantum fluctuations inevitably diverge near the singularity. It is shown further that the root cause of this divergence lies in the fact that the Green's function for the conformally invariant scalar wave equation diverges at the singularity. The limitations on the validity of classical general relativity near the space-time singularity are discussed and it is argued that the notion of singularity itself needs to be radically modified once the quantum effects are taken into account. (shrink)

This thesis introduces a new theoretical tool to explore the notion of time and temporal order in quantum mechanics: the relativistic quantum "clock" framework. It proposes novel thought experiments showing that proper time can display quantum features, e.g. when a "clock" runs different proper times in superposition. The resulting new physical effects can be tested in near-future laboratory experiments (with atoms, molecules and photons as "clocks"). The notion of time holds the key to the regime where quantum theory and (...) general relativity overlap, which has not been directly tested yet and remains largely unexplored by the theory. The framework also applies to scenarios in which causal relations between events become non-classical and which were previously considered impossible to address without refuting quantum theory. The relativistic quantum "clock" framework offers new insights into the foundations of quantum theory and general relativity. (shrink)

Using linear invariant operators in a constructive way we find the most general thermal density operator and Wigner function for time-dependent generalized oscillators. The general Wigner function has five free parameters and describes the thermal Wigner function about a classical trajectory in phase space. The contour of the Wigner function depicts an elliptical orbit with a constant area moving about the classical trajectory, whose eccentricity determines the squeezing of the initial vacuum.

The relation between Emanuel Swedenborg and Immanuel Kant has been the subject of many discussions. The chief aim of this paper is not to elucidate this question from an historical point of view, but to compare the teachings of the two thinkers, as those teachings have come to us. Kant's "Träme eines Geistersehers" embodies a very unfavourable opinion about Swedenborg. It is a curious circumstance, that this judgement is not based on decisive arguments. On the contrary, Swedenborg's fundamental doctrines about (...) the existence of a spiritual world and the communication between the living and the dead, are accepted by Kant as plausible. Du Prel and others have concluded, that Kant was a Swedenborgian in his heart, and that his negative attitude was due to the fear of losing his scientific reputation. A careful consideration of the two philosophical systems does not tend to bear out this opinion; nevertheless, such a comparative study is very instructive. In the mental development of the two thinkers there are remarkable analogies. Both were occupied with the great problems of God and the human soul; and both were disappointed by the leading philosophical and theological doctrines of their days. To Swedenborg those doctrines seemed to lead straightforwardly to naturalism and atheism. Kant was struck by the diversity of the opinions expressed and by the succession of heterogeneous doctrines without lasting results. But the reactions of the two men in these circumstances were different. In his cosmological and anatomical works Swedenborg aims at acquiring a comprehensive view of the Universe, in which view God and the soul should obtain their proper places. When he had reached the age of about 55 years, a crisis set in, which he described as "the opening of his spiritual senses". From that time he could see the spiritual world and speak with its inhabitants; he could study the workings of God and of the soul with the help of living experience. Kant raised the question, whether there are departments of knowledge in which certainty is attainable, and what is the ground of this certainty. His answer is, that the fundamental propositions of mathematical physics are absolutely certain. The ground lies in the fact, that these propositions are not derived from experience, but that they are "synthetic judgments a priori". They express the workings of the "categories" and "forms of intuition". by means of which the mind constructs, out of a chaos of sense-impressions, the ordered universe of science. Of objects to which these propositions do not apply, e.g. God and the soul, no certain knowledge is possible. This precludes the knowledge of "another world", fundamentally different from our ordinary world. So there seems to be an irreconcilable opposition between the teachings of Kant and of Swedenborg, But further considerations tend to lessen this contrast. Notwithstanding his own teaching, Kant accepted a life after death and he even speculated on it. If we follow this example, we come to remarkable conclusions. It is reasonable to suppose, that the spirits, who have been men, use the same categories as we do. Then out of the impressions which reach them, they will construct a world built on the same pattern as our earthly world. So life before and after death will not be very different. And this is precisely Swedenborg's teaching. This may be confirmed by the experiences of our dream-life. In dreams, our mind out of different impressions builds a world closely resembling our ordinary world. The spiritual world, as described by Swedenborg, presents many analogies with the world of our dreams. Now it is a very remarkable circumstance, that modern physics has been under the necessity of modifying the system of categories as described by Kant. In quantum mechanics the connection between cause and effect is less stringent than in classical mechanics. This adds fresh interest to the study of a system like that of Swedenborg, where quantitative laws are largely replaced by qualitative laws. (shrink)

In this study, we build on a recent social data scientific mapping of Danish environmentalist organizations and activists during the COVID-19 lockdown in order to sketch a distinct genre of digital social research that we dub a quali-quantitative micro-history of ideas in real-time. We define and exemplify this genre by tracing and tracking the single political idea and activist slogan of grøn genstart across Twitter and other public–political domains. Specifically, we achieve our micro-history through an iterative and mutual attuning (...) between computational and netnographic registers and techniques, in ways that contribute to the nascent field of computational anthropology. By documenting the serial ways in and different steps through which our inquiry was continually fed and enhanced by crossing over from ethnographic observation to computational exploration, and vice versa, we offer up our grøn genstart case account as exemplary of wider possibilities in this line of inquiry. In particular, we position the genre of micro-history of ideas in real-time within the increasingly wide and heterogeneous space of digital social research writ large, including its established concerns with ‘big and broad’ social data, the repurposing of computational ‘interface’ techniques for socio-cultural research, as well as diverse aspirations for deploying digital data within novel combinations of qualitative and quantitative methods. (shrink)

Richard Feynman has claimed that anti-particles are nothing but particles `propagating backwards in time'; that time reversing a particle state always turns it into the corresponding anti-particle state. According to standard quantum field theory textbooks this is not so: time reversal does not turn particles into anti-particles. Feynman's view is interesting because, in particular, it suggests a nonstandard, and possibly illuminating, interpretation of the CPT theorem. In this paper, we explore a classical analog of Feynman's view, in the context of (...) the recent debate between David Albert and David Malament over time reversal in classical electromagnetism. (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)

Time, along with concepts as space and matter, is bound to be a central concept of any physical theory. The chapter first discusses how time is treated similarly in quantum and classical theories. It then provides a few references on time‐reversal. The chapter discusses three chosen authors' (Paul Busch, Jan Hilgevoord and Jos Uffink) clarifications of uncertainty principles in general. Next, the chapter follows Busch in distinguishing three roles for time in quantum physics. They are external time, intrinsic time and (...) observable time. It also provides a brief discussion on time operators, in particular Pauli's influential proof. Finally, the chapter talks about time‐energy uncertainty principles with intrinsic times. (shrink)

The present article analyses the qualitative and quantitative parameters of the execution of foreign policy in the Constitution of the Republic of Lithuania. It should be noted that the matters of foreign policy were on the brink of constitutional regulation for a long time. The powers of institutions of the state in the field of foreign relations were established laconically by the Constitutions of first and second “waves” of establishment of constitutionalism. It was argued that the choices of (...) decisions and the execution of foreign policy were determined by political reasons and the law could only fix the results of that policy. That is why these constitutions should be seen as establishing quantitative characteristics of action of the state institutions in the field of foreign policy. As a result of the changes in the concept of the Constitution and the general recognition of the relevance of constitutional regulation from the middle of the twentieth century the constitutional acts began to define not only the powers of certain state institutions in the field of the foreign policy but also the objectives and principles of this policy. These objectives and principles are qualitative parameters of the action of state institutions, which are mandatory constitutional requirements to all subjects engaged in foreign policy. From a qualitative standpoint, the powers of the state institutions can be exercised only by taking the constitutional objectives into account and by respecting the Constitution. The Constitution establishing both qualitative and quantitative characteristics of the execution of foreign policy becomes an actual basis of this policy. It is unlawful to execute foreign policy without complying with its objectives and constitutional principles. The institutions of constitutional review have the powers to determine the constitutionality of legal acts related to the execution of foreign policy. Constitutional regulations previous to the Constitution of the Republic of Lithuania of 1992 only defined the powers of state institutions, i.e. the quantitative parameters of their action. The Lithuanian Constitution of 1992 also established the constitutional objectives and principles of foreign policy. This area of constitutional regulation has been enhanced by the participation of the Republic of Lithuania in the European Union. The author suggests analysing this matter as an autonomous constitutional principle and not only as a case of participation in international organisations or an integral element of the principle of geopolitical orientation. Constitutional objectives and principles of foreign policy, as well as the other provisions of the Constitution regarding the exercise of foreign policy, are interpreted in constitutional jurisprudence. In cases concerning the constitutionality of international treaties, laws and other legislative acts directly related to the exercise of foreign policy, the Constitutional Court reveals the content and meaning of the qualitative and quantitative constitutional parameters of foreign policy. Despite the fragmented nature of the case law one can see the precise contours of the foreign policy system. (shrink)

The dichotomy between the qualitative and the quantitative has been a classic throughout the history of science. As will be seen, this dichotomy permeates all ontological levels of reality. In this work, phenomenological examples potentially related to semiosis are presented at the different levels established by Mario Bunge and Josep Ferrater Mora, contrasting the qualitative categorizations with the quantifiable physical reality. Likewise, the need to continue in the quantification of the biosemiotic and linguistic studies will be presented, (...) while, in contrast, the need to establish a qualitative framework in the little-addressed study of technosemiotics will be raised, of potential interest given the notable advances that are expected in communication systems for inert artifacts in the next years. In short, in the thesis defended here the qualitative precedes the quantitative in the defining path of science. (shrink)

Time is absolute in standard quantum theory and dynamical in general relativity. The combination of both theories into a theory of quantum gravity leads therefore to a “problem of time”. In my essay, I investigate those consequences for the concept of time that may be drawn without a detailed knowledge of quantum gravity. The only assumptions are the experimentally supported universality of the linear structure of quantum theory and the recovery of general relativity in the classical limit. Among the consequences (...) are the fundamental timelessness of quantum gravity, the approximate nature of a semiclassical time, and the correlation of entropy with the size of the Universe. (shrink)

In this article I expound an understanding of the quantum mechanics of so-called “indistinguishable” systems in which permutation invariance is taken as a symmetry of a special kind, namely the result of representational redundancy. This understand- ing has heterodox consequences for the understanding of the states of constituent systems in an assembly and for the notion of entanglement. It corrects widespread misconceptions about the inter-theoretic relations between quantum mechanics and both classical particle mechanics and quantum field theory. The most striking (...) of the heterodox consequences are: that fermionic states ought not always to be considered entangled; it is possible for two fermions or two bosons to be discerned using purely monadic quantities; and that fermions may always be so discerned. (shrink)

The problem of time’s arrow is (roughly) to understand why macroscopic physical processes typically evolve in a specific direction (the one we call “the future”) even though the underlying laws of physics describing the individual microscopic systems are time-reversal invariant. The standard answer to this problem is given by Boltzmann’s explanation of the II law of thermodynamics: a classical system starting in a non-equilibrium state spontaneously (i.e. with a high level of probability) tends towards equilibrium, thus implementing an irreversible process. (...) However, this explanation has two drawbacks: 1. it needs a further assumption on the entropy of the initial state of the universe (past hypothesis); 2. microscopic systems (e.g. molecules in a box) should be represented as quantum states and not classical states. In this talk, I want to propose a different hypothesis to explain the origin of time’s arrow, based on quantum mechanics, specifically on decoherence theory. Differently from isolated systems, open quantum systems described by decoherence theory show irreversible behavior, as they evolve towards decoherence and von Neumann entropy increase. Is this behavior a sign of genuine irreversibility? And, if so, can this be linked to thermodynamic irreversibility? (shrink)

We discuss the issue of quantum-classical transition in a system of a single particle with and without external potential. This is done by elaborating the notion of self-trapped wave function recently developed by the author. For a free particle, we show that there is a subset of self-trapped wave functions which is particle-like. Namely, the spatially localized wave packet is moving uniformly with undistorted shape as if the whole wave packet is indeed a classical free particle. The length of the (...) spatial support of the wave packet is given by the Compton wavelength so that the wave packet is more localized for particle with larger mass. Whereas for a particle of mass m in a macroscopic external potential, we show that the time needed by the corresponding self-trapped wave function to depart from a classical trajectory is of the order ∼m 2 c/ℏ. We argue that it is the Compton wavelength that matters and not the de Broglie wavelength as in conventional semiclassical approach. (shrink)

It has often been suggested that retrocausality offers a solution to some of the puzzles of quantum mechanics: e.g., that it allows a Lorentz-invariant explanation of Bell correlations, and other manifestations of quantum nonlocality, without action-at-a-distance. Some writers have argued that time-symmetry counts in favour of such a view, in the sense that retrocausality would be a natural consequence of a truly time-symmetric theory of the quantum world. Critics object that there is complete time-symmetry in classical physics, and yet no (...) apparent retrocausality. Why should the quantum world be any different? This note throws some new light on these matters. I call attention to a respect in which quantum mechanics is different, under some assumptions about quantum ontology. Under these assumptions, the combination of time-symmetry without retrocausality is unavailable in quantum mechanics, for reasons intimately connected with the differences between classical and quantum physics (especially the role of discreteness in the latter). Not all interpretations of quantum mechanics share these assumptions, however, and in those that do not, time-symmetry does not entail retrocausality. (shrink)

I consider a quantum system that possesses key features of quantum shape dynamics and show that the evolution of wave-packets will become increasingly classical at late times and tend to evolve more and more like an expanding classical system. At early times however, semiclassical effects become large and lead to an exponential mismatch of the apparent scale as compared to the expected classical evolution of the scale degree of freedom. This quantum inflation of an emergent and effectively classical (...) system, occurs naturally in the quantum shape dynamics description of the system, while it is unclear whether and how it might arise in a constrained Hamiltonian quantization. (shrink)

Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and intermediate-scale systems are on the horizon, capable of calculating numeric results or simulating physical systems far beyond what humans can do by hand. However, to be commercially viable, they must surpass what our wildly successful, highly advanced classical computers can already do. At the same time, those classical (...) computers continue to advance, but those advances are now constrained by thermodynamics, and will soon be limited by the discrete nature of atomic matter and ultimately quantum effects. Technological advances benefit both quantum and classical machinery, altering the competitive landscape. Can we build quantum computing systems that out-compute classical systems capable of some $10^{30}$ logic gates per month? This article will discuss the interplay in these competing and cooperating technological trends. (shrink)

Time is often said to play in quantum mechanics an essentially different role from position: whereas position is represented by a Hermitian operator, time is represented by a c-number. This discrepancy has been found puzzling and has given rise to a vast literature and many efforts at a solution. In this paper it is argued that the discrepancy is only apparent and that there is nothing in the formalism of quantum mechanics that forces us to treat position and time differently. (...) The apparent problem is caused by the dominant role point particles play in physics and can be traced back to classical mechanics. (shrink)

We propose a solution to the problem of time for systems with a single global Hamiltonian constraint. Our solution stems from the observation that, for these theories, conventional gauge theory methods fail to capture the full classical dynamics of the system and must therefore be deemed inappropriate. We propose a new strategy for consistently quantizing systems with a relational notion of time that does capture the full classical dynamics of the system and allows for evolution parametrized by an equitable internal (...) clock. This proposal contains the minimal temporal structure necessary to retain the ordering of events required to describe classical evolution. In the context of shape dynamics (an equivalent formulation of general relativity that is locally scale invariant and free of the local problem of time) our proposal can be shown to constitute a natural methodology for describing dynamical evolution in quantum gravity and to lead to a quantum theory analogous to the Dirac quantization of unimodular gravity. (shrink)

The Riemannian manifold structure of the classical (i.e., Einsteinian) space-time is derived from the structure of an abstract infinite-dimensional separable Hilbert space S. For this S is first realized as a Hilbert space H of functions of abstract parameters. The space H is associated with the space of states of a macroscopic test-particle in the universe. The spatial localization of state of the particle through its interaction with the environment is associated with the selection of a submanifold M of realization (...) H. The submanifold M is then identified with the classical space (i.e., a space–like hypersurface in space-time). The mathematical formalism is developed which allows recovering of the usual Riemannian geometry on the classical space and, more generally, on space and time from the Hilbert structure on S. The specific functional realizations of S are capable of generating spacetimes of different geometry and topology. Variation of the length-type action functional on S is shown to produce both the equation of geodesics on M for macroscopic particles and the Schrödinger equation for microscopic particles. (shrink)

Time is often said to play in quantum mechanics an essentially different role from position: whereas position is represented by a Hermitian operator, time is represented by a c-number. This discrepancy has been found puzzling and has given rise to a vast literature and many efforts at a solution. In this paper it is argued that the discrepancy is only apparent and that there is nothing in the formalism of quantum mechanics that forces us to treat position and time differently. (...) The apparent problem is caused by the dominant role point particles play in physics and can be traced back to classical mechanics. (shrink)

It is difficult to find agreement on what constitutes perceiving.at Rovereto, Italy. The term is used in a wide array of domains ranging from psychology to physiology to aesthetics, and over time it has also acquired diverse connotations within various disciplines. Current perceptual science, however, even when it deals with qualitative aspects of experience, for example phenomena of lightness and colour, almost exclusively explains them in terms of primary qualities or stimuli quantitatively understood. The fact that science treats (...) class='Hi'>qualitative experiences in terms of stimuli is important, because almost nothing of phenomenal perception as such is quantitative in nature. The paper argues for a qualitative science of perceiving, its methodology, its laws, and its possible developments. (shrink)

This paper considers the possibility that nonrelativistic quantum mechanics tells us that Nature cares about time reversal. In a classical world we have a fundamentally reversible world that appears irreversible at higher levels, e.g., the thermodynamic level. But in a quantum world we see, if I am correct, a fundamentally irreversible world that appears reversible at higher levels, e.g., the level of classical mechanics. I consider two related symmetries, time reversal invariance and what I call ‘Wigner reversal invariance.’ Violation of (...) the first is interesting, for not only would it fly in the face of the usual story about temporal symmetry, but it also appears to imply (as I’ll explain) that time is ‘handed’, or as some have misleadingly said in the literature, ‘anisotropic’. Violation of the second is, as I hope to show, even more interesting. The paper also contains a discussion of two mostly neglected topics: what it means to say time is handed and what warrants such an attribution to time. (shrink)

The renewed interest in the foundations of quantum statistical mechanics in recent years has led us to study John von Neumann’s 1929 article on the quantum ergodic theorem. We have found this almost forgotten article, which until now has been available only in German, to be a treasure chest, and to be much misunderstood. In it, von Neumann studied the long-time behavior of macroscopic quantum systems. While one of the two theorems announced in his title, the one he calls the (...) “quantum H-theorem,” is actually a much weaker statement than Boltzmann’s classical H-theorem, the other theorem, which he calls the “quantum ergodic theorem,” is a beautiful and very non-trivial result. It expresses a fact we call “normal typicality” and can be summarized as follows: For a “typical” finite family of commuting macroscopic observables, every initial wave function ψ0 from a micro-canonical energy shell so evolves that for most times t in the long run, the joint probability distribution of these observables obtained from ψ is close to.. (shrink)

The two-state-vector formalism presents a time-symmetric approach to the standard quantum mechanics, with particular importance in the description of experiments having pre- and post-selected ensembles. In this paper, using the correspondence limit of the quantum harmonic oscillator in the two-state-vector formalism, we produce harmonic oscillators that possess a classical behavior while having a complex-valued position and momentum. This allows us to discover novel effects that cannot be achieved otherwise. The proposed classical behavior does not describe the classical physics in the (...) usual sense since this behavior is subjected to the feature that only after the final measurement is performed, as a boundary condition, the complex-valued classical effects occur between the initial and the final boundary conditions. This classical behavior breaks down if one does not follow the decided boundary conditions during the experiment, since otherwise, one will contradict the impossibility of retrocausality. (shrink)

Quantum Theory, similar to Relativity Theory, requires a new concept of space-time, imposed by a universal constant. While velocity of lightcnot being infinite calls for a redefinition of space-time on large and cosmological scales, quantization of action in terms of a finite, i.e. non vanishing, universal constanthrequires a redefinition of space-time on very small scales. Most importantly, the classical notion of “time”, as one common continuous time variable and nature evolving continuously “in time”, has to be replaced by an infinite (...) manifold of transition rates for discontinuous quantum transitions. The fundamental laws of quantum physics, commutation relations and quantum equations of motion, resulted from Max Born’s recognition of the basic principle of quantum physics:To each change in nature corresponds an integer number of quanta of action. Action variables may only change by integer values ofh, requiring all other physical quantities to change by discrete steps, “quantum jumps”. The mathematical implementation of this principle led to commutation relations and quantum equations of motion. The notion of “point” in space-time looses its physical significance; quantum uncertainties of time, position, just as any other physical quantity, are necessary consequences of quantization of action. (shrink)

Using a model quantum clock, I evaluate an expression for the time of a nonrelativistic quantum particle to transit a piecewise geodesic path in a background gravitational field with small spacetime curvature (gravity gradient), in the case that the apparatus is in free fall. This calculation complements and extends an earlier one (Davies 2004) in which the apparatus is fixed to the surface of the Earth. The result confirms that, for particle velocities not too low, the quantum and classical transit (...) times coincide, in conformity with the principle of equivalence. I also calculate the quantum corrections to the transit time when the de Broglie wavelengths are long enough to probe the spacetime curvature. The results are compared with the calculation of Chiao and Speliotopoulos (2003), who propose an experiment to measure the foregoing effects. (shrink)

Although the rapid growth of digital data and computationally advanced methods in the social sciences has in many ways exacerbated tensions between the so-called ‘quantitative’ and ‘qualitative’ approaches, it has also been provocatively argued that the ubiquity of digital data, particularly online data, finally allows for the reconciliation of these two opposing research traditions. Indeed, a growing number of ‘qualitatively’ inclined researchers are beginning to use computational techniques in more critical, reflexive and hermeneutic ways. However, many of these (...) claims for ‘quali-quantitative’ methods hinge on a single technique: the network graph. Networks are relational, allow for the questioning of rigid categories and zooming from individual cases to patterns at the aggregate. While not refuting the use of networks in these studies, this paper argues that there must be other ways of doing quali-quantitative methods. We first consider a phenomenon which falls between quantitative and qualitative traditions but remains elusive to network graphs: the spread of information on Twitter. Through a case study of debates about nuclear power on Twitter, we develop a novel data visualisation called the modulation sequencer which depicts the spread of URLs over time and retains many of the key features of networks identified above. Finally, we reflect on the role of such tools for the project of quali-quantitative methods. (shrink)

It has been suggested that some of the puzzles of QM are resolved if we allow that there is retrocausality in the quantum world. In particular, it has been claimed that this approach offers a path to a Lorentz-invariant explanation of Bell correlations, and other manifestations of quantum "nonlocality", without action-at-a-distance. Some writers have suggested that this proposal can be supported by an appeal to time-symmetry, claiming that if QM were made "more time-symmetric", retrocausality would be a natural consequence. Critics (...) object that there is complete time-symmetry in classical physics, and yet no apparent retrocausality. Why should QM be any different? In this note I call attention to a respect in which QM is different, under some assumptions about quantum ontology. Under these assumptions, the option of time-symmetry without retrocausality is not available in QM, for reasons intimately connected with the fundamental differences between classical and quantum physics (especially the role of discreteness in the latter). (shrink)

ABSTRACTThe emergence of dimensional analysis in the early nineteenth century involved a redefinition of the pre-existing concepts of homogeneity and dimensions, which entailed a shift from a qualitative to a quantitative conception of these notions. Prior to the nineteenth century, these concepts had been used as criteria to assess the soundness of operations and relations between geometrical quantities. Notably, the terms in such relations were required to be homogeneous, which meant that they needed to have the same geometrical (...) dimensions. The latter reflected the nature of the quantities in question, such as volume vs area. As natural philosophy came to encompass non-geometrical quantities, the need arose to generalize the concept of homogeneity. In 1822, Jean Baptiste Fourier consequently redefined it to be the condition an equation must satisfy in order to remain valid under a change of units, and the ‘dimension' correspondingly became the power of a conversion factor. When these innovations eventually found an echo in France and Great Britain, in the second half of the century, tensions arose between the former, qualitative understanding of dimensions as reflecting the nature of physical quantities, and the new, quantitative conception based on unit conversion and measurement. The emergence of dimensional analysis thus provides a case study of how existing rules and concepts can find themselves redefined in the context of wider conceptual changes; in the present case this redefinition involved a generalization, but also a shift in meaning which led to conceptual tensions. (shrink)

The imprints left by quantum mechanics in classical (Hamiltonian) mechanics are much more numerous than is usually believed. We show that the Schrödinger equation for a nonrelativistic spinless particle is a classical equation which is equivalent to Hamilton’s equations. Our discussion is quite general, and incorporates time-dependent systems. This gives us the opportunity of discussing the group of Hamiltonian canonical transformations which is a non-linear variant of the usual symplectic group.

The tension between the generality of approach in causally-driven quantitative educational research and the individuality of particular cases is exemplified in the types of reasoning employed. Unlike the scientific search for antecedents, still popular in some forms of educational research, investigating particular persons and policies necessarily requires a form of practical reasoning. In order to ease this tension between qualitative and quantitative research, this essay asks questions as to what is to be described and how this is (...) to be done. Responding to these questions, it is argued, necessarily draws attention to a range of ethical issues often ignored. (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 aim of this paper is to reconcile the two modes of description of macrosystems, i.e., to remove certain inconsistencies between the classical phenomenological and the quantum-theoretical descriptions of a macrosystem. Starting from Ludwig's formulation of a general framework for classical theories and his ansatz for a compatibility condition between the quantum theoretical and the classical mode of description for a macrosystem, we try to make clear what the “classical content” of many-body quantum theory really is. It is shown that (...) this classical content may be described by a certain “observable,” i.e., an operator-valued measure over the Borel sets of the classical trajectory space. There exists a reduced time evolution within this classical content which has the structure of a true semigroup in case of an irreversible classical time evolution. (shrink)

We give a partial answer to the question whether the Schrödinger equation can be derived from the Newtonian mechanics of a particle in a potential subject to a random force. We show that the fluctuations around the classical motion of a one dimensional harmonic oscillator subject to a random force can be described by the Schrödinger equation for a period of time depending on the frequency and the energy of the oscillator. We achieve this by deriving the postulates of Nelson’s (...) stochastic formulation of quantum mechanics for a random force depending on a small parameter. We show that the same result applies to small potential perturbations around the harmonic oscillator. We also show that the noise spectrum can be chosen to obtain the result for all oscillator frequencies for fixed mass. We discuss heuristics to generalize the result for a particle in one dimension in a potential where the motion can be described using action-angle variables. The main motivation of this paper is to provide a step for constructing a Newtonian theory which would approximately reproduce quantum mechanics both in unitary evolution and measurement regimes. (shrink)

The Arabic documentary papyri are precious wit- nesses to the day-to-day written Arabic of their time. These texts exhibit consider- able variation in grammar and orthography. Classical Arabic and the prescriptive attitudes of the Arabic grammarians traditionally provided the lens through which the earliest documents of the Islamic period have been read. Since Classical Ara- bic was only fully canonized in the tenth century, approaching the early Arabic papyri, and the variation attested in them, through this standard is anachronistic. This (...) article seeks to understand the language of these documents on their own terms. It employs a quantitative approach to investigate the nominal case system, focusing on the form of ʾab in construct, producing a fine-grained analysis of how inflection operated in early documentary Arabic, and attempts to account for points of divergence within a historical and sociolinguistic framework. (shrink)