This useful anthology comprises seventy-nine selections arranged under three headings. Part I is titled "Ancient and Classical Ideas of Space"; part II, "The Classical and Ancient Concepts of Time"; part III, "Modern Views of Space and Time and their Anticipations." According to the general editors of the Boston series, R. S. Cohen and Marx W. Wartofsky, Capek’s choice of contents was governed by the desire to show that "parts of our view of nature greatly and mutually (...) influence other parts, and that our conception of the world keeps evolving. Thus, ideas of time intertwine with ideas of space, and both with ideas of matter and force." F. M. Cornford’s essays, "The Invention of Space" and "The Elimination of Time by Parmenides," introduce parts I and II respectively. In part I, while Descartes, Pascal, Gassendi, Newton, etc., speak for themselves, the ancients and medievals are given other mouthpieces—Duhem’s monumental Le système du monde, for Plato, Aristotle, and the medievals; C. Bailey, for Leucippus, Epicurus and Lucretius; Koyré, Höffding, Jammer, for the period from Bradwardine to William Gilbert. On the subject of time, however, both ancient and classical authors are allowed to express their opinions in their own words, with the understandable exception of the Stoics. Part III begins with the prerelativistic critique of Newton as well as the well-known Clarke-Leibniz discussion on the nature of space and time. This third part, however, is dominated largely by the implications of Einstein’s general and special relativity theories. For instance, we have Minkowski’s "Union of Space and Time." Four items, at least, are devoted to the twin-paradox. Some argue for a static, subjective, or even idealistic conception of space-time whereas positivists like Frank attack Sir James Jeans’ and other idealistic interpretations of relativity as instances of meaningless metaphysics. Part III concludes with Weyl’s objectivistic interpretation of quantum-mechanical indeterminacy. While it is difficult to find an anthology that will please all readers or teachers, this work goes far towards dealing comprehensively with the subject of space and time. As Cohen and Wartofsky note, what is distinctive of Capek’s approach within the field of philosophy of nature and its history is that "he is greatly appreciative of Bergson, James, Peirce and Whitehead" and though influenced by them, he is also critical because of the "understanding of the philosophical import that contemporary physics brings into our picture of the world." In a lengthy introduction, the editor explains his rationale for each item he includes. In general this is very helpful, but in some instances the suggested historical connections are misleading at best, if not simply false or questionable. Einstein for instance is said to have "rejected any absolute frame of reference which would be a substrate of absolutely simultaneous events... within the context of Michelson’s vain search for the absolute motion of the earth." This seems to imply—as many others have claimed—that the negative results of the ether-drift experiment influenced Einstein in formulating his relativity theory, whereas historians have pointed out that if Einstein referred to the experiment, it would have to be as a confirmation of his theory, since he did not learn of the results obtained by Michelson and Morley until after the publication of his revolutionary paper in 1905. Though there are other generalizations in the introduction which might be open to dispute, Capek’s prefatory remarks are in general helpful, and the essay collection as a whole stands on its own feet. It is valuable, if for no other reason, that a number of the selections appear in English translation for the first time.—A.B.W. (shrink)

There is an apparent tension in Shepherd’s accounts of space and time. Firstly, Shepherd explicitly claims that we know that the space and time of the unperceived world exist because they cause our phenomenal experience of them. Secondly, Shepherd emphasizes that empty space and time do not have the power to effect any change in the world. My proposal is that for Shepherd time has exactly one causal power: to provide for the continued (...) existence of self-same or changing objects. Because Shepherd takes causation to be a relation whereby two objects combine to form a third, their effect, whenever we perceive a continually existing object, since time is a proper part of such objects, our perception of time is caused by time itself. Likewise, space’s causal power is to provide for the possibility of the motion or rest of objects, and so when we perceive objects with space as a proper part, we come into causal contact with space. (shrink)

The Dimensions of Difference examines space, time, and bodies in the works of three contemporary women directors and four continental philosophers, leading to a new approach to the question of sexual difference and its place within film criticism.

This collection of essays is unlike others in the field of African studies, for it is based on three very precisely delineated focal points: a particular geographical region, the sub-Sahara; specific modes of cultural production, literature and cinema; and a focus on works of French expression. This three-fold approach to exploring the relationships between power and culture in a non-Western environment greatly contributes to making this book unique from a variety of perspectives: African, Francophone and postcolonial studies, as well as (...) cross-disciplinary, cultural, transnational and diasporic studies. Moreover, the book offers deft and innovative analyses that move beyond the rhetoric of crises on the African continent we so very often hear of, so as to present a critical reflection on the subject at hand that is specific to the sub-Sahara and at the same time intimately linked to global culture, economy and politics. The authors' three-fold approach also presupposes that disciplinary compartmentalization increases power conflicts in academia. If only in part, compartmentalization is the result of antagonistic and competitive relations between specialization and multidisciplinary education. This book is thus a modest attempt at presenting an alternative to excessively fixed and homogeneous academic frontiers while considering that disciplinary expertise remains a must. Keeping in mind that an increasing number of scholars in Anglophone Postcolonial studies and Francophone African studies have been attempting for quite some time now to open interstices and build crossroads that can better connect them to each other, keeping in mind that these scholars work at revealing mechanisms by which any antagonistic discourses can mix, influence, act upon or react to one another, this book seeks to take a constructive step in establishing enduring grounds for multidisciplinary, cross-disciplinary and transnational academic research and collaboration. (shrink)

Tractatus Logico-Pilosophicus, the only book published during Ludwig Wittgenstein's lifetime , has since attracted the imagination of generations of philosophers as a work of great philosophical genius. Nonetheless, even today, more than eighty years later, philosophers are struggling to reconcile its diverse themes within a single, coherent picture. The present work is an attempt to meet this challenge. ;Wittgenstein considered the single proposition as a concrete model for the fact. The challenge is to show how a system of propositions can (...) serve as a model of reality. My work concentrates on three pillars of the logic of the Tractatus: the picture theory, negation as "reversal of sense," the independence of elementary propositions. Using a simple scenario of the ordering of objects or letters on a line, I examine the conflict generated by the attempt to adequately accommodate all three themes and offer my own solution. My solution brings implications to the problem of negation and to the Tractatus's thesis that the possibilities of logical space are spanned by the possible configurations of the ultimately simple objects. One such implication, which stands in contrast to the common reading, is that in atomic facts we have 'complex objects' as constituents. ;The resolution offered, furthermore, exposes an intrinsic difficulty in the Tractatus, for which I have reserved the term arbitrary choice. The difficulty is manifested in the lack of assurance---from the perspective of logic---that a concept-word will preserve its 'standard' meaning when it is reapplied or when its scope of application varies. In this I uncover the seed of central themes in Wittgenstein's later philosophy, e.g. the rule-following argument, as present already in the Tractatus. ;In the concluding chapter, I suggest a new account for the nature of the proposition by connecting the analysis offered in the Tractatus with the subject of time and motion. The picture with which the work concludes then considers language not as corresponding to reality, but as engaged or synchronized with reality---if you will, it is a picture of language and reality in a dance. (shrink)

In Time, Existential Presence and the Cinematic Image, Sam B. Girgus relates Laura Mulvey's theory of 'delayed cinema' to ideas on time and the relationship to the other in the writings of Jean-Luc Nancy, Emmanuel Levinas and Julia Kristeva, among others. The sustained tension in film between, in Mulvey's phrase, 'stillness and the moving image' enacts a drama of existential emergence. The stillness of the framed image in relation to the moving image opens 'free' cinematic time and (...) space for a fresh engagement with crucial ethical and cultural issues. With close readings of films such as The Bicycle Thieves, Two Days, One Night, The Three Burials of Melquiades Estrada, The Revenant and The Age of Innocence, this book proposes a fresh approach to reading film in the context of emerging existential presence and the ethical imperative. (shrink)

A “frame of reference” is a standard relative to which motion and rest may be measured; any set of points or objects that are at rest relative to one another enables us, in principle, to describe the relative motions of bodies. A frame of reference is therefore a purely kinematical device, for the geometrical description of motion without regard to the masses or forces involved. A dynamical account of motion leads to the idea of an “inertial frame,” (...) or a reference frame relative to which motions have distinguished dynamical properties. For that reason an inertial frame has to be understood as a spatial reference frame together with some means of measuring time, so that uniform motions can be distinguished from accelerated motions. The laws of Newtonian dynamics provide a simple definition: an inertial frame is a reference-frame with a time-scale, relative to which the motion of a body not subject to forces is always rectilinear and uniform, accelerations are always proportional to and in the direction of applied forces, and applied forces are always met with equal and opposite reactions. It follows that, in an inertial frame, the center of mass of a system of bodies is always at rest or in uniform motion. It also follows that any other frame of reference moving uniformly relative to an inertial frame is also an inertial frame. For example, in Newtonian celestial mechanics, taking the “fixed stars” as a frame of reference, we can determine an inertial frame whose center is the center of mass of the solar system; relative to this frame, every acceleration of every planet can be accounted for as a gravitational interaction with some other planet in accord with Newton 's laws of motion. (shrink)

In Newtonian physics, all phenomena take place in absolute space, which is a fixed scenario, and are referred to absolute time, which rules all processes. Motion is governed by a set of basic differential equations, and it is possible, at least in principle, to deduce future events from present initial conditions.

This article describes the debate about space and time in the early modern period focusing on the exchange between Gottfried Leibniz and Isaac Newton. It provides a brief account of Galileo's critique of medieval cosmology, the finite, two-sphere cosmos with fixed places as well as a beginning and an end in time, the related account of motion as finite and in need of an external agent, and the too-limited use of geometry in mechanics. The article reviews (...) in some detail the achievements of Leibniz and Newton in order to make clear the differences in their views about space and time, construed in mathematical, metaphysical, and physical terms as they emerged in the Leibniz/Clarke correspondence. (shrink)

The genesis of space and time is investigated within the rotational-monadic paradigm. It is established that the essence of the phenomenon of space is revealed through the dialectical synthesis of its two aspects — ideal and material, where the material aspect is represented by the metaphysical construct of protomonad. It is shown that basic physical distinctions such as motion, mass, gravitation find a meaningful hermeneutic through the material aspect of space, which has a purely discrete (...) structure, while the contradiction about finitude — infinity is resolved by juxtaposing metaphysical and ontic spaces, where the Universe is represented as an “egg”. The analysis of temporality is preceded by remarks on the relational and substantive concepts of time, consideration of the discreteness-continuity dilemma, and criticism of the absolutization of discreteness in the temporality representation. It is argued that discreteness and continuity are combined dialectical oppositions through which the temporal reality is actualized, where continuity is hidden from observation in the metaphysical world and discreteness is manifested explicitly in the physical world. Three dimensions of time — Present, Past and Future — are discussed, as a result of which it is stated that in the primary way time is found as an attribute of consciousness and only in the secondary way it correlates with phenomenological reality. New differentiations of time are revealed: interval Present, embracing as a universum other moduses of the Present, and two- component time in the form of cyclic and linear components which allow us to make a justified positive conclusion about the existence of transcendental subjectivity, being the basis of absolute temporality. (shrink)

A discussion of Einstein's great theory of the universe, the theory of relativity, covering the factors of space, motion, time, energy, inertia, and gravity.

In view of the primacy assigned to the 'present' in traditional metaphysics, in terms of the ways in which questions about existence are expressed, the following discussion takes the question of the temporalizing of the present as its theme. This involves unravelling the historical traces of the thought of the present as a finite, closed, objective point of a successive continuum of discrete moments (a real oscillation between the now and the not-now) by returning to the phenomenological sense of the (...) present as the stretching out of an opening – the 'living Present' (lebendige Gegenwart) – which bears its continuity of presence and non-presence within itself (without restriction to linearity). The transition itself suggests something like a quantum-leap and, in another sense, it also extends beyond the bounds of this simile (and the discontinuity that is implied) by evoking the image of a 'twist' or a 'turn.’ In order to grasp the significance of this turn we shall first examine – re turn to – its main obstacle: the concept of time as a linear and corpuscular continuum. The traditional model of time as a succession of 'now-points' (a notion that 1 still infects discourse on temporality) has always undermined our understanding of 'presence' as that which maintains itself (abides) through succession. In effect, presence must be 'maintained' [maintenant] within the 'now.' Yet, if the 'now' is constantly shifting into non-being through its replacement by a new 'now' then presence must be infused with its own negation and a certain discontinuity. How is it possible, then, to speak of the 'persistence' of 'identity' as something unitary (simultaneous with itself) existing through plurality and successive fragmentation into non-being? Furthermore, in reference to motion, what is entailed in the possibility of experiencing the transition of a selfsame (particular) object from one spatial location to another: how is it that the object 'endures' through its spatial and temporal transition? Since antiquity the question of simultaneity has been taken for granted – generally being consigned to mere spatial models.. (shrink)

Contemporary psychiatry faces serious challenges because it has failed to incorporate accumulated knowledge from basic neuroscience, neurophilosophy, and brain–mind relation studies. As a consequence, it has limited explanatory power, and effective treatment options are hard to come by. A new conceptual framework for understanding mental health based on underlying neurobiological spatial-temporal mechanisms of mental disorders (already gained by the experimental studies) is beginning to emerge.

This book presents fresh interpretations of Gottfried Leibniz's theories of time, space, and the relativity of motion, based on a thorough examination of Leibniz's manuscripts as well as his published papers. These are analysed in historical context, but also with an eye to their contemporary relevance.

The most reliable source for a reconstruction of Galileo's progress toward a science of motion is the series of undated fragmentary notes on that subject preserved in Codex A of the Galilean manuscripts at Florence. A gathering of such fragments was published by Favaro in the National Edition of Galileo's works, following the Discorsi. The more sophisticated fragments are clearly associated with the composition of that work, and show a definite and consistent understanding of acceleration. Eliminating those, it will (...) be found that the earlier notes fall into recognizable groups. First, there are some that refer to “moment of gravity”, or to the impetus of a body along a line of descent, and are associated with the discussion of inclined planes in De motu. Second, some refer to descent along arcs and chords of circles, associated with Galileo's letter of 29 November 1602 to Guido Ubaldo. These first two groups of notes do not explicitly refer to accelerated motion, and should not be assumed to do so implicity, where such an assumption can be avoided. (shrink)

The disciplinary enterprises engaged in the study of consciousness now extend beyond their original paradigms providing additional knowledge toward an overall understanding of the fundamental meaning and scope of consciousness. A new transdisciplinary domain has resulted from the syncretism of several approaches bringing about a new paradigm. The background for this overarching enterprise draws from a variety of traditions. In this paper however elaboration is restricted to the quantum-mechanical account in David Bohm’s theoretical work in relation to his ideas about (...) “active information”, “protointelligence”, and “non-locality”. This leads to an adapted version of Bohm’s thesis concerning the implicate order and explicate order of the Universe - the Impression Order and the Expression Order, respectively. On this view, the Universe is formed on an actual-material level, the apparent properties of things, and a potential-material level, a constant process of becoming that exerts an attractive force on the present. The central thesis emerges from a radical reformulation of certain core concepts that transforms many ontological assumptions about the material basis of consciousness. That is, the above platform inclusively connects to a hypothesis that the concepts of ‘space’, ‘time’, ‘event’, and ‘motion’ can be unified to capture the notion of simultaneous activity at reducing levels to the Impression order. This notion coheres with a physical-theoretical model of Signature-Energy-Frequency which has been well demonstrated in the atomic, chemical, and information fields. This study embraces a holistic and creative worldview based on a triadic model wherein consciousness itself is postulated as the most basic, primordial stratum. Importantly, both orders are constantly conjoined since the Impression Order exists as potential energy of the quantum vacuum. The physical realm is formed by the proposed Triangulate-Three conditions as a principle of animation and ‘being’: Consciousness, Body-of-Experience and Intellect-Reflective in the Expression Order, one aspect of which emerge as lifelike properties. This Triangulate-Three principle inheres in every particle and organism to which it guides its development, adaptation, and survival. The conscious being thus possesses all three conditions in Expression Order through STEM-interactions via SEF transmissions, as a self-organising organism. (shrink)

The content of this paper is primarily the product of an attempt to understand consciousness by working through the Gestell - conventionalised epistemology, at least some of several foundational concepts. This paper indirectly addresses the ancient question: “How is objective reference – or intentionality, possible? How is it possible for one thing to direct its thoughts upon another thing?” As such, I have adopted a holistic methodology; one in which I develop a framework based on a form of process philosophy (...) and descriptive emergentism. Many of the problems associated within the philosophy of mind arise because of a failure to understand the interrelations among the concepts we employ when we talk about consciousness and perception. These concepts are generally associated with certain structural features of reality. Hence, the paper advances through a series of attempts at defining the concept of time, moving through to some of the central figures, their thoughts and arguments and problems associated within the philosophy of time. Given the intertwined nature of the associated concepts, I have expanded on these to a level of conceptual integration. (shrink)

This book explores the shared experiential ground of cinema, art, and architecture. Pallasmaa carefully examines how the classic directors Alfred Hitchcock, Stanley Kubrick, Michelangelo Antonioni, and Andrei Tarkovsky used architectural imagery to create emotional states in their movies. He also explores the startling similarities between the landscapes of painting and those of movies.

What is the relationship between space and time in the human mind? Studies in adults show an asymmetric relationship between mental representations of these basic dimensions of experience: Representations of time depend on space more than representations of space depend on time. Here we investigated the relationship between space and time in the developing mind. Native Greek‐speaking children watched movies of two animals traveling along parallel paths for different distances or durations and (...) judged the spatial and temporal aspects of these events (e.g., Which animal went for a longer distance, or a longer time?). Results showed a reliable cross‐dimensional asymmetry. For the same stimuli, spatial information influenced temporal judgments more than temporal information influenced spatial judgments. This pattern was robust to variations in the age of the participants and the type of linguistic framing used to elicit responses. This finding demonstrates a continuity between space‐time representations in children and adults, and informs theories of analog magnitude representation. (shrink)

The picture which one naturally presents of the situation is that which would arise before an observer placed outside the earth, who could watch the light wave starting from the central mirror and pursuing the distant mirror, catching up with it at some distance beyond the point at which it was when the light wave started. In this case the observer is able to locate the points at which the parts of the apparatus were at different moments and to measure (...) the distances between. We could simulate this situation on the earth by assuming an enclosed square car, from some point in which two balls were shot out in directions at right angles to each other to the walls of the car, bounding back to the point at which they started. We will assume that the balls move with uniform velocity going and coming, and we will assume that the car is moving. An observer outside the car who marked the point on the rail directly over the starting point and the points reached by the balls when they struck the sides of the car, and then measured the distances which the balls travelled, would find that the ball which travelled with the car covered a greater distance than that traversed by the ball which went at right angles to the direction of the train, and yet the balls would return to the starting point at the same moment, provided they travelled over both their paths at the same velocity during their entire trajects, i.e., the same velocity measured within the car. The observer would be at no difficulty to explain this, for he would see that the velocity in the direction of its motion of the car had to be added to that of balls within the car. That is not the case of the light wave. The velocity of a moving shining body is not added to that of the light wave. The wave motion being set up in ether travels with its own uniform velocity of approximately 300,000 kilometers a second. The light waves then, from the standpoint of the observer outside the earth, traverse through the stagnant ether different distances at a uniform velocity and yet the ether waves exhibit on their return none of the evidence which they should exhibit in the interferometer. (shrink)

In Marx’s analysis of capitalism, time and motion are central to the dynamics of the system. In the twenty-first century, capital deployed new forms of technology and logistical planning to increase profits and reduce the circulation phase of the turnover time of capital. The introduction of fibre optic cable, data centres, the transformation of the warehouse into a site of movement, the rise of third-party logistics (3PL) firms, and improvements in infrastructure all promoted ‘the annihilation of (...) class='Hi'>space by time’ in the effort to increase profitability. As increased velocity of value became central to capital, the system in turn became more vulnerable to disruption by labour. (shrink)

Most research on metaphors that construe time as motion (motion metaphors of time) has focused on the question of whether it is the times or the person experiencing them (ego) that moves. This paper focuses on the equally important distinction between metaphors that locate times relative to ego (the ego-based metaphors Moving Ego and Moving Time) and a metaphor that locates times relative to other times (sequence is relative position on a path). Rather than a (...) single abstract target domain TIME, these two kinds of temporal metaphor metaphorize different kinds of temporal concept—perspective-specific vs. perspective-neutral temporal concepts. Recognition of this distinction enhances the explanatory potential of conceptual metaphor theory (Lakoff and Johnson 1980). An example involves the interaction of deixis and the temporal reference crosslinguistically of vocabulary with the spatial meanings in-front and behind. More generally, this approach refines our ability to describe the temporal concepts involved in motion metaphors of time. Such temporal concepts are present not only in the target domains, but also in the source domains of motion metaphors of time, where we find space-to-time metonymy, which may play a role in motivating the metaphors. In order to distinguish such metonymy from metaphor, we need to characterize metaphor as a mapping across frames rather than domains. (shrink)

The idea of obtaining a pilot-wave quantum theory on a lattice with discrete time is presented. The motion of quantum particles is described by a \-distributed Markov chain. Stochastic matrices of the process are found by the discrete version of the least-action principle. Probability currents are the consequence of Hamilton’s principle and the stochasticity of the Markov process is minimized. As an example, stochastic motion of single particles in a double-slit experiment is examined.

Retrospective issues: the discursive approach to genre and the misdirection film -- -- The truth is out there: manufacturing conspiratorial narrative coherence -- Constructing the (im)perfect cover: masculine masquerade and narrative agency -- -- Start making sense: narrative complexity, DVD, and online fandom -- The masters of misdirection: branding M. Night Shyamalan and Christopher Nolan -- Genre prestige: the misdirection film as blockbuster and middlebrow art -- Conclusion.

Among the dubious theses "proved" by the author of this classic example of pseudo-scientific literature are: relativistic physics is incorrect, the quantum theory is incorrect, "the success of quantum theory is purely mathematical," time, like space, has three dimensions, inductance and mass are equivalent, there is such a thing as absolute motion, and "All properties which are possessed by either space or time individually are.... properties of both space and time." What makes this (...) book unusual is the fact that the immense number of citations and footnotes refer to almost all of the important books and articles in the field of the philosophical foundations of physics. Larson therefore has accomplished one outstanding task: he has succeeded in immersing himself in some of the most philosophically and scientifically compelling literature of recent times and has emerged unscathed by a single intelligible idea.—H. P. K. (shrink)

Time, space and matter are the most pervasive and inescapable aspects of the physical universe. And yet, notwithstanding the fact that they represent the most fundamental and ubiquitous characteristics of reality, they have always presented elements of mystery to the human mind. Thus on the level of common thought we ponder how the withering hand of time reaches from out the past into the future to bring decay and destruction to all things; and on the more sophisticated (...) level, after the fashion of Immanuel Kant, we are puzzled by certain antinomies of thought concerning the necessity for an origin, and an end, of the universe in time and space, in the face of the equally necessary reasons for regarding the universe as being unlimited in its space and time dimensions. In either case, however, we are paying tribute to the tantalizing nature of these problems concerning the cosmic framework of space-time-matter in which we live, and move, and have our being. Indeed, it is not too much to say that genuine philosophy took its origin in Zeno's paradoxes of motion, and will have its final consummation when it solves Kant's antinomies. (shrink)

Aimed at linguists and computer scientists working on natural language processing, this is the first book that shows, at a large scale, how to do semantics for spatio-temporal information based on annotation structures that conform to ISO international standards such as ISO-TimeML or ISO-Space.

In Part 2, drawing on the results of Part 1, I will present my own interpretation of Leibniz’s philosophy of space and time. As regards Leibniz’s theory of geometry and space, De Risi’s excellent work appeared in 2007, so I will depend on this work. However, he does not deal with Leibniz’s view on time, and moreover, he seems to misunderstand the essential part of Leibniz’s view on time. Therefore I will begin with Richard Arthur’s (...) paper, and J. A. Cover’s improvement. Despite some valuable insights contained in their papers, I have to conclude their attempts fail in one way or another, because they disregard the order of state-transition of a monad, which is, on my view, one of the essential features of the monads. By reexamining Leibniz’s important text Initia Rerum, I arrived at the following interpretation. Since the realm of monads is timeless, the order of state-transition of a monad provides only the basis of time in phenomena. What Leibniz calls “simultaneity” should be understood as a unique 1- to-1 correspondence of the states of different monads. With this understanding, whatever is correct in Arthur’s and Cover’s interpretation can be reproduced in my interpretation. On this basis, we can introduce a metric of time based on congruence of duration. Leibniz connected time with space in Initia Rerum by means of motion, and introduced the notion of path of a moving point; thus the congruence of duration can be reduced to congruence of distance. Then, I can show both classical metric and relativistic metric can be reconstructed on the same basis, depending on the coding for phenomena. The relativistic metric can be combined with Leibniz’s idea of internal living force, suggesting a relation of mass with energy. However, since Leibniz has never shown the ground of constant speed of an inertial motion, there may be a vicious circle. In order to avoid this, we can extend the notion of path to whole situation, thus yielding a trajectory of the whole phenomenal world. Then, by applying optimality to possible paths, we may arrive at the law of motion, without vicious circle. A comparison of Leibniz’s dynamics with Barbour’s concludes Part 2. (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)

Textbooks present classical particle and field physics as theories of physical systems situated in Newtonian absolute space. This absolute space has an influence on the evolution of physical processes, and can therefore be seen as a physical system itself; it is substantival. It turns out to be possible, however, to interpret the classical theories in another way. According to this rival interpretation, spatiotemporal position is a property of physical systems, and there is no substantival spacetime. The traditional objection (...) that such a relationist view could not cope with the existence of inertial effects and other manifestations of the causal efficacy of spacetime can be answered successfully. According to the new point of view, the spacetime manifold of classical physics is a purely representational device. It represents possible locations of physical objects or events; but these locations are physical properties inherent in the physical objects or events themselves and having no existence independently of them. In relativistic quantum field theory the physical meaning of the spacetime manifold becomes even less tangible. Not only does the manifold lose its status as a substantival container, but also its function as a representation of spacetime properties possessed by physical systems becomes problematic. 'Space and time' become ordering parameters in the web of properties of physical systems. They seem to regain their traditional meaning only in the non-relativistic limit in which the classical particle concept becomes approximately applicable. (shrink)

In Part 2, drawing on the results of Part 1, I will present my own interpretation of Leibniz’s philosophy of space and time. As regards Leibniz’s theory of geometry and space, De Risi’s excellent work appeared in 2007, so I will depend on this work. However, he does not deal with Leibniz’s view on time, and moreover, he seems to misunderstand the essential part of Leibniz’s view on time. Therefore I will begin with Richard Arthur’s (...) paper, and J. A. Cover’s improvement. Despite some valuable insights contained in their papers, I have to conclude their attempts fail in one way or another, because they disregard the order of state-transition of a monad, which is, on my view, one of the essential features of the monads. By reexamining Leibniz’s important text Initia Rerum, I arrived at the following interpretation. Since the realm of monads is timeless, the order of state-transition of a monad provides only the basis of time in phenomena. What Leibniz calls “simultaneity” should be understood as a unique 1-to-1 correspondence of the states of different monads. With this understanding, whatever is correct in Arthur’s and Cover’s interpretation can be reproduced in my interpretation. On this basis, we can introduce a metric of time based on congruence of duration. Leibniz connected time with space in Initia Rerum by means of motion, and introduced the notion of path of a moving point; thus the congruence of duration can be reduced to congruence of distance. Then, I can show both classical metric and relativistic metric can be reconstructed on the same basis, depending on the coding for phenomena. The relativistic metric can be combined with Leibniz’s idea of internal living force, suggesting a relation of mass with energy. However, since Leibniz has never shown the ground of constant speed of an inertial motion, there may be a vicious circle. In order to avoid this, we can extend the notion of path to whole situation, thus yielding a trajectory of the whole phenomenal world. Then, by applying optimality to possible paths, we may arrive at the law of motion, without vicious circle. A comparison of Leibniz’s dynamics with Barbour’s concludes Part 2. (shrink)

Quantum gravity is expected to require modifications of the notions of space and time. I discuss and clarify how this happens in Loop Quantum Gravity.

This book presents an elementary but complete exposition of the relativistic theory of the measurement of intervals in space & time.

The article is devoted to the problem of time in modern science, where in recent years there have been major changes related to the latest discoveries in the field of the foundations of quantum theory. The author refers to works of K.-F. von Weizsacker (which works are not well-known in Russian-speaking field). Weizsacker deploys a large-scale program of building modern physics, while starting (not only as a physicist, but also a professional philosopher) with questions of philosophical interpretation of postulates (...) of modern physics, especially quantum mechanics. His key thesis is that time in physics is fundamentally distinct, which represents the whole physics as an integral scientific discipline. Weizsacker comes from physical and philosophical reflections, that give a special value to his work. Analyzing the conclusions of theoretical physics, namely the issues of substantiation of statistical mechanics, thermodynamics, and, above all, quantum mechanics, Weizsacker comes to the key idea of the structure of time in the substantiation of physical theory. The author in this conclusion disagrees with the opinion of most modern physicists that time has a subjective character, and the modus of the past, present and future reflects its essential character. The allocation of the time structure requires special logic. Such a logic is temporal and quantum. Starting from temporal logic, introducing the concept of possibility and probability, he comes to the substantiation of quantum mechanics. Being modal logic, it is based on the concept of possibility and probability. Key concept for Weizsacker is a binary alternative (Uralternative), closely related to the principle of superposition in quantum mechanics. By introducing the concept of certain alternatives, essentially actualized alternatives, Weizsacker shows how one can get the theory of relativity with its space-time structure. Further, he shows that based on its structure, you can get the theory of relativity. The space-time structure in this case is secondary, relational, as understood by Leibniz, Mach, and Einstein. (shrink)

Kedrov has reminded us that the development of knowledge proceeds from appearance to essence. That was also true of the development of notions about space and time. Leibniz, for example, defined space as the order of things existing at the same time. However, that definition is rather superficial, and it is only the development of physics, specifically relativity theory, which made it possible to penetrate more deeply into the nature of space and time and (...) to ascribe a precise and mathematically expressible notion to the well-known judgment to the effect that space and time are forms of the existence of matter. (shrink)

Tracing the many aesthetic, philosophical, and technological parallels between cinema and astronomy, Hannah Goodwin demonstrates how filmmakers have used cosmic imagery and themes to respond to the twentieth century's moments of existential dread. As our outlook on the future continues to change, Stardust illuminates the promise of cinema to bear witness to humanity's fragile existence within the vast expanse of the universe.