This book focuses on the phenomena of inertia and gravitation, one objective being to shed some new light on the basic laws of gravitational interaction and the fundamental nature and structures of spacetime. Chapter 1 is devoted to an extensive, partly new analysis of the law of inertia. The underlying mathematical and geometrical structure of Newtonian spacetime is presented from a four-dimensional point of view, and some historical difficulties and controversies - in particular the concepts of free particles and (...) straight lines - are critically analyzed, while connections to projective geometry are also explored. The relativistic extensions of the law of gravitation and its intriguing consequences are studied in Chapter 2. This is achieved, following the works of Weyl, Ehlers, Pirani and Schild, by adopting a point of view of the combined conformal and projective structure of spacetime. Specifically, Mach's fundamental critique of Newton's concepts of 'absolute space' and 'absolute time' was a decisive motivation for Einstein's development of general relativity, and his equivalence principle provided a new perspective on inertia. In Chapter 3 the very special mathematical structure of Einstein's field equations is analyzed, and some of their remarkable physical predictions are presented. By analyzing different types of dragging phenomena, Chapter 4 reviews to what extent the equivalence principle is realized in general relativity - a question intimately connected to the 'new force' of gravitomagnetism, which was theoretically predicted by Einstein and Thirring but which was only recently experimentally confirmed and is thus of current interest. (shrink)

In connection with the "Philosophy of Science" research program conducted by the Deutsche Forschungsgemeinschaft a colloquium was held in Munich from 18th to 20th May 1919. This covered basic structures of physical theories, the main emphasis being on the interrelation of space, time and mechanics. The present volume contains contributions and the results of the discussions. The papers are given here in the same order of presentation as at the meeting. The development of these "basic structures of (...) physical theories" involved diverging trends arising from different starting points in philosophy and physics. In order to obtain a clear comparison between these schools of thought, it was appropriate to concentrate discussion on geometry and chronology as the common foundation of classical and quantum mechanics. As a rather simple and "Tell prepared field of study, geochronometry seemed suited to analysing these mutually exclusive positions. vii D. Mayr and G. Sussmann (eds.), Space, Time, and Mechanics, vii. Copyright © 1983 by D. Reidel Publishing Company. ACKNOWLEDGEMENT The editors gratefully appreciate the sponsorship of the Deutsche Forschungsgemeinschaft and the cooperation of the authors and publisher. It is also a pleasure to thank Frau M.-L. Grohmann and Frau I. Thies for their organisational and especially Frau B. Grund for typing and clerical work. D. MAYR G. SUSSMANN 1982 University of Munich viii INTRODUCTION The distinct positions present at the symposium may be roughly divided into three schools that differ in their philosophical interpretation of physics and their meta-... ~. (shrink)

The aim of this paper is to discuss the relation between the observation basis and the theoretical principles of General Relativity. More specifically, this relation is analyzed with respect to constructive axiomatizations of the observation basis of space-time theories, on the one hand, and in attempts to complete them, on the other. The two approaches exclude one another so that a choice between them is necessary. I argue that the completeness approach is preferable for methodological reasons.

In this paper I attempt to trace certain aspects of the evolution of theories of space-time and mechanics as revealed by a brief comparative study of Newtonian theory, Robb's theory, general relativity, and Milne's kinematical relativity. The first object is to emphasise how each theory leaves us in a position in which the succeeding one appears as a perfectly natural next step in the development of ideas. The second object is to show how, in spite of superficial (...) differences in character, the theories all necessarily possess the same general structure constituted by the presence of hypotheses, from which certain general mathematical relations are deduced, which in their turn are used to predict relations between observable quantities. (shrink)

The history and philosophy of science are destined to play a fundamental role in an epoch marked by a major scientific revolution. This ongoing revolution, principally affecting mathematics and physics, entails a profound upheaval of our conception of space, space–time, and, consequently, of natural laws themselves. Briefly, this revolution can be summarized by the following two trends: by the search for a unified theory of the four fundamental forces of nature, which are known, as of now, as (...) gravity, electromagnetism, and strong and weak nuclear forces; by the search for new mathematical concepts capable of elucidating and therefore explaining such a relationship. In fact, the first search is essentially dependent on the second; that is to say, that in order for a new theory of physics to come to light, the development of a deeper geometric theory capable of explaining the structure of space–time on a quantum scale appears to be necessary. On careful consideration, we notice that both of these developments converge in the direction of a unitary and fundamental tendency of modern science—which is the geometrization of theoretical physics and of natural sciences. This new emergent situation carries within it a profound conceptual change, affecting the way in which relations are conceived of, first and foremost, between mathematics and physics. This new paradigm can be summed up by the intimately interdependent points: the immense variety of physical phenomena and of natural forms follows from the equally infinite variety of geometric and topological objects that can be made out in space and from which space is made up; the second point, which ensues from the former one and which is of great historical and epistemological significance, is that mathematics is involved in rather than applied to phenomena. In other words, phenomena are effects that emerge from the geometrical structure of space–time. There is no doubt that this new conception of the relationship between the universe of mathematical ideas and objects and the world of natural phenomena is the true scientific revolution of our century, of great conceptual importance, and consequently, capable of changing our view of science and of nature at one and the same time. It is all at once of a scientific, philosophical and aesthetic order. (shrink)

The current technoscientific progress has led to a sectorization in the philosophy of science. Today the philosophy of science isn't is informal interested in studying old problems about the general characteristics of scientific practice. The interest of the philosopher of science is the study of concepts, problems and riddles of particular disciplines. Then, within this progress of philosophy of science, neuroscientific research stands out, because it invades issues traditionally addressed by the humanities, such as the nature of consciousness, action, knowledge, (...) normativity, etc. As a result, the new area of interdisciplinary study of neuroscience and philosophy arises: neurophilosophy. This emerging area applies neuroscientific concepts to traditional philosophical questions, limiting their responses to neuroscientific revelations about nervous systems. Neurophilosophy research focuses on problems related to the indirect nature of mind and brain, computational or representative analysis of brain process, relationships between psychological and neuroscientific research, adequate adaptations of physical and philosophical concepts in neuroscience and the place of cognitive functions. Now, the temporal representation of conscious experience and the types of the neural architecture to represent objects in time have aroused scientific interest. Under these interests, we focus on the studies on the temporary triadic structure of phenomenological consciousness in Dan Lloyd and Rick Grush. From Grush’s studies, the importance of Kantian ideas for cognitive neuroscience emerges, due to the active way in which Kant conceived space and time as forms of intuition, within which the mind interprets its experience. Under this perspective, the theoretical arguments of Dennett-Kinsbourne and Eagleman-Sejnowski represent winks in the direction of Kant-Husserl within the neuroscientific goal while considering that the contents provided by the mind included space, objects and perception of causal relationships. Then, theories of cognitive neuroscience are beginning to suggest that these elements are also, as Kant argued, interpretative elaborations provided by mind / brain, and not only content received from outside. In other words, current cognitive neuroscientific theories try to pass from its Humean phase to a Kantian phase. So, the challenge has been to explain that these elements are provided by the mind and the world itself, and how they have the content they have come from. These are lacking in current studies. Filling this gap helps to involve the analysis of the scientist’s experience in his theoretical attitude. In this sense, an investigation under the Kantian-Husserlian approach that involves pure intuitions a priori with the experience of the scientific and neuroscientific concepts represents a ground-breaking. At present, a neurophilosophical study about this does not exist. In this sense, one feasible proposal for research would be based on the application of neuroscientific results of Moser-Britt to philosophical problems of foundational notions in relativistic physics: space, time, space-time, field, etc., under the Kantian-Husserlian approach, which allows to demonstrate the multidisciplinary link between neurophilosophy and physics. This represents a ground-breaking area in current interests in scientific research, with a positive impact in the field of neuroscience, and contributing to the study of abstraction emphasizing the importance of Kant’s Copernican turn and Husserl’s phenomenological ideas in the construction of physical theories. -/- . (shrink)

INTRODUCTION In Einstein's theory of gravitation matter and its dynamical interaction are based on the notion of an intrinsic geometric structure of the space -time continuum. The ideal aspiration, the ultimate aim, of the theory is not more and ...

By analyzing a gedanken experiment designed to measure the distance l between two spatially separated points, we find that this distance cannot be measured with uncertainty less than (ll 2 P) 1/3 , considerably larger than the Planck scale lP (or the string scale in string theories), the conventional-wisdom uncertainty in distance measurements. This limitation to space-time measurements is interpreted as resulting from quantum fluctuations of space-time itself. Thus, at very short distance scales, space- (...) class='Hi'>time is “foamy.” This intrinsic foaminess of space-time provides another source of noise in the interferometers. The LIGO/VIRGO and LISA generations of gravity-wave interferometers, through future refinements, are expected to reach displacement noise levels low enough to test our proposed degree of foaminess in the structure of space-time. (shrink)

The generator of electromagnetic gauge transformations in the Dirac equation has a unique geometric interpretation and a unique extension to the generators of the gauge group SU(2) × U(1) for the Weinberg-Salam theory of weak and electromagnetic interactions. It follows that internal symmetries of the weak interactions can be interpreted as space-time symmetries of spinor fields in the Dirac algebra. The possibilities for interpreting strong interaction symmetries in a similar way are highly restricted.

An axiomatic foundation of a quantum theory for microsystems in the presence of external fields is developed. The space-time structure is introduced by considering the invariance of the theory under a kinematic invariance group. The formalism is illustrated by the example of charged particles in electromagnetic potentials. In the example, gauge invariance is discussed.

In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. This theory leads (i) to a generalization of possible physically relevant fractal laws, written as partial differential equation acting in the space of scales, and (ii) to a new geometric foundation of quantum mechanics and gauge field theories and their possible generalisations. In the second part, (...) we discuss some examples of application of the theory to various sciences, in particular in cases when the theoretical predictions have been validated by new or updated observational and experimental data. This includes predictions in physics and cosmology (value of the QCD coupling and of the cosmological constant), to astrophysics and gravitational structure formation (distances of extrasolar planets to their stars, of Kuiper belt objects, value of solar and solar-like star cycles), to sciences of life (log-periodic law for species punctuated evolution, human development and society evolution), to Earth sciences (log-periodic deceleration of the rate of California earthquakes and of Sichuan earthquake replicas, critical law for the arctic sea ice extent) and tentative applications to systems biology. (shrink)

In the standard formalism of quantum gravity, black holes appear to form statistical distributions of quantum states. Now, however, we can present a theory that yields pure quantum states. It shows how particles entering a black hole can generate firewalls, which however can be removed, replacing them by the ‘footprints’ they produce in the out-going particles. This procedure can preserve the quantum information stored inside and around the black hole. We then focus on a subtle but unavoidable modification of the (...) topology of the Schwarzschild metric: antipodal identification of points on the horizon. If it is true that vacuum fluctuations include virtual black holes, then the structure of space-time is radically different from what is usually thought. (shrink)

An analysis of the extension of the Hawking-Penrose singularity theorem to Riemann-Cartan U4 space-times with torsion and spin density is undertaken. The minimal coupling principle in U4 is used to formulate a new expression for the convergence condition autoparallels in Einstein-Cartan theory. The Gödel model with torsion is given as an example.

General relativity is commonly thought to imply the existence of a unique metric structure for space-time. A simple example is presented of a general relativistic theory with ambiguous metric structure. Brans-Dicke theory is then presented as a further example of a space-time theory in which the metric structure is ambiguous. Other examples of theories with ambiguous metrical structure are mentioned. Finally, it is suggested that several new and interesting philosophical questions arise (...) from the sorts of theories discussed. (shrink)

Bohmian mechanics and the Ghirardi-Rimini-Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wave function, whereas the latter implements spontaneous collapses of the wave function by a nonlinear and stochastic modification of Schrödinger's equation. Still, both theories, when understood appropriately, share the following structure: They are ultimately not about wave functions but about 'matter' moving in space, represented by either particle trajectories, fields on space-time, (...) or a discrete set of space-time points. The role of the wave function then is to govern the motion of the matter. (shrink)

Physical Relativity explores the nature of the distinction at the heart of Einstein's 1905 formulation of his special theory of relativity: that between kinematics and dynamics. Einstein himself became increasingly uncomfortable with this distinction, and with the limitations of what he called the 'principle theory' approach inspired by the logic of thermodynamics. A handful of physicists and philosophers have over the last century likewise expressed doubts about Einstein's treatment of the relativistic behaviour of rigid bodies and clocks in motion in (...) the kinematical part of his great paper, and suggested that the dynamical understanding of length contraction and time dilation intimated by the immediate precursors of Einstein is more fundamental. Harvey Brown both examines and extends these arguments, after giving a careful analysis of key features of the pre-history of relativity theory. He argues furthermore that the geometrization of the theory by Minkowski in 1908 brought illumination, but not a causal explanation of relativistic effects. Finally, Brown tries to show that the dynamical interpretation of special relativity defended in the book is consistent with the role this theory must play as a limiting case of Einstein's 1915 theory of gravity: the general theory of relativity.Appearing in the centennial year of Einstein's celebrated paper on special relativity, Physical Relativity is an unusual, critical examination of the way Einstein formulated his theory. It also examines in detail certain specific historical and conceptual issues that have long given rise to debate in both special and general relativity theory, such as the conventionality of simultaneity, the principle of general covariance, and the consistency or otherwise of the special theory with quantum mechanics. Harvey Brown' s new interpretation of relativity theory will interest anyone working on these central topics in modern physics. (shrink)

In "The Epistemology of Geometry" Glymour proposed a necessary structural condition for the synonymy of two space-time theories. David Zaret has recently challenged this proposal, by arguing that Newtonian gravitational theory with a flat, non-dynamic connection (FNGT) is intuitively synonymous with versions of the theory using a curved dynamical connection (CNGT), even though these two theories fail to satisfy Glymour's proposed necessary condition for synonymy. Zaret allowed that if FNGT and CNGT were not equally well (bootstrap) (...) tested by the relevant phenomena, the two theories would in fact not be synonymous. He argued, however, that when electrodynamic phenomena are considered, the two theories are equally well tested. We show that it is not FNGT and CNGT which are equally well tested when the electrodynamic phenomena are considered, but only suitable extensions of FNGT and CNGT. Thus, there is good reason to consider FNGT and CNGT to be non-synonymous. We further show that the two extensions of FNGT and CNGT which are equally well tested when electrodynamic phenomena are considered (and which could be considered intuitively synonymous) not only satisfy Glymour's original proposed necessary condition for the synonymy of space-time theories, they satisfy a plausible stronger condition as well. (shrink)

This chapter contains sections titled: Coordinate Systems: Euclidean Space Invariant Quantities Classical Space‐times Special Relativity Consequences of the Lorentz Transformation Lorentz Invariant Quantities.

What if gravity satisfied the Klein-Gordon equation? Both particle physics from the 1920s-30s and the 1890s Neumann-Seeliger modification of Newtonian gravity with exponential decay suggest considering a "graviton mass term" for gravity, which is _algebraic_ in the potential. Unlike Nordström's "massless" theory, massive scalar gravity is strictly special relativistic in the sense of being invariant under the Poincaré group but not the 15-parameter Bateman-Cunningham conformal group. It therefore exhibits the whole of Minkowski space-time structure, albeit only indirectly (...) concerning volumes. Massive scalar gravity is plausible in terms of relativistic field theory, while violating most interesting versions of Einstein's principles of general covariance, general relativity, equivalence, and Mach. Geometry is a poor guide to understanding massive scalar gravity: matter sees a conformally flat metric due to universal coupling, but gravity also sees the rest of the flat metric in the mass term. What is the 'true' geometry, one might wonder, in line with Poincaré's modal conventionality argument? Infinitely many theories exhibit this bimetric 'geometry,' all with the total stress-energy's trace as source; thus geometry does not explain the field equations. The irrelevance of the Ehlers-Pirani-Schild construction to a critique of conventionalism becomes evident when multi-geometry theories are contemplated. Much as Seeliger envisaged, the smooth massless limit indicates underdetermination of theories by data between massless and massive scalar gravities---indeed an unconceived alternative. At least one version easily could have been developed before General Relativity; it then would have motivated thinking of Einstein's equations along the lines of Einstein's newly re-appreciated "physical strategy" and particle physics and would have suggested a rivalry from massive spin 2 variants of General Relativity. The Putnam-Grünbaum debate on conventionality is revisited with an emphasis on the broad modal scope of conventionalist views. Massive scalar gravity thus contributes to a historically plausible rational reconstruction of much of 20th-21st century space-time philosophy in the light of particle physics. An appendix reconsiders the Malament-Weatherall-Manchak conformal restriction of conventionality and constructs the 'universal force' influencing the causal structure. Subsequent works will discuss how massive gravity could have provided a template for a more Kant-friendly space-time theory that would have blocked Moritz Schlick's supposed refutation of synthetic _a priori_ knowledge, and how Einstein's false analogy between the Neumann-Seeliger-Einstein modification of Newtonian gravity and the cosmological constant \Lambda generated lasting confusion that obscured massive gravity as a conceptual possibility. (shrink)

The experimental testing of the Lorentz transformations is based on a family of sets of coordinate transformations that do not comply in general with the principle of equivalence of the inertial frames. The Lorentz and Galilean sets of transformations are the only member sets of the family that satisfy this principle. In the neighborhood of regular points of space-time, all members in the family are assumed to comply with local homogeneity of space-time and isotropy of (...) class='Hi'>space in at least one free-falling elevator, to be denoted as Robertson'sab initio rest frame [H. P. Robertson,Rev. Mod. Phys. 21, 378 (1949)].Without any further assumptions, it is shown that Robertson's rest frame becomes a preferred frame for all member sets of the Robertson family except for, again, Galilean and Einstein's relativities. If one now assumes the validity of Maxwell-Lorentz electrodynamics in the preferred frame, a different electrodynamics spontaneously emerges for each set of transformations. The flat space-time of relativity retains its relevance, which permits an obvious generalization, in a Robertson context, of Dirac's theory of the electron and Einstein's gravitation. The family of theories thus obtained constitutes a covering theory of relativistic physics.A technique is developed to move back and forth between Einstein's relativity and the different members of the family of theories. It permits great simplifications in the analysis of relativistic experiments with relevant “Robertson's subfamilies.” It is shown how to adapt the Clifford algebra version of standard physics for use with the covering theory and, in particular, with the covering Dirac theory. (shrink)

Foundations of Space-Time Theories, by Michael Friedman, falls naturally into two parts. In the first, he presents the general framework within which he will characterize and discuss space-time theories, and then he devotes a chapter each to Newtonian physics, special relativity, and general relativity. Although there is some rich philosophical discussion along the way, these chapters are, of necessity, somewhat technical expositions of the general framework in action. It is in the second part, consisting (...) of two substantial chapters, one on relationalism, the other on conventionalism, that more general philosophical issues are addressed. (shrink)

The application of the general theory of relativity to the cosmological plane has led to a significant change in traditional notions on the space-time structure of the universe. This has been expressed in a new formulation and solution of cosmological problems such as that of a single world space and time, the problem of selection of a cosmological model for description of the universe, and the problem of the infinity of the universe.

Although the name of Immanuel Kant has survived in the history of culture as the name of one of the greatest philosophers of modern times, Kant's role as a scientist is also very important. His work in the field of cosmology and physics is directly related to philosophy. Kant's development of the transcendental method was a direct result of thinking about the relationship between mathematics and experiment. Transcendentalism and Kant's theory of subjectivity continue the development of physics from Galileo to (...) Newton and Leibniz. This is especially true of his theory of space and time. All this should have turned transcendental aesthetics into a turning point in the development of mathematical natural science. However, in practice, the alienation of the natural sciences from philosophy has only intensified. An analysis of the scientific revolution at the beginning of the 20th century shows the enormous role of Kant's ideas in it in repulsing scientists from Kantianism. Weinert, a researcher of the relationship of 20th century physics to Kant's philosophy, shows that Einstein, being a Kantian as a philosopher, opposed Kantianism as a physicist. He enthusiastically accepted the Kantian idea of the autonomy of theoretical knowledge, but did not accept the concept a priori. An approach in which experience and theory do not precede each other, but are in constant interaction, is defined in the article as experimental transcendentalism. With the methodological difference between physics and philosophy, the concept of space and time in modern physics has a deep similarity with the transcendental doctrine. The definition of the qualitative structure of space (Analysis Situs), including the theoretical substantiation of its three dimensions, was the subject of reflections of scientists from Galileo, Leibniz and Kant to Einstein and Poincaré. (shrink)

Could space consist entirely of extended regions, without any regions shaped like points, lines, or surfaces? Peter Forrest and Frank Arntzenius have independently raised a paradox of size for space like this, drawing on a construction of Cantor’s. I present a new version of this argument and explore possible lines of response.

In lieu of an abstract, here is a brief excerpt of the content:SPACE-TIME AND THE COMMUNITY OF BEINGS: SOME COSMOLOGICAL SPECULATIONS INTRODUCTION XERT EINSTEIN, in his essay "Relativity and the Problem of Space," makes several interesting comments on the implications of relativity theory for the Newtonian concepts of absolute space and time. Among these are the following: Since the special theory of relativity revealed the physical equivalence of all inertial systems, it proved the untenability of (...) the hypothesis of an aether at rest. It was therefore necessary to renounce the idea that the electromagnetic field is to be regarded as a state of a material carrier. The field then becomes an irreducible element of physical description, irreducible in the same sense as the concept of matter in the theory of Newton.1 On the basis of the general theory of relativity..., space, as opposed to" what fills space," which is dependent on the coorrdinates, has no separate existence.2 There is no such thing as empty space, i.e., a space without field. Space-time does not claim existence on its own but only as a structural quality of the field. Thus Descartes was not so far from the truth when he believed he must exclude the existence of an empty space. The notion indeed appears absurd, as long as physical reality is seen exclusively in ponderable bodies. It requires the idea of the field as the representative of reality, in combination with the general principle of relativity, to show the true kernel of Descartes' idea; there exists no space " empty of field." 3 1 Albert Einstein, Relativity: The Special and the General Theory (New York, 1961), pp. 149-150. 2 Ibid., p. 155. s Ibid., pp. 155-156. 480 SPACE-TIME AND THE COMMUNITY OF BEING 481 Space-time is not necessarily something to which one can ascribe a separate existence, independently of the actual objects of physical reality. Physical objects are not in space, but these objects are spatially extended. In this way, the concept "empty space " loses its meaning.4 These statements raise some interesting questions for the philosopher working within the Judaeo-Christian metaphysical and cosmological tradition. Einstein's concept of the spacetime continuum constituted by the field (or by the plurality of fields seen as interrelated) amounts in effect to a reduction of space-time to relation, to that which is constituted by a universal relational network. One may ask whether this concept is, as many seem to believe, a demolition of the classical and Christian view of the world, or whether, on the contrary, it amounts to a rediscovery of that view from the perspective of the vocabulary of contemporary physics. To ask the question in a slightly different way: Does relativity have anything to do with relativism and hence with the anti-ontological thrust of the latter? This question inevitably involves us in the more general question how the physical structure of the cosmos does or does not reflect the ontological structure of being-i.e., how is the cosmos as known by physics related to the world-order as the intelligible object of a philosophical cosmology? How are the various levels of cosmic order, from inorganic matter to the human level, related to one another? It will be the contention of the present essay that the relativistic concept of the cosmos not only is not destructive of the classical and Christian one, but converges with it, because the latter is grounded in the concept of being as being, and being in turn must be understood as the universal concept and reality which has reality by virtue of the community of beings, i.e., by virtue of relation. These concepts will be further clarified in the course of the discussion. Let it be clearly understood, however, that what follows does not pretend to constitute a rigorous logical derivation of a cosmological system but is 4 Ibid.," Note to the Fifteenth Edition," p. vi. 482 GEORGE A. KENDALL rather a series of speculations, of brief glimpses of areas of convergence which have drawn attention to themselves in the course of the struggle for ontological and cosmological truth. As such, they are presented as a step along the way in the search for understanding, not as... (shrink)

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)

When the German mathematician Hermann Minkowski first introduced the space-time diagrams that came to be associated with his name, the idea of picturing motion by geometric means, holding time as a fourth dimension of space, was hardly new. But the pictorial device invented by Minkowski was tailor-made for a peculiar variety of space-time: the one imposed by the kinematics of Einstein’s special theory of relativity, with its unified, non-Euclidean underlying geometric structure. By plo (...) tting two or more reference frames in relative motion on the same picture, Minkowski managed to exhibit the geometric basis of such relativistic phenomena as time dilation, length contraction or the dislocation of simultaneity. These disconcerting effects were shown to result from arbitrary projections within four-dimensional space-time. In that respect, Minkowski diagrams are fundamentally different from ordinary space-time graphs. The best way to understand their specificity is to realize how productively ambiguous they are. (shrink)

Space, Time, and Stuff is an attempt to show that physics is geometry: that the fundamental structure of the physical world is purely geometrical structure. Along the way, he examines some non-standard views about the structure of spacetime and its inhabitants, including the idea that space and time are pointless, the idea that quantum mechanics is a completely local theory, the idea that antiparticles are just particles travelling back in time, and the (...) idea that time has no structure whatsoever. The main thrust of the book, however, is that there are good reasons to believe that spaces other than spacetime exist, and that it is the existence of these additional spaces that allows one to reduce all of physics to geometry. Philosophy, and metaphysics in particular, plays an important role here: the assumption that the fundamental laws of physics are simple in terms of the fundamental physical properties and relations is pivotal."--P. [4] of cover. (shrink)

Under the assumption that the so-called space-time fluctuationy(x) in a classical sense, attached to each point of the gravitational field at some microscopic stage, is summarized as the metrical fluctuation in the formg λκ (x)=gλκ (x)·exp2σ(y(x)), some new physical aspects induced by the conformal scalarσ(x) (≡σ(y(x))) are found: By introducing the torsionT κ λμ (x) from a general standpoint, the resulting micro-gravitational field is made to have a conformally non-Riemannian structure, where a special form ofT κ λμ (...) (i.e.,T κ λμ =δ κ λ σμ−δ κ μ σλ(σμ=∂σ/∂x μ)) shows some peculiar features. An averaging process with respect toy is taken into account, by which the spatial structure of the corresponding macro-field is shown, in general, to have a somewhat “non”-Riemannian structure due to the contributions of the torsionT κ λμ. (shrink)

This concise book introduces nonphysicists to the core philosophical issues surrounding the nature and structure of space and time, and is also an ideal resource for physicists interested in the conceptual foundations of space-time theory. Tim Maudlin's broad historical overview examines Aristotelian and Newtonian accounts of space and time, and traces how Galileo's conceptions of relativity and space-time led to Einstein's special and general theories of relativity. Maudlin explains special relativity (...) using a geometrical approach, emphasizing intrinsic space-time structure rather than coordinate systems or reference frames. He gives readers enough detail about special relativity to solve concrete physical problems while presenting general relativity in a more qualitative way, with an informative discussion of the geometrization of gravity, the bending of light, and black holes. Additional topics include the Twins Paradox, the physical aspects of the Lorentz-FitzGerald contraction, the constancy of the speed of light, time travel, the direction of time, and more.Introduces nonphysicists to the philosophical foundations of space-time theory Provides a broad historical overview, from Aristotle to Einstein Explains special relativity geometrically, emphasizing the intrinsic structure of space-time Covers the Twins Paradox, Galilean relativity, time travel, and more Requires only basic algebra and no formal knowledge of physics. (shrink)

The mathematical and physical aspects of the conformal symmetry of space-time and of physical laws are analyzed. In particular, the group classification of conformally flat space-times, the conformal compactifications of space-time, and the problem of imbedding of the flat space-time in global four-dimensional curved spaces with non-trivial topological and geometrical structure are discussed in detail. The wave equations on the compactified space-times are analyzed also, and the set of their elementary solutions (...) constructed. Finally, the implications of global compactified space-times for cosmology are discussed. It is argued that the recent discovery of periodic structure of matter distribution on large distances strongly suggests that the global cosmological space-time should be close. Next we analyze the inflation scalar field in the inflationary model of universe evolution considered on the spatially compact Robertson-Walker space-time. It is shown that the energy distribution in this model is periodic and the periods and density decrease with increasing distance, in striking agreement with experimental data. Our model of the universe also provides a definite predictions for the energy distribution, polar and azimuthal, considered as a function of angles θ and φ. These predictions should be tested with the new astronomical data. (shrink)

We derive the first analytical formula for the density of "Dark Matter" (DM) at all length scales, thus also for the rotation curves of stars in galaxies, for the baryonic Tully–Fisher relation and for planetary systems, from Einstein's equations (EE) and classical approximations, in agreement with observations. DM is defined in Part I as the energy of the coherent gravitational field of the universe, represented by the additional equivalent ordinary matter (OM), needed at all length scales, to explain classically, with (...) inclusion of the OM, the _observed coherent_ gravitational field. Our derivation uses both EE and the Newtonian approximation of EE in Part I, to describe semi-classically in Part II the advection of DM, created at the level of the universe, into galaxies and clusters thereof. This advection happens proportional with their own classically generated gravitational field g, due to self-interaction of the gravitational field. It is based on the universal formula ρ D = λgg′ 2 for the density ρ D of DM advected into medium and lower scale structures of the observable universe, where λ is a universal constant fixed by the Tully–Fisher relations. Here g′ is the gravitational field of the universe; g′ is in main part its own source, as implied in Part I from EE. We start from a simple electromagnetic analogy that helps to make the paper generally accessible. This paper allows for the first time the exact calculation of DM in galactic halos and at all levels in the universe, based on EE and Newtonian approximations, in agreement with observations. (shrink)

The work of Foucault and Elias has been compared before in the social sciences and humanities, but here I argue that the main distinction between their approaches to the construction of subjectivity is the relative importance of space and time in their accounts. This is not just a matter of the “history of ideas,” as providing for the temporal dimension more fully in theories of subjectivity and the habitus allows for a greater understanding of how ways of (...) being, acting and feeling in different spaces are related but largely unintended. Here I argue that discursive practices, governmental operations and technologies of the self (explanatory claims of both Foucault and the Foucauldian tradition) take shape as processes within the continuities of the figurational flow connecting people across space and time. Continuity should not be understood as stability or sameness over time, but as the contingent relations between successive social formations. As Elias argues, there is a structure or order to long-term social change, albeit unplanned, and this ultimately provides the broader social explanation for the historicity of the subject. Though discursive practices happen in particular spaces, we must recognise these spaces, and the practices therein, as socially constructed over time in response to largely unplanned moral and cultural developments. (shrink)

A Hilbert-space model for quantum logic follows from space-time structure in theories with consistent state collapse descriptions. Lorentz covariance implies a condition on space-like separated propositions that if imposed on generally commuting ones would lead to the covering law, and such a generalization can be argued if state preparation can be conditioned to space-like separated events using EPR-type correlations. The covering law is thus related to space-time structure, though a final (...) understanding of it, through a self-consistency requirement, will probably require quantum space-time. (shrink)

Research in quantum gravity strongly suggests that our world in not fundamentally spatiotemporal, but that spacetime may only emerge in some sense from a non-spatiotemporal structure, as this paper illustrates in the case of causal set theory and loop quantum gravity. This would raise philosophical concerns regarding the empirical coherence and general adequacy of theories in quantum gravity. If it can be established, however, that spacetime emerges in the appropriate circumstances and how all its relevant aspects are explained (...) in fundamental non-spatiotemporal terms, then the challenge is fully met. It is argued that a form of spacetime functionalism offers the most promising template for this project. (shrink)

It is argued that Minkowski space-time cannot serve as the deep structure within a ``constructive'' version of the special theory of relativity, contrary to widespread opinion in the philosophical community.

The theory of branching space-times, put forward by Belnap, considers indeterminism as local in space and time. In the axiomatic foundations of that theory, so-called choice points mark the points at which the possible future can turn out in different ways. Working under the assumption of choice points is suitable for many applications, but has an unwelcome topological consequence that makes it difficult to employ branching space-times to represent a range of possible physical space-times. Therefore (...) it is interesting to develop a branching space-times theory without choice points. This is what we set out to do in this paper, providing new foundations for branching space-times in terms of choice sets rather than choice points. After motivating and developing the resulting theory in formal detail, we show that it is possible to translate structures of one style into structures of the other style and vice versa. This result shows that the underlying idea of indeterminism as the branching of spatio-temporal histories is robust with respect to different implementations, making a choice between them a matter of expediency rather than of principle. (shrink)

We discuss the question of whether or not a general Weyl structure is a suitable mathematical model of space–time. This is an issue that has been in debate since Weyl formulated his unified field theory for the first time. We do not present the discussion from the point of view of a particular unification theory, but instead from a more general standpoint, in which the viability of such a structure as a model of space– (...) class='Hi'>time is investigated. Our starting point is the well known axiomatic approach to space–time given by Elhers, Pirani and Schild. In this framework, we carry out an exhaustive analysis of what is required for a consistent definition for proper time and show that such a definition leads to the prediction of the so-called “second clock effect”. We take the view that if, based on experience, we were to reject space–time models predicting this effect, this could be incorporated as the last axiom in the EPS approach. Finally, we provide a proof that, in this case, we are led to a Weyl integrable space–time as the most general structure that would be suitable to model space–time. (shrink)

The sample space of the chance distribution at a given time is a class of possible worlds. Thanks to this connection between chance and modality, one’s views about modal space can have significant consequences in the theory of chance and can be evaluated in part by how plausible these implications are. I apply this methodology to evaluate certain forms of modal contingentism, the thesis that some facts about what is possible are contingent. Any modal contingentist view that (...) meets certain conditions that I specify generates difficulties in the philosophy of chance, including a problem usually associated with Humeanism that is known as ‘the problem of undermining futures’. I consider two well-known versions of modal contingentism that face this difficulty. The first version, proposed by Hugh Chandler and Nathan Salmon, rests on an argument for the claim that many individuals have their modal features contingently. The second version is motivated by the thesis that the existence of a possible world depends on the existence of the contingent individuals inhabiting it, and that many worlds are therefore contingent existents. (shrink)

permits a sound and rigorously definable notion of ‘originating cause’ or causa causans—a type of transition event—of an outcome event. Mackie has famously suggested that causes form a family of ‘inus’ conditions, where an inus condition is ‘an insufficient but non-redundant part of an unnecessary but sufficient condition’. In this essay the needed concepts of BST theory are developed in detail, and it is then proved that the causae causantes of a given outcome event have exactly the structure of (...) a set of Mackie inus conditions. The proof requires the assumption that there is no EPR-like ‘funny business’. This seems enough to constitute a theory of ‘causation’ in at least one of its many senses. Introduction The cement of the universe Preliminaries 3.1 First definitions and postulates 3.2 Ontology: propositions 3.3 Ontology: initial events 3.4 Ontology: outcome events 3.5 Ontology: transition events 3.6 Propositional language applied to events Causae causantes 4.1 Causae causantes are basic primary transition events 4.2 Causae causantes of an outcome chain 4.3 No funny business Causae causantes and inns and inus conditions 5.1 Inns conditions of outcome chains: not quite 5.2 Inns conditions of outcome chains 5.3 Inns conditions of scattered outcome events 5.4 Inus conditions for disjunctive outcome events 5.5 Inns and inus conditions of transition events Counterfactual conditionals Appendix: Tense and modal connectives in BST. (shrink)

This book, explores the conceptual foundations of Einstein's theory of relativity: the fascinating, yet tangled, web of philosophical, mathematical, and physical ideas that is the source of the theory's enduring philosophical interest. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of (...) the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

I address a question recently raised by Simon Saunders concerning the relationship between the space-time structure of Newton-Cartan theory and that of what I will call “Maxwell-Huygens space-time.” This discussion will also clarify a connection between Saunders’s work and a recent paper by Eleanor Knox.

In this paper, I examine a number of alternative global structures for Newtonian space-time, and corresponding Newtonian theories of mechanics and gravitation. I argue that since these theories differ only with respect to questions concerning the relative distribution of inertial and gravitational forces, the choice between them is a matter of convention. Therefore, the global structure of Newtonian space-time is also a matter of convention. Since this result is based on a consideration of (...) the nature of inertial and gravitational forces, rather than on general reductionist principles, it is a "limited conventionalist" result. (shrink)

This chapter contains sections titled: Non‐Euclidean Geometry The General Theory Superluminal Constraints and the GTR Lorentz Invariance and the GTR Quantum Theories in Non‐Minkowski Space‐times The GTR to the Rescue?