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)

The fall of the Berlin wall, the uprising at Tiananmen Square, the war in the Persian Gulf, the conflict in Bosnia—such events have been fundamentally affected by modern technology. As we become instant spectators of war, famine, and revolution, time and space assume new global meanings. This provocative volume presents an eclectic group of contributors who attempt to make sense of the "now" and the "here" that define the modern age. The essays, by anthropologists, religionists, geographers, linguists, (...) sociologists, and historians, explore the temporal and spatial facets of social life. Their range is remarkable and includes English landscape painting, talk in corporations, agoraphobic women, the ecological structure of Los Angeles, the cosmology of the Holocaust, and the ritual spaces of Buddhist Japan and the Church of the Holy Sepulchre in Jerusalem. The editors' introduction addresses the diversity of these empirical concerns and positions them within a rapidly expanding theoretical landscape. David Hockney's striking painting on the book jacket captures the tension between somewhere and everywhere, between space and place, now and just a moment ago—hence "nowhere" or "now/here.". (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 ...

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)

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.

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)

Spaces of Geographical Thought examines key ideas like space and place - which inform the geographic imagination. The text: discusses the core conceptual vocabulary of human geography: agency: structure; state: society; culture: economy; space: place; black: white; man: woman; nature: culture; local: global; and time: space; explains the significance of these binaries in the constitution of geographic thought; and shows how many of these binaries have been interrogated and re-imagined in more recent geographical thinking. (...) A consideration of these binaries will define the concepts and situate students in the most current geographical arguments and debates. The text will be required reading for all modules on the philosophy of geography and on geographical theory. (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.

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)

The A-Theory of time has long struggled with the results of special relativity. One proposed solution is to stipulate the existence of a physically or metaphysically privileged frame which defines the global present for all observers. Recently this proposal has cropped up in literature on spatially closed universes (SCUs) which seem to naturally instantiate such structures. This paper examines the privileged frame proposal through the lens of SCUs, arguing that even in these space-times which seem overwhelmingly friendly (...) to A-theoretic accounts the theory face insurmountable challenges. (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)

Published online: 01 Dec 2006 See pg. 7-9 of pdf to view this book review.

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, Waters introduces American Indians who hold a Ph.D. in philosophy. Waters explains that because American Indians are unable to garner the financial, collegial, and academic support needed to rise to inclusive positions in the philosophical profession, most of our colleagues and students remain uneducated and ignorant about indigenous people and our philosophies that are still alive today on this shared American continent. America’s indigenous philosophers have important contributions to make to philosophy and culture; yet our conceptual nonexistence (...) exacerbates our veridical non- integration. It is a cultural luxury for the APA to not address these problems. In some moral worlds, the APA Board might have a positive obligation to address the status of American Indian philosophy with all due haste. Three possible ways of indexing American Indian philosophy for inclusion in the discipline are presented, each raising unique and particular problems for the profession. It is suggested a field of Indigenous philosophy (global) could emerge over time, having subfields of diverse cultural philosophies, not necessarily linked to nation states or current geopolitical regions. Concluding, given issues of invisibility, alliances, and responsibility, the APA remains historically morally bound to address and perhaps even redress American Indian exclusionism in the profession upon which it acts, and in the culture it complicitly creates. (shrink)

In the 4th century BC, the Greek philosopher Diodoros Chronos gave a temporal definition of necessity. Because it connects modality and temporality, this definition is of interest to philosophers working within branching time or branching space-time models. This definition of necessity can be formalized and treated within a logical framework. We give a survey of the several known modal and temporal logics of abstract space-time structures based on the real numbers and the integers, considering three (...) different accessibility relations between spatio-temporal points. (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.

This paper sets out a moderate version of metaphysical structural realism that stands in contrast to both the epistemic structural realism of Worrall and the—radical—ontic structural realism of French and Ladyman. According to moderate structural realism, objects and relations (structure) are on the same ontological footing, with the objects being characterized only by the relations in which they stand. We show how this position fares well as regards philosophical arguments, avoiding the objections against the other two versions of structural (...) realism. In particular, we set out how this position can be applied to space-time, providing for a convincing understanding of space-time points in the standard tensor formulation of general relativity as well as in the fibre bundle formulation. (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)

It is shown that the covariance together with the quantum principle speak for an affinely connected structure which, for distances greater than Planck’s length, goes over in a metrically connected structure of space-time.

It is shown that the covariance together with the quantum principle speak for an affinely connected structure which, for distances greater than Planck’s length, goes over in a metrically connected structure of space-time.

In the history of Newtonian Mechanics physicists and astronomers did not rely on so-called inertial frames, indeed they were not able to identify such frames. So the usual neo-Newtonian formalism of Newtonian Mechanics contains some superfluous components. In the present paper I will formulate a formal system for classical particle mechanics in Leibnizian space-time, where a relation, a counterpart of the second law of motion, between force on bodies and derivative of their momentum will be defined relative to (...) every, inertial or not, reference frame. And I will present a view that in the research process under Newtonian mechanics the accumulation of those models of the relation that satisfied some realistic conditions determined an additional structure of non-rotating frames to Leibnizian space-time. (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)

The two books discussed here make important contributions to our understanding of the role of spacetime concepts in physical theories and how that understanding has changed during the evolution of physics. Both emphasize what can be called a ‘dynamical’ account, according to which geometric structures should be understood in terms of their roles in the laws governing matter and force. I explore how the books contribute to such a project; while generally sympathetic, I offer criticisms of some historical claims concerning (...) Newton, and argue that the dynamical account does not undercut ontological issues as the books claim. (shrink)

The two books discussed here make important contributions to our understanding of the role of spacetime concepts in physical theories and how that understanding has changed during the evolution of physics. Both emphasize what can be called a ‘dynamical’ account, according to which geometric structures should be understood in terms of their roles in the laws governing matter and force. I explore how the books contribute to such a project; while generally sympathetic, I offer criticisms of some historical claims concerning (...) Newton, and argue that the dynamical account does not undercut ontological issues as the books claim. *Received January 2009; revised March 2009. †To contact the author, please write to: Department of Philosophy, 1423 University Hall MC 267, University of Illinois at Chicago, 601 S. Morgan Street, Chicago, IL 60607; e‐mail: [email protected]. (shrink)

Spaces of Geographical Thought examines key ideas – like space and place - which inform the geographic imagination. The text: discusses the core conceptual vocabulary of human geography: agency: structure; state: society; culture: economy; space: place; black: white; man: woman; nature: culture; local: global; and time: space; explains the significance of these binaries in the constitution of geographic thought; and shows how many of these binaries have been interrogated and re-imagined in more recent geographical (...) thinking. A consideration of these binaries will define the concepts and situate students in the most current geographical arguments and debates. The text will be required reading for all modules on the philosophy of geography and on geographical theory. (shrink)

In the existing expositions of the Károlyházy model, quantum mechanical uncertainties are mimicked by classical spreads. It is shown how to express those uncertainties through entities of the future unified theory of general relativity and quantum theory.

The paper presents the reflection on philosophical foundations of contemporary physical concepts of global history and global structure of Universe. It shows that Democritus's dualism of "matter and void" is changed now in dualism of "matter and energy" in the frame of the strings theory, where anything what looks like "a void" is absent. At the same time the Poincare-Perelman's theorem calls to rethink Democritus's philosophy in the light of "space and hole" discourse and call (...) it to come back. On the level of philosophy doctrines for contemporary fundamental physics it in necessary to combine dialectically the concept of "matter and void/hole" and the concept "matter and energy" (or "matter and singular conditions"). It is possible to do on the way of rethinking of H. Bergson's ideas presented in his book "Matter and memory". The conclusion is that fundamental dualism consists the relation "visible matter - invisible historical memory" inside of Universe. (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)

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.

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)

Whatever the answer to Molyneux's question is, it is certainly not obvious that the answer is ‘yes’. In contrast, it seems clear that we should answer affirmatively a temporal variation on Molyneux's question, introduced by Gareth Evans. I offer a phenomenological explanation of this asymmetry in our responses to the two questions. This explanation appeals to the modality-specific spatial structure of perceptual experience and its amodal temporal structure. On this explanation, there are differences in the perception of spatial (...) properties in different modalities, but these differences do not stand in the way of the objectivity of perceptual experience. (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.

One standard criterion for there being objectivity in an area of discourse is that there is conceptual space between what someone thinks to be the case and what actually is the case. That is, participants can be mistaken. This article explores one aspect of the objectivity debate as regards law: does it make sense to say that all legal officials or practitioners in a jurisdiction are mistaken (over a significant period of time) about some legal proposition? The possibility (...) of legal error is important to discourse within and about the law. In contrast to the views of some American legal realists, it is important to deny that law is only what the officials declare it to be. However, as this article argues, claims of long-term global error in law are more problematic. The truth of legal propositions seems to be a complex function of official actions and the meaning of the terms used in authoritative legal texts. Because of the conventional nature of law, there are problems with claiming global error regarding propositions of (within) law, the existence of legal norms, and structural priorities among types of legal norms. At times, the law may in fact simply be what officials (collectively) say it is, over the long term. However, the article also notes areas where claims of long-term global error are more sustainable: where the law incorporates a term from another discourse, or where the law purports to interpret an authoritative text. (shrink)