We consider a sequence of absolute-space kinematical theories which differ more or less from the special theory of relativity (STR) in the amount of clock retardation which they predict, but which agree with STR with respect to roundtrip light experiments, such as Michelson-Morley and Kennedy-Thorndike. This sequence of theories is imbedded in the synchrony-free formulation of STR developed by Winnie by modifying the equal passage time principle. The paper has bearing on the relationship between the slow clock transport behavior (...) of clocks and the one-way velocity of light. Experiments which claim to measure the latter are discussed. (shrink)

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

Summary From the following discussion, we conclude that: (a) the homogeneity of space implies (in special relativity) the homogeneity of time, and vice versa; (b) the assumption of homogeneity of space (or time) implies that the transformation formulae must be linear (see Equations (10) and (17)).

It will be shown that, in comparison with the pre-relativistic Galileo-invariant conceptions, special relativity tells us nothing new about the geometry of spacetime. It simply calls something else "spacetime", and this something else has different properties. All statements of special relativity about those features of reality that correspond to the original meaning of the terms "space" and "time" are identical with the corresponding traditional pre-relativistic statements. It will be also argued that special relativity and Lorentz theory are completely identical (...) in both senses, as theories about spacetime and as theories about the behavior of moving physical objects. (shrink)

This book examines Space, as Time and Motion, as a complex, evolving topic, from the special perspective of modern semiotics. The distinguished community of scholars explore concepts of locus, boundary, grounding, borders, sites, and cultural surrounds as aspects of the idea of semiotic space. This collection is international and transdisciplinary in range and insight. A common theme which binds these viewpoints into a cohesive text is Law with respect to that Space called human affairs.

We establish the following results: 1. In ZF (i.e., Zermelo-Fraenkel set theory minus the Axiom of Choice AC), for every set I and for every ordinal number α ≥ ω, the following statements are equivalent: (a) The Tychonoff product of| α| many non-empty finite discrete subsets of I is compact. (b) The union of| α| many non-empty finite subsets of I is well orderable. 2. The statement: For every infinite set I, every closed subset of the Tychonoff product [0, 1] (...) I which consists of functions with finite support is compact, is not provable in ZF set theory. 3. The statement: For every set I, the principle of dependent choices relativised to I implies the Tychonoff product of countably many non-empty finite discrete subsets of I is compact, is not provable in ZF⁰ (i.e., ZF minus the Axiom of Regularity). 4. The statement: For every set I, every ℵ₀-sized family of non-empty finite subsets of I has a choice function implies the Tychonoff product of ℵ₀ many non-empty finite discrete subsets of I is compact, is not provable in ZF⁰. (shrink)

In this thesis the author focuses on the metaphysical implications of the realist interpretation of special relativity. The realist interpretation is found wanting in coherence as it utilizes metaphysical concepts (as causation) that are left unjustified if the theory is taken at face value. The author points at a possible re-interpretation of special relativity that allows for a coherent metaphysical basis while containing the mathematical structure of the theory.

In this paper, I try to refute the Kantian a priorism. At the same time, I try to explain the existence of an a priori concerning space and time on the basis of contemporary neuro-physiology. This a priori is the opposite of the a-historical a priori of Kant. Concerning space and time, I argue that relativity concords with the philosophical thesis that space and time are forms of existence of matter. On the basis of this ontological principle, (...) I support that by accepting the existence of local absolute systems of reference, it is possible to explain some paradoxes of special relativity and at the same time to refute the relativism related to the theory of Einstein. (shrink)

Abstract:Arguments against physicians’ claims of a right to refuse to provide tests or treatments to patients based on conscientious objection often depend on two premises that are rarely made explicit. The first is that the protection of religious liberty (broadly construed) should be limited to freedom of worship, assembly, and belief. The second is that because professions are licensed by the state, any citizen who practices a licensed profession is required to provide all the goods and services determined by the (...) profession to fall within the scope of practice of that professional specialty and permitted by the state, regardless of any personal religious, philosophical, or moral objection. In this article, I argue that these premises ought to be rejected, and therefore the arguments that depend on them ought also to be rejected. The first premise is incompatible with Locke’s conception of tolerance, which recognizes that fundamental, self-identifying beliefs affect public as well as private acts and deserve a broad measure of tolerance. The second premise unduly (and unrealistically) narrows the discretionary space of professional practice to an extent that undermines the contributions professions ought to be permitted to make to the common good. Tolerance for conscientious objection in the public sphere of professional practice should not be unlimited, however, and the article proposes several commonsense, Lockean limits to tolerance for physician claims of conscientious objection. (shrink)

Summary The paper deals with selected problems of the verbalization of the concepts “place”, “space” and “direction”, with a special consideration of their successive development in language and in language acquisition. The theoretical background are assumptions concerning the genesis of the concept of place and movement. Some of them claim that movement and direction precede the conceptualization of place and space. However, numerous linguistic phenomena seem to prove the opposite hypothesis, namely that the concept of place and, thus, (...) its verbalization by means of stative verbs, local adverbs and prepositional phrases is original, whereas the concepts of movement, especially of controlled, caused movement denoted by transitive, regular verbs is derived from the concept of locum encoded by irregular verbs. (shrink)

Withdrawn by the author! The main content of this paper has been moved into "Szabó, László E., Does special relativity theory tell us anything new about space and time? (ID Code:1321)".

We here present explicit relational theories of a class of geometrical systems (namely, inner product spaces) which includes Euclidean space and Minkowski spacetime. Using an embedding approach suggested by the theory of measurement, we prove formally that our theories express the entire empirical content of the corresponding geometric theory in terms of empirical relations among a finite set of elements (idealized point-particles or events) thought of as embedded in the space. This result is of interest within the general (...) phenomenalist tradition as well as the theory of space and time, since it seems to be the first example of an explicit phenomenalist reconstruction of a realist theory which is provably equivalent to it in observational consequences. The interesting paper "On the Space-Time Ontology of Physical Theories" by Ken Manders, Philosophy of Science, vol. 49, number 4, December 1982, p. 575-590, has significant affinities to this one. We both, in a sense, try to formally vindicate Leibniz's notion of a relational theory of space, by constructing theories of spatial relations among physical objects which are provably equivalent to the standard absolutist theories. The essential difference between our approaches is that Manders retains Leibniz's explicitly modal framework, whereas I do not. Manders constructs a spacetime theory which explicitly characterizes the totality of possible configurations of physical objects, using a modal language in which the notion of a possible configuration occurs as a primitive. There is no doubt that this is a more accurate realization of Leibniz's own conception of space than the embedding-based approach developed here. However, it also remains open to objections (such as those cited here from Sklar) on account of the special appeal to modal notions. Our approach here, by contrast, aims to avoid the special appeal to modal notions by giving directly a set of laws which are satisfied by a configuration individually, if and only if it is one of the allowable ones. One thus avoids the need for reference to possible but not actual configurations or objects, in the statement of the spacetime laws. We may then take this alternative set of laws as the actual geometric theory, and do away with the hypothetical entity called 'space'. Yet at the same time there is no invocation of modality, except in the ordinary sense in which every physical theory constrains what is possible. So that a relationalist is not forced to utilize a modal language (though Leibniz certainly does.). (shrink)

Are probabilism and special relativity compatible? Dieks argues that they are. But the possible universe he specifies, designed to exemplify both probabilism and special relativity, either incorporates a universal “now”, or amounts to a many world universe, or fails to have any one definite overall Minkowskian-type space-time structure. Probabilism and special relativity appear to be incompatible after all. What is at issue is not whether “the flow of time” can be reconciled with special relativity, but rather whether explicitly probabilistic (...) versions of quantum theory should be rejected because of incompatibility with special relativity. (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)

In the late nineteenth and early twentieth centuries the need to rethink the status of space and time which Kant considered to be a priori forms of sensibility was prompted by the emergence of new approaches to the methodology of scientific cognition. In neo-Kantian interpretation these cognitive forms acquire a special epistemological status, manifesting themselves in theoretical research as “pre-given” foundations of knowledge. It seems necessary to conduct a comparative analysis of two interconnected neo-Kantian concepts, of Hermann Cohen and (...) Ivan Lapshin. Studying Kant’s philosophy since his student days, Lapshin gradually came to the conclusion that the need to clarify and develop Kant’s transcendental method was dictated by the development of scientific knowledge. Indeed, the works of the Russian neo-Kantian contain echoes and polemical adjustments of Cohen’s spatio-temporal ideas. Our study has revealed common epistemological attitudes in Cohen and Lapshin: the wish to improve elements of Kantian philosophy, adjusting them to prove the possibility of scientific-theoretical cognition and of overcoming psychologism and developing the logicistic approach to the critique of cognition. Each of the two authors developed their own “mechanism” of reducing space and time to a range of intellectual procedures for the construction of the object of knowledge. In Cohen’s account space and time pre-establish the language of observation and found all scientific-theoretical work. Lapshin, on the other hand, in discussing the formal and substantive features of these categories (the introduction of “axioms” of time, the need to specify the concepts of time and space through other categories), notes that their use in scientific judgment implies an epistemological givenness of the concept of the object. This I see as a variant of solving one and the same epistemological task. I submit that Lapshin worked out an independent concept of space and time as cognitive forms that are congruent with the spirit of European neo-Kantianism and contemporary science. (shrink)

The articles that comprise this special issue of Intellectual History Review are briefly described.

A description of consciousness leads to a contradiction with the postulation from special relativity that there can be no connections between simultaneous event. This contradiction points to consciousness involving quantum level mechanisms. The Quantum level description of the universe is re- evaluated in the light of what is observed in consciousness namely 4 Dimensional objects. A new improved interpretation of Quantum level observations is introduced. From this vantage point the following axioms of consciousness is presented. Consciousness consists of two distinct (...) components, the observed U and the observer I. The observed U consist of all the events I is aware of. A vast majority of these occur simultaneously. Now if I were to be an entity within the space-time continuum, all of these events of U together with I would have to occur at one point in space-time. However, U is distributed over a definite region of space-time (region in brain). Thus, I is aware of a multitude of space-like separated events. It is seen that this awareness necessitates I to be an entity outside the space-time continuum. With I taken as such, a new concept called concept A is introduced. With the help of concept A a very important axiom of consciousness, namely Free Will is explained. (shrink)

The primary objective of this study is to provide a description of the major ideas about void space within and beyond the world that were formulated between the fourteenth and early eighteenth centuries. The second part of the book - on infinite, extracosmic void space - is of special significance. The significance of Professor Grant's account is twofold: it provides the first comprehensive and detailed description of the scholastic Aristotelian arguments for and against the existence of void (...) class='Hi'>space; and it presents (again for the first time) an analysis of the possible influence of scholastic ideas and arguments on the interpretations of space proposed by the nonscholastic authors who made the Scientific Revolution possible. The concluding chapter of the book is unique in not only describing the conceptualizations of space proposed by the makers of the Scientific Revolution, but in assessing the role of readily available scholastic ideas on the conception of space adopted for the Newtonian world. (shrink)

In this paper, we are interested in parallels to the classical notions of special subsets in defined in the generalized Cantor and Baire spaces (2κ and ). We consider generalizations of the well‐known classes of special subsets, like Lusin sets, strongly null sets, concentrated sets, perfectly meagre sets, σ‐sets, γ‐sets, sets with the Menger, the Rothberger, or the Hurewicz property, but also of some less‐know classes like X‐small sets, meagre additive sets, Ramsey null sets, Marczewski, Silver, Miller, and Laver‐null sets. (...) We notice that many classical theorems regarding these classes can be relatively easy generalized to higher cardinals although sometimes with some additional assumptions. This paper serves as a catalogue of such results along with some other generalizations and open problems. (shrink)

In recent work, David Chalmers argues that “Edenic shapes”—roughly, the shape properties phenomenally presented in spatial experience—are not instantiated in our world. His reasons come largely from the theory of Special Relativity. Although Edenic shapes might have been instantiated in a classical Newtonian world, he maintains that they could not be instantiated in a relativistic world like our own. In this essay, I defend realism about Edenic shape, the thesis that Edenic shapes are instantiated in our world, against Chalmers’s challenge (...) from Special Relativity. I begin by clarifying the notion of an Edenic shape by reference to Chalmers’s notion of the “Edenic” content of perceptual experience. I then reconstruct Chalmers’s argument that Edenic shapes could not be instantiated in a relativistic world. His reasoning proceeds from two assumptions. The first is that the only shape properties instantiated in a relativistic world are those which somehow involve relations to frames of reference. This is thought to follow from the phenomenon of Lorentz contraction, a consequence of Special Relativity. The second assumption is that Edenic shapes do not involve relations to frames of reference. One reason to accept the second assumption is that it seems that Edenic shapes could be instantiated in a classical Newtonian world, where the notion of a frame-relative shape has no meaningful application. I then proceed to defend RES against Chalmers’s argument by arguing that Special Relativity, properly understood, provides no support for Chalmers’s first assumption. More generally, I argue, by way of a careful analysis of the geometric structure of Minkowski space–time and Galilean space–time Newtonian physics), that Edenic shapes are no less at home in a relativistic world than in a classical Newtonian world. (shrink)

The article introduces a special themed issue of Theory of Science on epistemologies of spaces and places. It provides a disciplinary context of the theme and reviews some of the key arguments that led to the so-called spatial turn in social sciences and the humanities. Science studies in the broad sense have also been affected by this shift of research interest to spatial aspects of science at both micro- and macro-levels. Scientific knowledge has been subject to analyses that stress its (...) local contingencies, mobility and dependencies on spatial arrangements. The ensuing new epistemologies require novel concepts or reconsideration of the older terms, such as universality or objectivity. (shrink)

That space and time should be integrated into a single entity, spacetime, is the great insight of Einstein's special theory of relativity, and leads us to regard spacetime as a fundamental context in which to make sense of the world around us. But it is not the only one. Causality is equally important and at least as far as the special theory goes, it cannot be subsumed under a fundamentally geometrical form of explanation. In fact, the agent of propagation (...) of causal influence is electromagnetic radiation. In this examination, the authors find support for a rationalist approach to physics, never neglecting experimentation, but rejecting a simple empiricist or positivist view of science. (shrink)

An investigation of the views on space and time of the Russian polymath Pavel Florensky. After a brief account of his life, I study Florensky’s conception of time in The Meaning of Idealism, where he first confronts Einstein’s theory of special relativity, comparing it to Plato’s metaphor of the Cave and Goethe’s myth of the Mothers. Later, in his Analysis of spatiality and time, Florensky speaks of a person’s biography as a four-dimensional unity, in which the temporal coordinate is (...) examined in sections. In On the Imaginaries in Geometry, Florensky argues that the speed of light is not, as in Relativity, an absolute speed limit in the universe. When bodies approach and then surpass the speed of light, they are transformed into unextended, eternal Platonic forms. Beyond this point, time runs in reverse, effects precede their causes, and efficient causality is transformed into final or teleological causality, a concept on which Florensky elaborates in his Iconostasis. Florensky thus transformed the findings of Einsteinian relativity in order to make room for Plato’s intelligible Ideas, the Aristotelian distinction between a changing realm of earth and the immutable realm of the heavens, and the notion of teleology or final causation. His notion that man can approximate God’s vision of past, present and future all at once, as if from above, is reminiscent of Boethius’ ideas. (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)

The ArgumentEmergency medicine, a new medical specialty in the United States, is an ethical practice that has developed through its interaction with the spaces in which it is situated. We discuss this claim in two steps followed by a demonstration. First we examine the historical evolution of the hospital, to provide the background for a lengthier account of the historical transformation of the emergency room. We then introduce Foucault's approach to ethics, to explain the sense in which emergency medicine is (...) an ethical practice constituted, in part, by its space(s) of operation. The preliminaries of the application of our historico-ethical framework to emergency medicine, are presented, focusing on cardiopulmonary resuscitation. Our intention is to provide a framework for the newest clinical specialty as an ethical practice in order to understand how to individuate its emerging ethical problems. The emphasis on space throughout enables us to integrate the historical development of emergency medicine with its present concrete setting, and to establish a basis for analyzing emergency medicine that does not rely uncritically on either a preferred ethical perspective or the perspective of its practitioners. (shrink)

A theoretical device, which incorporates the functions of clock, rod, nonrotating platform, and accelerometer, and whose operation depends on the properties of light rays and free particles, is defined. The device, which we call a metrosphere, is simple enough that it can be introduced at the starting point of relativity theory and versatile enough that it can serve as an aid in the development and conceptualization of the theory. Relative to an inertial frame, a moving metrosphere undergoes a Lorentz-Fitzgerald contraction (...) and the associated clock exhibits a Lorentz-Larmor rate retardation. From this fact and the assumption that there exists one inertial frame, it is possible to generate the kinematical results of special relativity. A metrosphere provides an observer with a local frame of reference, hence it is well adapted to the needs of general relativity, allows the equivalence principle to be introduced in a straightforward manner, and permits a smooth transition from special relativity to general relativity. (shrink)

The concept of inertial frame of reference in classical physics and special theory of relativity is analysed. It has been shown that this fundamental concept of physics is not clear enough. A definition of inertial frame of reference is proposed which expresses its key inherent property. The definition is operational and powerful. Many other properties of inertial frames follow from the definition, or it makes them plausible. In particular, the definition shows why physical laws obey space and time symmetries (...) and the principle of relativity, it resolves the problem of clock synchronization and the role of light in it, as well as the problem of the geometry of inertial frames. (shrink)

The open future view is the common-sense view that there is an ontological difference between the past, the present, and the future in the sense that the past and the present are real, whereas the future is not yet a part of reality. In this paper we develop a theory in which the open future view is consistently combined with special relativity. Technically, the heart of our contribution is a logical conservativity result showing that, although the open future view is (...) not definable inside the causal geometry of Minkowski space-time, it can be conservatively added to it. (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)

The main features of how to build a Born’s Reciprocal Gravitational theory in curved phase-spaces are developed. By recurring to the nonlinear connection formalism of Finsler geometry a generalized gravitational action in the 8D cotangent space (curved phase space) can be constructed involving sums of 5 distinct types of torsion squared terms and 2 distinct curvature scalars ${\mathcal{R}}, {\mathcal{S}}$ which are associated with the curvature in the horizontal and vertical spaces, respectively. A Kaluza-Klein-like approach to the construction of (...) the curvature of the 8D cotangent space and based on the (torsionless) Levi-Civita connection is provided that yields the observed value of the cosmological constant and the Brans-Dicke-Jordan Gravity action in 4D as two special cases. It is found that the geometry of the momentum space can be linked to the observed value of the cosmological constant when the curvature in $\mathit{momentum}$ space is very large, namely the small size of P is of the order of $( 1/R_{\mathit{Hubble}})$ . Finally we develop a Born’s reciprocal complex gravitational theory as a local gauge theory in 8D of the $\mathit{deformed}$ Quaplectic group that is given by the semi-direct product of U(1,3) with the $\mathit{deformed}$ (noncommutative) Weyl-Heisenberg group involving four $\mathit{noncommutative}$ coordinates and momenta. The metric is complex with symmetric real components and antisymmetric imaginary ones. An action in 8D involving 2 curvature scalars and torsion squared terms is presented. (shrink)

In the interview in this article, Randall Collins discusses various aspects of his oeuvre. First, he considers why interaction rituals (IRs) in religion are special emotional transformers. This is followed by a discussion of IRs in the digital age and the symbolic and economic power that is required to orchestrate IRs in politics and revolutions. Then comes a discussion of social scientific research into violence, in the past and more recently. The interview continues with a reflection on the notion of (...) attention space, a concept which Collins has applied in analyses of violent interactions and the intellectual struggles between philosophers. Finally, the article considers the state of the art of sociology and its future prospects, evaluating its potential for rapid discovery and its position on the abstraction-reflexivity continuum. As the interview demonstrates Collins’s insightful sociological craftsmanship, it provides social scientists with a strong and optimistic lead in how to do social theory. (shrink)

When people make sense of situations, illustrations, instructions and problems they do more than just think with their heads. They gesture, talk, point, annotate, make notes and so on. What extra do they get from interacting with their environment in this way? To study this fundamental problem, I looked at how people project structure onto geometric drawings, visual proofs, and games like tic tac toe. Two experiments were run to learn more about projection. Projection is a special capacity, similar to (...) perception, but less tied to what is in the environment. Projection, unlike pure imagery, requires external structure to anchor it, but it adds ‘mental’ structure to the external scene much like an augmented reality system adds structure to an outside scene. A person projects when they look at a chessboard and can see where a knight may be moved. Because of the cognitive costs of sustaining and extending projection, humans make some of their projections real. They create structure externally. They move the piece, they talk, point, notate, represent. Much of our interactivity during sense making and problem solving involves a cycle of projecting then creating structure. (shrink)

Einstein regarded as one of the triumphs of his 1915 theory of gravity - the general theory of relativity - that it vindicated the action-reaction principle, while Newtonian mechanics as well as his 1905 special theory of relativity supposedly violated it. In this paper we examine why Einstein came to emphasise this position several years after the development of general relativity. Several key considerations are relevant to the story: the connection Einstein originally saw between Mach's analysis of inertia and both (...) the equivalence principle and the principle of general covariance, the waning of Mach's influence owing to de Sitter's 1917 results, and Einstein's detailed correspondence with Moritz Schlick in 1920. (shrink)

Already in 1835 Lobachevski entertained the possibility of multiple geometries of the same type playing a role. This idea of rival geometries has reappeared from time to time but had yet to become a key idea in space-time philosophy prior to Brown's _Physical Relativity_. Such ideas are emphasized towards the end of Brown's book, which I suggest as the interpretive key. A crucial difference between Brown's constructivist approach to space-time theory and orthodox "space-time realism" pertains to modal (...) scope. Constructivism takes a broad modal scope in applying to all local classical field theories---modal cosmopolitanism, one might say, including theories with multiple geometries. By contrast the orthodox view is modally provincial in assuming that there exists a _unique_ geometry, as the familiar theories have. These theories serve as the "canon" for the orthodox view. Their historical roles also suggest a Whiggish story of inevitable progress. Physics literature after c. 1920 is relevant to orthodoxy primarily as commentary on the canon, which closed in the 1910s. The orthodox view explains the spatio-temporal behavior of matter in terms of the manifestation of the real geometry of space-time, an explanation works fairly well within the canon. The orthodox view, Whiggish history, and the canon have a symbiotic relationship. If one happens to philosophize about a theory outside the canon, space-time realism sheds little light on the spatio-temporal behavior of matter. Worse, it gives the _wrong_ answer when applied to an example arguably _within_ the canon, a sector of Special Relativity, namely, _massive_ scalar gravity with universal coupling. Which is the true geometry---the flat metric from the Poincare' symmetry group, the conformally flat metric exhibited by material rods and clocks, or both---or is the question faulty? How does space-time realism explain the fact that all matter fields see the same curved geometry, when so many ways to mix and match exist? Constructivist attention to dynamical details is vindicated; geometrical shortcuts can disappoint. The more exhaustive exploration of relativistic field theories in particle physics, especially massive theories, is a largely untapped resource for space-time philosophy. (shrink)

I take up Kant's remarks about a " transcendental deduction" of the "concepts of space and time". I argue for the need to make a clearer assessment of the philosophical resources of the Aesthetic in order to account for this transcendental deduction. Special attention needs to be given to the fact that the central task of the Aesthetic is simply the "exposition" of these concepts. The Metaphysical Exposition reflects upon facts about our usage to reveal our commitment to the (...) idea that these concepts refer to pure intuitions. But the legitimacy of these concepts still hangs in the balance: these concepts may turn out to refer to nothing real at all. The subsequent Transcendental Exposition addresses this issue. The objective validity of the concepts of space and time, and hence their transcendental deduction, hinges on careful treatment of this last point. (shrink)

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

We show that the special relativistic dynamics when combined with quantum mechanics and the concept of superstatistics can be interpreted as arising from two interlocked non-relativistic stochastic processes that operate at different energy scales. This interpretation leads to Feynman amplitudes that are in the Euclidean regime identical to transition probability of a Brownian particle propagating through a granular space. Some kind of spacetime granularity could be therefore held responsible for the emergence at larger scales of various symmetries. For illustration (...) we consider also the dynamics and the propagator of a spinless relativistic particle. Implications for doubly special relativity, quantum field theory, quantum gravity and cosmology are discussed. (shrink)

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

These are just some of the fundamental questions addressed in Time and Space. Writing for a primary readership of advanced undergraduate and graduate philosophy students, Barry Dainton introduces the central ideas and arguments that make space and time such philosophically challenging topics. Although recognising that many issues in the philosophy of time and space involve technical features of physics, Dainton has been careful to keep the conceptual issues accessible to students with little scientific or mathematical training. Surveying (...) historical debates and ideas at the forefront of contemporary thinking, the book is unrivaled in its coverage. Topics include McTaggart's argument for the unreality of change; static, tensed, and dynamic time; time travel and causal arrows; space as void, motion, and curved spac; as well as a non-technical introduction to the special theory of relativity and the key features of general relativity, spacetime, and strings. Dainton also addresses the relationship between the philosophy of time and broader human concerns involving actions, ethics, fatalism, and death. (shrink)

This article attempts to explain and analyse the nature and characteristic features of a person’s privacy in the on‐line environment in order to assess how these features shape the need for protection. Since the internet has invaded our everyday lives, individual privacy is exposed in different ways in cyberspace. It is important to note that the Internet lacks the traditional characteristics of a ‘physical’ space, but the interests and inherent values protected by privacy remain the same in cyberspace. The (...) article discusses the factors that shape a different nature of online privacy compared to its off line counterpart. Online privacy may not be a novel right, but it is definitely one exposed to a whole new environment which has its own special need for protection. (shrink)

Einstein acknowledged that his reading of Hume influenced the development of his special theory of relativity. In this article, I juxtapose Hume’s philosophy with Einstein’s philosophical analysis related to his special relativity. I argue that there are two common points to be found in their writings, namely an empiricist theory of ideas and concepts, and a relationist ontology regarding space and time. The main thesis of this article is that these two points are intertwined in Hume and Einstein.

This article is concerned to formulate some open problems in the philosophy of space and time that require methods characteristic of mathematical traditions in the foundations of geometry for their solution. In formulating the problems an effort has been made to fuse the separate traditions of the foundations of physics on the one hand and the foundations of geometry on the other. The first part of the paper deals with two classical problems in the geometry of space, that (...) of giving operationalism an exact foundation in the case of the measurement of spatial relations, and that of providing an adequate theory of approximation and error in a geometrical setting. The second part is concerned with physical space and space-time and deals mainly with topics concerning the axiomatic theory of bodies, the operational foundations of special relativity and the conceptual foundations of elementary physics. (shrink)

According to the Special Theory of Relativity, there is no such thing as absolute simultaneity, contrary to the view defended in the book. However, this chapter demonstrates that the Special Theory of Relativity can be modified so as to allow absolute simultaneity. This modification involves reference to absolute space and the causal relations between space‐time points, and drops the assumption that the one‐way speed of light is constant through all frames of reference. Contrary to the orthodox theory, the (...) modified version has the additional advantage of avoiding a clash with quantum mechanics, such as brought out by the Einstein‐Podolsky‐Rosen thought experiment and Bell's Theorem. (shrink)

For much of this century it was widely assumed in philosophical circles that the relational doctrine of space, time, and motion had finally been established beyond the point of reasonable controversy. In large part this was due to a widespread perception that the theory of relativity is itself a relational theory. Indeed, some of Einstein’s own pronouncements foster this impression. For example, in his definitive formulation of general relativity of 1916, he argued the need for a generalization of the (...) principle of special relativity in order to eliminate the “factitious” causal role he saw inertial frames playing in classical mechanics and special relativity. ‘The laws of physics must be of such a nature that they apply to systems of reference in any kind of motion’. Einstein claimed this requirement is fulfilled by satisfaction of the Principle of General Covariance—that the equations expressing the laws of nature remain valid under arbitrary coordinate substitutions. This, he says, ‘takes away from space and time the last remnant of physical objectivity.’. (shrink)

Special relativity has changed the fundamental view on space and time since Einstein introduced it in 1905. It substitutes four dimensional spacetime for the absolute space and time of Newtonian mechanics. It is believed that the validities of Lorentz invariants are fully confirmed empirically for the last one hundred years and therefore its status are canonical underlying all physical principles. However, spacetime metric is a geometric approach on nature when we interpret the natural phenomenon. A geometric flaw on (...) this will be exhibited and the alternative is suggested. The reasonable geometric model of space and time is a three dimensional space which is translating along the time direction. This model legitimately represents the true characteristic of nature. (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.

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 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)