The Schwarzschild solution (Schwarzschild, 1915/16) to Einstein’s General Theory of Relativity (GTR) is accepted in theoretical physics as the unique solution to GTR for a central-mass system. In this paper I propose an alternative solution to GTR, and argue it is both logically consistent and empirically realistic as a theory of gravity. This solution is here called K-gravity. The introduction explains the basic concept. The central sections go through the technical detail, defining the basic (...) solution for the geometric tensor, the Christoffel symbols, Ricci tensor, Ricci scalar, Einstein tensor, stress-energy tensor and density-pressure for the system. The density is integrated, and some consistency properties are demonstrated. A notable feature is the disappearance of the event horizon singularity, i.e. there are no black holes. So far this is for a single central mass. A generalization of the solution for multiple masses is then proposed. This is required to support K-gravity as a viable general interpretation of gravity. Then the question of empirical tests is discussed. It is argued that current observational data is almost but not quite sufficient to verify or falsify K-gravity. The Pioneer spacecraft trajectory data is of particular interest, as this is capable of providing a test; but the data (which originally showed anomalies that match K-gravity) is now uncertain. A new and very practical experiment is proposed to settle the matter. This would provide a novel test of GTR, and a novel test of the cause of the Pioneer anomalies. In conclusion, K-gravity has extensive ramifications for gravitational physics and for the philosophy of GTR and space-time. (shrink)

A number of different forms of the Schwarzschild solution are considered. The static forms all have a singularity at the Schwarzschild radius. This Schwarzschild singularity can be eliminated if one goes over to a stationary or time-dependent form of solution. However, the coordinate transformations needed for this have singularities. It is stressed that coordinate systems connected by singular transformations are not equivalent and the corresponding metrics may describe different physical situations.

The Schwarzschild solution has played a fundamental conceptual role in general relativity, and beyond, for instance, regarding event horizons, spacetime singularities and aspects of quantum field theory in curved spacetimes. However, one still encounters the existence of misconceptions and a certain ambiguity inherent in the Schwarzschild solution in the literature. By taking into account the point of view of an observer in the interior of the event horizon, one verifies that new conceptual difficulties arise. In this (...) work, besides providing a very brief pedagogical review, we further analyze the interior Schwarzschild black hole solution. Firstly, by deducing the interior metric by considering time-dependent metric coefficients, the interior region is analyzed without the prejudices inherited from the exterior geometry. We also pay close attention to several respective cosmological interpretations, and briefly address some of the difficulties associated to spacetime singularities. Secondly, we deduce the conserved quantities of null and timelike geodesics, and discuss several particular cases in some detail. Thirdly, we examine the Eddington–Finkelstein and Kruskal coordinates directly from the interior solution. In concluding, it is important to emphasize that the interior structure of realistic black holes has not been satisfactorily determined, and is still open to considerable debate. (shrink)

The special and general relativity theories are used to demonstrate that the velocity of an unradiative particle in a Schwarzschild metric background, and in an electrostatic field, is the group velocity of a wave that we call a “particle wave,” which is a monochromatic solution of a standard equation of wave motion and possesses the following properties. It generalizes the de Broglie wave. The rays of a particle wave are the possible particle trajectories, and the motion equation of (...) a particle can be obtained from the ray equation. The standing particle wave equation generalizes the Schrödinger equation of wave amplitudes. The particle wave motion equation generalizes the Klein–Gordon equation; this result enables us to analyze the essence of the particle wave frequency. The equation of the eikonal of a particle wave generalizes the Hamilton–Jacobi equation; this result enables us to deduce the general expression for the linear momentum. The Heisenberg uncertainty relation expresses the diffraction of the particle wave, and the uncertainty relation connecting the particle instant of presence and energy results from the fact that the group velocity of the particle wave is the particle velocity. A single classical particle may be considered as constituted of geometrical particle wave; reciprocally, a geometrical particle wave may be considered as constituted of classical particles. The expression for a particle wave and the motion equation of the particle wave remain valid when the particle mass is zero. In that case, the particle is a photon, the particle wave is a component a classical electromagnetic wave that is embedded in a Schwarzschild metric background, and the motion equation of the wave particle is the motion equation of an electromagnetic wave in a Schwarzschild metric background. It follows that a particle wave possesses the same physical reality as a classical electromagnetic wave. This last result and the fact that the particle velocity is the group velocity of its wave are in accordance with the opinions of de Broglie and of Schrödinger. We extend these results to the particle subjected to any static field of forces in any gravitational metric background. Therefore we have achieved a synthesis of undulatory mechanics, classical electromagnetism, and gravitation for the case where the field of forces and the gravitational metric background are static, and this synthesis is based only on special and general relativity. (shrink)

General Relativity’s Schwarzschild solution describes a spherically symmetric gravitational field as an utterly static thing. The Space Generation Model describes it as an absolutely moving thing. The light propagation time-delay experiment of Shapiro-Reasenberg [1] and the falling atomic clock experiment of Vessot-Levine [2] provide the ideal context for illustrating how, though the respective world views implied by these models are radically di fferent, they make nearly the same prediction for the results of these experiments.

Complete collection of Schwarzschild’s essays on the neo-Kantian Jewish philosopher Hermann Cohen. Steven S. Schwarzschild (1924–1989) was arguably the leading expositor of German-Jewish philosopher Hermann Cohen (1842–1918), undertaking a lifelong effort to reintroduce Cohen’s thought into contemporary philosophical discourse. In The Tragedy of Optimism, George Y. Kohler brings together all of Schwarzschild’s work on Cohen for the first time. Schwarzschild’s readings of Cohen are unique and profound; he was conversant with both worlds that shaped Cohen’s thought, (...) neo-Kantian German idealism and Jewish theology. The collection covers a wide range of subjects, from ethics, socialism, the concept of human selfhood, and the mathematics of the infinite to more explicitly Jewish themes. This volume includes two of Schwarzschild’s previously unpublished manuscripts and a scholarly introduction by Kohler. Schwarzschild shows that despite its seeming defeat by events of the twentieth century, Cohen’s optimism about human progress is a rational, indeed necessary, path to peace. George Y. Kohler is Director of the Joseph Carlebach Institute and Senior Lecturer of Jewish Philosophy at Bar Ilan University, Israel. He is the author of Reading Maimonides’ Philosophy in 19th Century Germany: The Guide to Religious Reform. (shrink)

This dissertation is based on the compositional model theoretic approach to natural language semantics that was initiated by Montague (1970) and developed by subsequent work. In this general approach, coordination and negation are treated following Keenan & Faltz (1978, 1985) using boolean algebras. As in Barwise & Cooper (1981) noun phrases uniformly denote objects in the boolean domain of generalized quanti®ers. These foundational assumptions, although elegant and minimalistic, are challenged by various phenomena of coordination, plurality and scope. The dissertation solves (...) these problems by developing a ¯exible process of meaning composition, as ®rst proposed by Partee & Rooth (1983). Flexible interpretation involves semantic operations without any phonological counterpart, which participate in the interpretation process and change meanings of overt expressions. The dissertation introduces a novel ¯exible system where a small number of operations describe the behaviour of complex phenomena such as `non-boolean' and, the scope of inde®nites and the semantics of collectivity with quanti®cational NPs. The proposed theory is based on a distinction between two features of meanings in natural language. (shrink)

I argue that Judaism and Jewish culture have paradigmatically and throughout history operated with a fundamental dichotomy between nature and ethics. Pagan ontologism, on the other hand, and the Christian synthesis of biblical transcendentalism and Greek incamationism result in human and historical submission to what are acclaimed as “natural forces.” Although in the history of Jewish culture such a heretical, quasi-pantheistic tendency asserted itself, first in mediaeval kabbalism and then in modem Zionism, from a traditional Jewish standpoint nature remains subject (...) to humanly enacted ends. Evidence for this general thesis can be found in biblical, Talmudic, medieval philosophic, and mystical literature, in modem religious, poetic, and Zionist literature, and in the history of general philosophy. (shrink)

This paper strives to characterize the relation between accent placement and discourse in terms of independent constraints operating at the interface between syntax and interpretation. The Givenness Constraint requires un-F-marked constituents to be given. Key here is our definition of givenness, which synthesizes insights from the literature on the semantics of focus with older views on information structure. AvoidF requires speakers to economize on F-marking. A third constraint requires a subset of F-markers to dominate accents.The characteristic prominence patterns of "novelty (...) focus" and "contrastive focus" both arise from a combination of the Givenness Constraint and AvoidF. Patterns of prominence in questions as well as in answers to questions are explained in terms of the constraints, thanks in part to the way in which the Givenness relation is defined. Head/argument asymmetries noted in the literature on Focus Projection are placed in the phonology-syntax interface, independent of discourse conditions. Deaccenting follows when AvoidF is ranked higher than constraint(s) governing head/argument asymmetries. (shrink)

An introductory text in linguistic semantics, uniquely balancing empirical coverage and formalism with development of intuition and methodology. -/- This introductory textbook in linguistic semantics for undergraduates features a unique balance between empirical coverage and formalism on the one hand and development of intuition and methodology on the other. It will equip students to form intuitions about a set of data, explain how well an analysis of the data accords with their intuitions, and extend the analysis or seek an alternative. (...) No prior knowledge of linguistics is required. After mastering the material, students will be able to tackle some of the most difficult questions in the field even if they have never taken a linguistics course before. -/- After introducing such concepts as truth conditions and compositionality, the book presents a basic symbolic logic with negation, conjunction, and generalized quantifiers, to serve as the basis for translation throughout the book. It then develops a detailed compositional semantics, covering quantification (scope and binding), adverbial modification, relative clauses, event semantics, tense and aspect, as well as pragmatic phenomena, notably deictic pronouns and narrative progression. -/- A Course in Semantics offers a large and diverse set of exercises, interspersed throughout the text; those labeled “Important practice and looking ahead” prepare students for material to come; those labeled “Thinking about ” invite students to think beyond the content of the book. (shrink)

(1) is an example of an adjectival comparative. In it, the adjective important is flanked by more and a comparative clause headed by than. This article is a survey of recent ideas about the interpretation of comparatives, including (i) the underlying semantics based on the idea of a threshold; (ii) the interpretation of comparative clauses that include quantifiers (brighter than on many other days); (iii) remarks on differentials such as much in (1) above: what they do in the comparative and (...) what they do elsewhere in the language; (iv) the relationship between comparatives and other Degree constructions (e.g. as important, too impor- tant); and (v) the types of phrases in which comparatives are found (adjective: tighter versus noun: more water). Given the nature and purpose of this essay, I have tried not to presuppose background in formal semantics and I have departed from standard practice in journal articles by, as much as possible, not interrupting the flow with footnotes and references. There are two appendices. The first provides more analytical detail and there I do rely on formal techniques of natural language semantics. The second covers the sources for the ideas surveyed here. (shrink)

In the formation of extended noun phrases, expressions are used that describe some dimension. Weight is described by each of the prenominal expressions in heavy rock, too much ballast, 2 lb rock, 2 lbs of rocks. The central claim of this paper is that the position of these types of expressions within the noun phrase limits the kinds of dimensions they may describe. The limitations have to do with whether or not the dimension tracks relevant part-whole relations. An analogy is (...) made between these constraints and the well-known constraints on thematic relations that are incurred by the position of a noun phrase in a clause. A proposal is made about the meanings of expressions like too much and 2 pounds which explains their common cross-categorial distribution and this informs the analysis of their use in noun phrases. A position is taken on the meaning of the count mass distinction which, in conjunction with the hypothesis about dimensions, explains asymmetries in the distribution of prenominal adjectives with count and mass nouns. (shrink)

This paper begins with a discussion ofcumulativity (e.g., ‘P(a) & P(b) implies P(a+b)’), formalized using a verb phrase operator. Next, the meanings of distributivity markers such aseach and non-distributivity indicators such astogether are considered. An existing analysis ofeach in terms of quantification over parts of a plurality is adopted. However,together is problematic, for it involves a cancellation or negation of the quantification associated witheach. (The four boys together owned exactly three cars could not be true if each of the boys (...) owned three cars, though the same sentence withouttogether could be.) A refinement of this idea of negated quantification over parts is proposed as an analysis for non-distributivity operators. It is then worked out in the system described in Cooper (1983), in which positive and negative extensions are assigned. Presuppositions connected with plural reference are considered at this point as well. Finally, the cumulativity operator is argued to be quantificational and therefore sensitive to contextual domain selection. This context sensitivity is claimed to be the source of distributive readings that appear in the absence of modifiers likeeach and non-distributive or collective readings that arise withouttogether. (shrink)

There are predicates that I call “stubbornly distributive” based on what happens when they are combined with plural count noun phrases. I will use these stubbornly distributive predicates to identify and analyze a certain subset of mass nouns which I call “multi-participant nouns”. Traffic and rubble are multi-participant nouns but furniture and luggage turn out not to be. Importantly, ‘typical’ mass nouns like water are multiparticipant nouns.

This paper grew out of a reaction to Elisabeth Selkirk's contribution to the Handbook of Phonology (Goldsmith 1996). Section 1.2 of that article is concerned with syntactic and semantic aspects of the placement of pitch accents in English. As will be seen in the data to be presented below, the constellation of pitch accents in an utterance is determined in part by properties of the preceding discourse, including the distinction between new and old information. This means for example, that a (...) phrase containing accent is appropriate in a different set of contexts than that same phrase unaccented. Since accents are assigned within words but the pragmatics can make reference to phrases, the following question arises. Given a word that is accented, which phrases count as containing accent as far as the pragmatics is concerned and which not? This question is known as the projection problem, though I have characterized it in slightly different terms than is normally done, for reasons to be made clear below. As Selkirk shows, projection is sensitive to argument structure and other syntactic notions (see Gussenhoven(1984), Rochement(1986), Schmerling(1976) and Selkirk 1984)). In Selkirk's system, a sentence can have one or more foci and these foci are marked with an F in the syntactic tree. Focussing a phrase leads to a certain kind of.. (shrink)

The association of only with focus is explained in terms of (a) a semantics for only which makes no mention of focus and (b) discourse appropriateness conditions on the use of focus and principles of quantifier domain selection. This account differs from previous ones in giving sufficient conditions for association with focus but without stipulating it in the meaning of lexical items. Detractors have contended that foci have different pragmatic import depending on whether or not they are associated with a (...) higher operator. I give evidence against this claim. Others argue that there is no deterministic connection between intonational focus and association. One argument for this is the fact that association readings are possible even when nothing in the scope of the operator is focussed. The present account predicts the absence of intonational focus in these cases and explains how the readings come about. The wide variety of associating operators provide incentive for pursuing accounts like the present one based on independent principles of grammar. (shrink)

The sentence Irving was closer to me than he was to most of the others contains a quantifier, most of the other, in the scope a comparative. The first part of this paper explains the challenges presented by such cases to existing approaches to the semantics of the comparative. The second part presents a new analysis of comparatives based on intervals rather than points on a scale. This innovation is analogized to the move from moments to intervals in tense semantics. (...) The remainder of the paper is concerned with an interval-based semantics of degree in relation to issues other than the comparative proper. The paper begins with a discussion of the role negative polarity has played in studies on the semantics of comparatives. (shrink)

I argue that Judaism and Jewish culture have paradigmatically and throughout history operated with a fundamental dichotomy between nature (“what is”) and ethics (i.e., God and man-“what ought to be”). Pagan ontologism, on the other hand, and the Christian synthesis of biblical transcendentalism and Greek incamationism result in human and historical submission to what are acclaimed as “natural forces.” Although in the history of Jewish culture such a heretical, quasi-pantheistic tendency asserted itself, first in mediaeval kabbalism and then in modem (...) Zionism, from a traditional Jewish standpoint nature remains subject to humanly enacted ends. Evidence for this general thesis can be found in biblical, Talmudic, medieval philosophic, and mystical literature, in modem religious, poetic, and Zionist literature, and in the history of general philosophy. (shrink)

This chapter contains sections titled: The Enlightenment and Its Antecedents Equal Rights and American Constitutional Law Liberty and Equality under the Constitution The Radical Critique and the Radical Dilemma Rawls Dworkin Equality of Capabilities Equality Unmodified or Spheres of Justice Is Equality a Value? References.

It is natural to think of comparisons in terms of points on a scale. Jack is taller than Jill if the point associated with Jack on the height scale is higher than Jill’s point. Jack is much taller than Jill is if Jack’s point is separated from Jill’s by a sizable amount. It is also natural to think of temporal discourse in terms of points on a time line. The analogy between the two is worth taking seriously.

Public law adjudication has grown dramatically in recent decades in many English-speaking countries. In the United States, and increasingly in other countries where it used to be rare for public questions to be decided in court, controversial questions of public policy are tried as constitutional or human rights issues and decided by court order. But in other areas of law - in everyday tort, contract, and property cases - court decisions are typically much less dramatic and seldom if ever announce (...) controversial innovations in public policy. Yet in private law cases too there are implicit questions of social justice.In common law countries, perhaps not surprisingly, tort, contract, and other private law cases are often decided on common law principles. Common law has a style and ethos of its own. It is based on precedent and, although precedent is open to modification, the common law style is anything but radical. With roots in the nineteenth century and earlier, common law often reflects classically liberal ideas, more or less consciously and more or less robustly.Instead of approaching private law cases with a common law mindset, should judges not treat these cases the way they might treat public law cases? Should courts not promote a vision of justice and human rights through private law adjudication, just as they sometimes - and in many countries increasingly - do in notable public law decisions?This article suggests several reasons why they should not. Turning private law more public in such a way would have considerable costs in legal stability, transparency, legitimacy, and judicial habits of neutrality and impartiality. Each of these considerations in turn is associated with what is generally thought of as the Rule of Law. The classically liberal ideas in the common law bloodstream themselves have at least some association with political freedom and the Rule of Law. And even if one is sceptical about classical liberalism and enthusiastic about today's public law, one might consider that public acceptance of ambitious public law adjudication may depend at least in part on the credit that courts build up through morally and politically unambitious day-to-day common law adjudication. (shrink)