A closer examination of scientific practice has cast doubt recently on the thesis that observation necessarily fails to determine theory. In some cases scientists derive fundamental hypotheses from phenomena and general background knowledge by means of demonstrative induction. This note argues that it is wrong to interpret such an argument as providing inductive support for the conclusion, e.g. by eliminating rival hypotheses. The examination of the deduction of the inverse square law of gravitation due to J. Bertrand, and R. Fowler's (...) deduction of the quantization of the linear harmonic oscillator's energy spectrum from Planck's radiation law illustrates this point. It is suggested that demonstrative induction is a computational step in fitting a theoretical model and a set of phenomena, with little direct confirmational impact. The thesis of underdetermination, whatever one may think of it, is not threatened by demonstrative induction. (shrink)

In this essay, I examine the curved spacetime formulation of Newtonian gravity known as Newton–Cartan gravity and compare it with flat spacetime formulations. Two versions of Newton–Cartan gravity can be identified in the physics literature—a ‘‘weak’’ version and a ‘‘strong’’ version. The strong version has a constrained Hamiltonian formulation and consequently a well-defined gauge structure, whereas the weak version does not (with some qualifications). Moreover, the strong version is best compared with the structure of what Earman (...) (World enough and spacetime. Cambridge: MIT Press) has dubbed Maxwellian spacetime. This suggests that there are also two versions of Newtonian gravity in flat spacetime—a ‘‘weak’’ version in Maxwellian spacetime, and a ‘‘strong’’ version in Neo-Newtonian spacetime. I conclude by indicating how these alternative formulations of Newtonian gravity impact the notion of empirical indistinguishability and the debate over scientific realism. r 2004 Elsevier Ltd. All rights reserved. (shrink)

The paper investigates the status of gravitational energy in Newtonian Gravity, developing upon recent work by Dewar and Weatherall. The latter suggest that gravitational energy is a gauge quantity. This is potentially misleading: its gauge status crucially depends on the spacetime setting one adopts. In line with Møller-Nielsen’s plea for a motivational approach to symmetries, we supplement Dewar and Weatherall’s work by discussing gravitational energy–stress in Newtonian spacetime, Galilean spacetime, Maxwell-Huygens spacetime, and Newton–Cartan Theory. Although we ultimately (...) concur with Dewar and Weatherall that the notion of gravitational energy is problematic in NCT, our analysis goes beyond their work. The absence of an explicit definition of gravitational energy–stress in NCT somewhat detracts from the force of Dewar and Weatherall’s argument. We fill this gap by examining the supposed gauge status of prima facie plausible candidates—NCT analogues of gravitational energy–stress pseudotensors, the Komar mass, and the Bel-Robinson tensor. Our paper further strengthens Dewar and Weatherall’s results. In addition, it sheds more light upon the subtle link between sufficiently rich inertial structure and the definability of gravitational energy in NG. (shrink)

Newtonian gravity is modified minimally to obtain a Lorentz covariant theory of gravity in a background flat space. Gravity is assumed to appear as a potential. Constraint Hamiltonian dynamics is used to determine particle trajectories in a manifestly covariant fashion. The resulting theory is significantly different from the general theory of relativity. However, all known experimental results (precession of planetary orbits, bending of the path of light near the sun, and gravitational spectral shift) are still explained (...) by this theory. (shrink)

In Newtonian gravity it is a moot question whether energy should be localized in the field or inside matter. An argument from relativity suggests a compromise in which the contribution from the field in vacuum is positive definite. We show that the same compromise is implied by Noether’s theorem applied to a variational principle for perfect fluids, if we assume Dirichlet boundary conditions on the potential. We then analyse a thought experiment due to Bondi and McCrea that gives (...) a clean example of inductive energy transfer by gravity. Some history of the problem is included. (shrink)

This thesis concerns the metaphysics of scale. It investigates the implications of a physical determinable being dimensionful. In particular, it considers the case study of mass, as it features within Newtonian Gravity. Nevertheless, most of the terminology, methodology and arguments developed should be relatively straightforwardly applicable to other determinables and theories. -/- Weak Absolutism about mass holds that mass ratios obtain in virtue of absolute masses. Weak Comparativism denies this. In the first five chapters I argue in favour (...) of Weak Absolutism over Weak Comparativism. The sixth chapter argues against reducing mass to other non-mass facts. The overall conclusion is Strong Absolutism about mass within Newtonian Gravity: mass ratios obtain in virtue of absolute masses, which themselves are fundamental (i.e. they do not require anything further in order to obtain). -/- Comparativism promises to recover all the virtues of absolutism, in particular its empirical adequacy, but at a lower 'metaphysical cost'. Special attention is given to Dasgupta's recent comparativist proposal. Dasgupta interprets the requirement of empirical adequacy in terms of the undetectability of the absolute mass scale. I argue that undetectability is an unsuitable way of understanding empirical adequacy and that we would do better to understand it in terms of a theory's ability to correctly generate the set of empirically possible worlds (or at least the actual world). I refute Dasgupta's comparativism both on my terms and on his own terms. I subsequently develop and strongly criticise alternative versions of comparativism. Chapter five sheds doubt on the supposed 'metaphysical parsimony' of comparativism. -/- This debate should be of particular interest to readers who engage with the substantivalism-relationalism debate. These debates are much more entwined than previously acknowledged, which provides a significant source of mutual inspiration, although I do also draw out some important disanalogies. -/- . (shrink)

Comparativism—the view that mass ratios are not grounded in absolute masses—faces a challenge by Baker which suggests that absolute masses are empirically meaningful. Regularity comparativism uses a liberalized version of the Mill-Ramsey-Lewis Best Systems Account to have both the laws of Newtonian gravity and the absolute mass scale supervene on a comparativist Humean mosaic as a package deal. I discuss three objections to this view and conclude that it is untenable. The most severe problem is that once we (...) have reduced away the absolute masses, there is nothing that stops us from also reducing the mass ratios. (shrink)

I state and prove, in the context of a space having only the metrical structure imposed by the geometrized version of Newtonian gravitational theory, a theorem analagous to that of Weyl's in a Lorentzian space. The theorem, loosely speaking, says that a projective structure and a suitably defined compatible conformal structure on such a space jointly suffice for fixing the metrical structure of a Newtonian spacetime model up to constant factors. It allows one to give a natural, physically (...) compelling interpretation of the spatiotemporal geometry of a geometrized Newtonian gravity spacetime manifold, in close analogy with the way Weyl's Theorem allows one to do in general relativity. (shrink)

This paper introduces a possible alternative model of gravity based on the theory of fractional-dimension spaces and its applications to Newtonian gravity. In particular, Gauss’s law for gravity as well as other fundamental classical laws are extended to a D-dimensional metric space, where D can be a non-integer dimension. We show a possible connection between this Newtonian Fractional-Dimension Gravity (NFDG) and Modified Newtonian Dynamics (MOND), a leading alternative gravity model which accounts for (...) the observed properties of galaxies and other astrophysical structures without requiring the dark matter hypothesis. The MOND acceleration constant $${a_{0}} \simeq 1.2 \times 10^{-10} \text {m}\, \text{s}^{-2}$$ can be related to a natural scale length $$l_{0}$$ in NFDG, i.e., $$a_{0} \approx GM/l_{0}^{2}$$, for astrophysical structures of mass M, and the deep-MOND regime is present in regions of space where the dimension is reduced to $$D \approx 2$$. For several fundamental spherically-symmetric structures, we compare MOND results, such as the empirical Radial Acceleration Relation (RAR), circular speed plots, and logarithmic plots of the observed radial acceleration $$g_{obs}$$ vs. the baryonic radial acceleration $$g_{bar}$$, with NFDG results. We show that our model is capable of reproducing these results using a variable local dimension $$D\left( w\right)$$, where $$w =r/l_{0}$$ is a dimensionless radial coordinate. At the moment, we are unable to derive explicitly this dimension function $$D\left( w\right)$$ from first principles, but it can be obtained empirically in each case from the general RAR. Additional work on the subject, including studies of axially-symmetric structures, detailed galactic rotation curves fitting, and a possible relativistic extension, will be needed to establish NFDG as a viable alternative model of gravity. (shrink)

Kant’s ‘Newtonianism’ has been rightly highlighted by figures like Friedman. The follow-up debates led to a more adequate view on Kant’s natural philosophy and in particular his relation towards Newton. But the discussion that evolved did not point to the asynchronicity that takes place in Kant’s struggle with the central Newtonian concepts. Newtonian space and gravity, in revised form, are of central concern to Kant’s critical philosophy. But Kant adapted and re-evaluated these two concepts in an asynchronous (...) way. While Kant tries to integrate a notion of gravity into his theory of matter in his very first published writing, he has at this stage no adequate notion of space. At this time, as in regard to space, he can neither be called a Newtonian nor a proper Leibnizian and misconceives the necessity of an independent space for the foundations of physics. This perspective changes under the influence of Euler at the end of the fifties of the eighteenth century and finally leads to his writing of 1768 and the adoption of transcendental idealism in 1770. In the following, I depict this asynchronicity by taking central pre-critical writings into account while discussing Kant’s concept of space and gravity. This sharpens the picture of Kant’s work and the different stages his philosophy of nature went through. Further, it helps to understand the influence of Euler on Kant’s development in natural philosophy and his critical philosophy in general, as Kant under the influence of Euler formed deeper-going reflections on Newton’s theory of space and these mark turning points of his development. (shrink)

We investigate the evolution of linear density contrasts obtained with respect to a homogeneous spatially flat Friedman-Lemaître–Robertson–Walker background by solving the density contrast equations governed by Newtonian and MONDian force laws using symmetry-based approach. We find eight-parameter Lie group symmetries for the linear order density perturbation equation for the Newtonian case whereas the density contrast equation follows only one parameter Lie group symmetry in MONDian case. We use Lie symmetries to find the group invariant solutions from invariant curve (...) condition. The physical features of the evolution for various mode of density contrast with respect to the global cosmic background density in homogeneous isotropic cosmological models have been investigated using analytical group invariant solutions along with their numerical solutions. An account for cosmological density contrast and mass fluctuation also have been provided. We also have shown that the MONDian force law generates higher amplitudes in the density fluctuation, results in a more rapid structure formation that cannot be possible under the Newtonian force law. (shrink)

Equation in the published paper is incorrect. The divergence of a vector field is obviously a scalar field, even when this operator is acting on a D-dimensional space.

I argue that the best spacetime setting for Newtonian gravitation (NG) is the curved spacetime setting associated with geometrized Newtonian gravitation (GNG). Appreciation of the ‘Newtonian equivalence principle’ leads us to conclude that the gravitational field in NG itself is a gauge quantity, and that the freely falling frames are naturally identified with inertial frames. In this context, the spacetime structure of NG is represented not by the flat neo-Newtonian connection usually made explicit in formulations, but (...) by the sum of the flat connection and the gravitational field. 1 Introduction2 Newtonian Gravity: The Orthodox Approach3 Newtonian Gravity: Additional Symmetries4 Cosmological Considerations5 A Newtonian Equivalence Principle: Inertial Frames in Newtonian Gravitation6 Theory Equivalence?7 Conclusion. (shrink)

I point out a radical indeterminism in potential-based formulations of Newtonian gravity once we drop the condition that the potential vanishes at infinity. This indeterminism, which is well known in theoretical cosmology but has received little attention in foundational discussions, can be removed only by specifying boundary conditions at all instants of time, which undermines the theory's claim to be fully cosmological, i.e., to apply to the Universe as a whole. A recent alternative formulation of Newtonian (...) class='Hi'>gravity due to Saunders pp.22-48) provides a conceptually satisfactory cosmology but fails to reproduce the Newtonian limit of general relativity in homogenous but anisotropic universes. I conclude that Newtonian gravity lacks a fully satisfactory cosmological formulation. (shrink)

One prominent criticism of Newtonianism held that gravitational attraction is an occult quality. The charge, pressed most forcefully by Leibniz, claims that Newton had abandoned the intelligibility of mechanism and allowed for an unexplained and inexplicable force in nature. This paper focuses on one of Newton’s replies to this accusation: his claim that gravitation is no more mysterious than phenomena like inertia and impenetrability. I argue that we can understand and motivate this Newtonian position by looking at the account (...) of material substance developed in Newton’s early manuscript essay De gravitatione. This account makes clear Newton’s sensitivity to the explanatory limits of mechanism. Newton was perceptive in noting that while the mechanical philosophy sought to provide explanations in terms of matter and motion, it failed to explain matter and motion themselves. This sheds light on the motivations behind the theory of bodies in De gravitatione. And it helps to explain why he was so unmoved by what many saw as a serious challenge to his theory of gravity. (shrink)

Laplace wondered about the minimal choice of initial variables and parameters corresponding to a well-posed initial value problem. Discussions of Laplace’s problem in the literature have focused on choosing between spatiotemporal variables relative to absolute space or merely relative to other material bodies and between absolute masses or merely mass ratios. This paper extends these discussions of Laplace’s problem, in the context of Newtonian Gravity, by asking whether mass needs to be included in the initial state at all, (...) or whether a purely spatiotemporal initial state suffices. It is argued that mass indeed needs to be included; removing mass from the initial state drastically reduces the predictive and explanatory power of Newtonian Gravity. (shrink)

It is argued that Newtonian mass cannot be reduced to kinematical quantities---distance, velocity and acceleration---without losing the explanatory and predictive power of Newtonian Gravity.

Philosophers of science have written at great length about the geometric structure of physical space. But they have devoted their attention primarily to the question of the epistemic status of our attributions of geometric structure. They have debated whether our attributions are a priori truths, empirical discoveries, or, in a special sense, matters of stipulation or convention. lt is the goal of this paper to explore a quite different issue the role played by assumptions of spatial geometry within physical theory, (...) specifically within Newtonian gravitational theory. (shrink)

Recently there has been a great deal of interest in tabletop experiments intended to exhibit the quantum nature of gravity by demonstrating that it can induce entanglement. In order to evaluate these experiments, we must determine if there is any interesting class of possibilities that will be convincingly ruled out if it turns out that gravity can indeed induce entanglement. In particular, since one argument for the significance of these experiments rests on the claim that they demonstrate the (...) existence of superpositions of spacetimes, it is important to keep in mind that different interpretations of quantum mechanics may make different predictions about superpositions of spacetimes. ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-complete interpretations of quantum mechanics, like the Everett interpretation, almost universally predict the existence of superpositions of spacetimes, whereas in ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-incomplete, ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-nonphysical interpretations it seems more natural to predict that spacetime superpositions are not possible. Meanwhile ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-incomplete, ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-supplemented interpretations present us with a more complex picture where we may or may not end up predicting that spacetime superpositions are possible, depending on the particular way in which the coupling between spacetime and matter is constructed. This line of reasoning suggests that what would be ruled out by a successful result to these tabletop experiments is a class of quantum gravity models that we refer to as ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-incomplete quantum gravity —i.e. models of the interaction between quantum mechanics and gravity in which gravity is coupled to non-quantum beables rather than quantum beables. It follows that the results of tabletop experiments can also be regarded as giving us new evidence about the interpretation of quantum mechanics: roughly speaking, a positive result to these experiments should increase our confidence in ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-complete interpretations, whilst a negative result should instead increase our confidence in ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-incomplete interpretations. We introduce these ideas in Sect. 1, and then in Sect. 2 we make the reasoning more precise by presenting a set of inferences that may be made about the ontology of quantum mechanics based on the results of tabletop experiments. In Sect. 3 we discuss some existing PIQG models and consider what more needs to be done to make these sorts of approaches more appealing. There are two competing paradigms for the interpretation of these experiments, which have been dubbed the ‘Newtonian’ paradigm and the ‘tripartite’ paradigm: here we largely work within the tripartite paradigm, because the tripartite view is specifically concerned with ontological aspects of the mediating gravitational interaction and that makes it a suitable setting for enquiries about the ontology of quantum mechanics, but in Sect. 4 we consider what conclusions can be drawn if one does not presuppose the tripartite view. Finally in Sect. 5 we discuss a cosmological phenomenon which could be regarded as providing evidence for PIQG models. (shrink)

Using as a starting point recent and apparently incompatible conclusions by Saunders and Knox, I revisit the question of the correct spacetime setting for Newtonian physics. I argue that understood correctly, these two versions of Newtonian physics make the same claims both about the background geometry required to define the theory, and about the inertial structure of the theory. In doing so I illustrate and explore in detail the view—espoused by Knox, and also by Brown —that inertial structure (...) is defined by the dynamics governing subsystems of a larger system. This clarifies some interesting features of Newtonian physics, notably the distinction between using the theory to model subsystems of a larger whole and using it to model complete universes, and the scale-relativity of spacetime structure. _1_ Introduction _2_ Newtonian Mechanics and Galilean Spacetime _3_ Vector Relationism and Maxwellian Spacetime _4_ Recovering the Galilei Group: Dynamics of Subsystems _5_ Knox on Inertial Structure _6_ Connections on Maxwellian Spacetime _7_ Knox on Newtonian Gravity _8_ Vector Relationism and Newton–Cartan Theory _9_ Inertial Structure in Newton–Cartan Gravity _10_ Reconciling Knox and Saunders _11_ Conclusions. (shrink)

Newton’s impact on Enlightenment natural philosophy has been studied at great length, in its experimental, methodological and ideological ramifications. One aspect that has received fairly little attention is the role Newtonian “analogies” played in the formulation of new conceptual schemes in physiology, medicine, and life science as a whole. So-called ‘medical Newtonians’ like Pitcairne and Keill have been studied; but they were engaged in a more literal project of directly transposing, or seeking to transpose, Newtonian laws into quantitative (...) models of the body. I am interested here in something different: neither the metaphysical reading of Newton, nor direct empirical transpositions, but rather, a more heuristic, empiricist construction of Newtonian analogies. Figures such as Haller, Barthez, and Blumenbach constructed analogies between the method of celestial mechanics and the method of physiology. In celestial mechanics, they held, an unknown entity such as gravity is posited and used to mathematically link sets of determinate physical phenomena (e.g., the phases of the moon and tides). This process allows one to remain agnostic about the ontological status of the unknown entity, as long as the two linked sets of phenomena are represented adequately. Haller et. al. held that the Newtonian physician and physiologist can similarly posit an unknown called ‘life’ and use it to link various other phenomena, from digestion to sensation and the functioning of the glands. These phenomena consequently appear as interconnected, goal-oriented processes which do not exist either in an inanimate mechanism or in a corpse. In keeping with the empiricist roots of the analogy, however, no ontological claims are made about the nature of this vital principle, and no attempts are made to directly causally connect such a principle and observable phenomena. The role of the “Newtonian analogy” thus brings together diverse schools of thought, and cuts across a surprising variety of programs, models and practices in natural philosophy. (shrink)

We construct a notion of teleparallelization for Newton-Cartan theory, and show that the teleparallel equivalent of this theory is Newtonian gravity; furthermore, we show that this result is consistent with teleparallelization in general relativity, and can be obtained by null-reducing the teleparallel equivalent of a five-dimensional gravitational wave solution. This work thus strengthens substantially the connections between four theories: Newton-Cartan theory, Newtonian gravitation theory, general relativity, and teleparallel gravity.

Absolutism about mass claims that mass ratios obtain in virtue of absolute masses. Comparativism denies this. Dasgupta, Oxford studies in metaphysics, Oxford University Press, Oxford, 2013) argues for comparativism about mass, in the context of Newtonian Gravity. Such an argument requires proving that comparativism is empirically adequate. Dasgupta equates this to showing that absolute masses are undetectable, and attempts to do so. This paper develops an argument by Baker to the contrary: absolute masses are in fact empirically meaningful, (...) that is detectable. Additionally, it is argued that the requirement of empirical adequacy should not be cashed out in terms of undetectability in the first place. The paper closes by sketching the possible strategies that remain for the comparativist. Along the way a framework is developed that is useful for thinking about these issues: Ozma games—how could one explain to an alien civilisation what an absolute mass is? (shrink)

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

The parametrized post-Newtonian (PPN) approximation is generalized to accommodate Rastall's modification of Einstein's theory of gravity, which allows nonzero divergence of the energy-momentum tensor. Rastall's theory is then shown to have consistent field equations, gauge conditions, and the correct Newtonian limit of the equations of motion. The PPN parameters are obtained and shown to agree experimentally with those for the Einstein theory. In light of the nonzero divergence condition, integral conservation laws are investigated and shown to yield (...) conserved energy-momentum and angularmomentum. We conclude that the above generalization of metric theories, within the PPN framework, is a natural extension of the concept of metric theories. (shrink)

Our long experience with Newtonian potentials has inured us to the view that gravity only produces local effects. In this paper we challenge this quite deeply ingrained notion and explicitly identify some intrinsically global gravitational effects. In particular we show that the global cosmological Hubble flow can actually modify the motions of stars and gas within individual galaxies, and even do so in a way which can apparently eliminate the need for galactic dark matter. Also we show that (...) a classical light wave acquires an observable, global, pathdependent phase in traversing a gravitational field. Both of these effects serve to underscore the intrinsic difference between nonrelativistic and relativistic gravity. (shrink)

Locke’s metaphysical commitments are a matter of some controversy. Further controversy attends the issue of whether and how Locke adapts his views in order to accommodate the success of Newton’s Principia. The chapter lays out an interpretation of Locke’s commitments according to which Locke’s response to Newton on gravity does not require the positing of brute powers and is consistent with his core essentialism. The chapter raises the question of how the hypothesis concerning the creation of matter, alluded to (...) at 4.10.18, fits with these commitments. The chapter concludes that the De grav hypothesis would represent a significant revision to the background metaphysical picture of the Essay, but that nevertheless its attractions to Locke are intelligible and illuminating. (shrink)

What is a self? I will try to answer this question by developing an analogy with something much simpler, something which is nowhere near as puzzling as a self, but has some properties in common with selves. What I have in mind is the center of gravity of an object. This is a well-behaved concept in Newtonian physics. But a center of gravity is not an atom or a subatomic particle or any other physical item in the (...) world. It has no mass; it has no color; it has no physical properties at all, except for spatio-temporal location. It is a fine example of what Hans Reichenbach would call an abstractum. It is a purely abstract object. It is, if you like , a theorist's fiction. It is not one of the real things in the universe in addition to the atoms. But it is a fiction that has nicely defined, well delineated and well behaved role within physics. (shrink)

In the static field configuration, a spatially-Variable Speed of Light (VSL) scalar gravity model with Lorentz-Poincaré interpretation was shown to reproduce the phenomenology implied by the Schwarzschild metric. In the present development, we effectively cover configurations with source kinematics due to an induced sweep velocity field w. The scalar-vector model now provides a Hamiltonian description for particles and photons in full accordance with the first Post-Newtonian (1-PN) approximation of General Relativity Theory (GRT). This result requires the validity of (...) Poincaré’s Principle of Relativity, i.e. the unobservability of ‘preferred’ frame movement. Poincaré’s principle fixes the amplitude of the sweep velocity field of the moving source, or equivalently the ‘vector potential’ ξ of GRT (e.g.; S. Weinberg, Gravitation and cosmology, [1972]), and provides the correct 1-PN limit of GRT. The implementation of this principle requires acceleration transformations derived from gravitationally modified Lorentz transformations. A comparison with the acceleration transformation in GRT is done. The present scope of the model is limited to weak-field gravitation without retardation and with gravitating test particles. In conclusion the model’s merits in terms of a simpler space, time and gravitation ontology—in terms of a Lorentz-Poincaré-type interpretation—are explained (e.g. for ‘frame dragging’, ‘harmonic coordinate condition’). (shrink)

This is a well-behaved concept in Newtonian physics. But a center of gravity is not an atom or a subatomic particle or any other physical item in the world. It has no mass; it has no color; it has no physical properties at all, except for spatio-temporal location. It is a fine example of what Hans Reichenbach would call an abstractum. It is a purely abstract object. It is, if you like , a theorist's fiction. It is not (...) one of the real things in the universe in addition to the atoms. But it is a fiction that has nicely defined, well delineated and well behaved role within physics. (shrink)

This book continues the classical Newtonian theory in both its initial spirit and the spirit of general relativity. It throws a bridge between classical Newtonian theory of forces and some contemporary concepts of the atomic, nuclear and particle theories. This book takes the Skyrme theory of nuclear matter mainly from the point of view that it allows the initial analogy between the atomic edifice and the solar system in all details. Especially important is the detail that the atomic (...) nucleus works exactly like the Sun, and they can be described in the same way. Based on this unitary description, the authors go further on, in showing that the Skyrme theory is the only theory naturally suited for the explanation of structure of nuclear matter. Thus it should be actually a classical theory, inasmuch as it simply carries over into microcosmos the very Newtonian theory of forces extracted from the planetary Keplerian synthesis of celestial motions. By this the problem of structure of the nucleus becomes actually a problem of classical physics. (shrink)

Absolutism about mass within Newtonian gravity claims that mass ratios obtain in virtue of absolute masses. Comparativism denies this. Defenders of comparativism promise to recover all the empirical and theoretical virtues of absolutism, but at a lower ‘metaphysical cost’. This article develops a Machian form of comparativism about mass in Newtonian gravity, obtained by replacing Newton’s constant in the law of universal gravitation by another constant divided by the sum over all masses. Although this form of (...) comparativism is indeed empirically equivalent to the absolutist version of Newtonian gravity—thereby meeting the challenge posed by the comparativist’s bucket argument—it is argued that the explanatory power and metaphysical parsimony of comparativism are highly questionable. (shrink)

Spontaneous collapse models are modifications of standard quantum mechanics in which a physical mechanism is responsible for the collapse of the wavefunction, thus providing a way to solve the so-called “measurement problem”. The two most famous of these models are the Ghirardi–Rimini–Weber (GRW) model and the Continuous Spontaneous Localisation (CSL) models. Here, we propose a new kind of non-relativistic spontaneous collapse model based on the idea of collapse points situated at fixed spacetime coordinates. This model shares properties of both GRW (...) and CSL models, while starting from different assumptions. We show that it can lead to a dynamics quite similar to that of the GRW model while also naturally solving the problem of indistinguishable particles. On the other hand, we can also obtain the same master equation of the CSL models. Then, we show how our proposed model solves the measurement problem in a manner conceptually similar to the GRW model. Finally, we show how the proposed model can also accommodate for Newtonian gravity by treating the collapses as gravitational sources. (shrink)

Einsteinian gravity, of which Newtonian gravity is a part, is fraught with the problem of singularity that has been established as a theorem by Hawking and Penrose. The _hypothesis_ that founds the basis of both Einsteinian and Newtonian theories of gravity is that bodies with unequal magnitudes of masses fall with the same acceleration under the gravity of a source object. Since, the Einstein’s equations is one of the assumptions that underlies the proof of (...) the singularity theorem, therefore, the above hypothesis is implicitly one of the founding pillars of the same. In this work, I demonstrate how one can possibly write a non-singular theory of gravity which manifests that the above mentioned hypothesis is only valid in an approximate sense in the “large distance” scenario. To mention a specific instance, under the gravity of the earth, a 5 kg and a 500 kg fall with accelerations which differ by approximately \(113.148\times 10^{-32}\) meter/sec \(^2\) and the more massive object falls with less acceleration. Further, I demonstrate why the concept of gravitational field is not definable in the “small distance” regime which automatically justifies why the Einstein’s and Newton’s theories fail to provide any “small distance” analysis. In course of writing down this theory, I demonstrate why the continuum hypothesis as spelled out by Goedel, is undecidable. The theory has several aspects which provide the following realizations: (i) Descartes’ self-skepticism concerning exact representation of numbers by drawing lines (ii) Born’s wish of taking into account “natural uncertainty in all observations” while describing “a physical situation” by means of “real numbers” (iii) Klein’s vision of having “a fusion of arithmetic and geometry” where “a point is replaced by a small spot” (iv) Goedel’s assertion about “non-standard analysis, in some version” being “the analysis of the future”. (shrink)

By mass-energy equivalence, the gravitational field has a relativistic mass density proportional to its energy density. I seek to better understand this mass of the gravitational field by asking whether it plays three traditional roles of mass: the role in conservation of mass, the inertial role, and the role as source for gravitation. The difficult case of general relativity is compared to the more straightforward cases of Newtonian gravity and electromagnetism by way of gravitoelectromagnetism, an intermediate theory of (...) gravity that resembles electromagnetism. (shrink)

What does quilting have to do with electric circuit theory? The answer is just one of the fascinating ways that best-selling popular math writer Paul Nahin illustrates the deep interplay of math and physics in the world around us in his latest book of challenging mathematical puzzles, Mrs. Perkins's Electric Quilt. With his trademark combination of intriguing mathematical problems and the historical anecdotes surrounding them, Nahin invites readers on an exciting and informative exploration of some of the many ways math (...) and physics combine to create something vastly more powerful, useful, and interesting than either is by itself. In a series of brief and largely self-contained chapters, Nahin discusses a wide range of topics in which math and physics are mutually dependent and mutually illuminating, from Newtonian gravity and Newton's laws of mechanics to ballistics, air drag, and electricity. The mathematical subjects range from algebra, trigonometry, geometry, and calculus to differential equations, Fourier series, and theoretical and Monte Carlo probability. Each chapter includes problems--some three dozen in all--that challenge readers to try their hand at applying what they have learned. Just as in his other books of mathematical puzzles, Nahin discusses the historical background of each problem, gives many examples, includes MATLAB codes, and provides complete and detailed solutions at the end. Mrs. Perkins's Electric Quilt will appeal to students interested in new math and physics applications, teachers looking for unusual examples to use in class--and anyone who enjoys popular math books. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Seeking Nature’s Logic: Natural Philosophy in the Scottish EnvironmentFrancesca di PoppaDavid B. Wilson. Seeking Nature’s Logic: Natural Philosophy in the Scottish Environment. University Park, PA: The Pennsylvania State University Press, 2009. Pp. xvi + 344. Cloth, $55.00.This book promises to tell “the untold story of the principal historical path from Isaac Newton to Albert Einstein” (xii). It is an ambitious promise. In explaining the influence of Reid’s philosophy (...) on how Scottish scientists addressed phenomena such as light, heat, electricity, etc., Wilson addresses the exquisitely “Scottish” flavor of the contributions of Joseph Black, John Anderson, John Robinson, Dugald Stewart, Joseph Boscovitch, and several others. While the alleged goal is projected toward late nineteenth- and early twentieth-century discoveries, the discussion never loses sight of its historical context, by stressing the importance of theological consideration in scientific arguments (e.g. Robinson’s critique of Laplacian mechanics as an “atheistic perversion” of Newtonian gravity), and by tracing the influence of past philosophers on Scottish eighteenth-century science.Wilson begins with a survey of major seventeenth-century philosophers, from Descartes to Leibniz, who influenced later developments. But some of his remarks are problematic. For example, he asserts that in Descartes’ discussion of empty space, “the implication was that even God could not conceive of void space” (11–12). Considering Descartes’ attitude toward divine omnipotence, and his position that God created “necessary truths” (e.g. in his correspondence with Mersenne), at the very least this claim needs to be argued for, rather than simply stated.Likewise, Wilson’s attempt to trace each scientist’s attitude to a major figure from the past is not always successful. For example, in chapter 4 Wilson argues, persuasively, that Reidian epistemology influenced Robinson’s attitudes toward certain hypotheses. But then he claims that Black “represented the realism of Newton’s Query 31,” as opposed to Robinson’s “Reidian skepticism” (157). This claim is puzzling. Wilson nicely explains how Query 31 of Newton’s Opticks, with its defense of the notion of real attractive and repulsive forces and its sections on scientific reasoning, influenced Black. Wilson also shows that Robinson was somewhat critical of Newton. But the disagreements discussed do not concern issues of realism versus skepticism. Wilson himself shows that Robinson agreed with some of Black’s realist positions. In fact, Wilson writes that Robinson approved of Newton’s notion of attraction, which is argued for extensively in Newton’s Query 31.One of the most important debates discussed by Wilson concerns the nature of heat and light. After Newton, scientists were supposed to avoid “wild hypotheses,” for fear of being derided as Descartes was for his theory of vortices. Merely describing experienced regularities, however, rather than finding explanatory causes, seemed insufficient. Wilson emphasizes Reid’s influence in restoring the epistemic status of inductive experimental knowledge in a post-Humean world, and shows the ambivalence of post-Reidian scientists toward hypotheses. A good example is his chapter 4 discussion of Robinson’s attitude toward heat. After rejecting the two main alternatives (heat as vibratory motion of the particles of bodies, and heat as a fluid whose particles are in continual vibratory motion) because both are inconsistent with experimental evidence, Robinson recommends considering heat as a “cause” in the “constant conjunction” sense, because its nature and mechanism are not known. However, Wilson quotes passages from notebooks in which Robinson endorses a form of the fluid theory of heat. Robinson also approved of Stahl’s phlogiston theory, and agreed with Black’s “negative weight” solution to the problem that bodies gain weight when [End Page 501] phlogiston leaves them (a solution that Black abandoned after learning of Lavoisier’s, Priestley’s, and Scheele’s work). While a realist about phlogiston, however, Robinson criticized Black’s identification of phlogiston with Newtonian aether: Robinson’s criticism is described as a “Reid-like” argument against the abuse of analogies in natural philosophy. As can be seen from this and other discussions, Reid’s warnings against the abuse of conjectures and analogies were not always consistently applied.Despite offering an informative overview of the contributions of Scottish natural philosophers, the information in the book is somewhat poorly... (shrink)

Many physicists view the most sublime task of physics in presenting some day a world formula or a simple Theory of Everything that accounts for all major physical theories and from which everything follows by pure deduction.1 This striving for universality can look back on a long history, which contains the failed attempts to incorporate electrodynamics into universal mechanics, Einstein’s einheitliche Feldtheorie and Heisenberg’s explicit proposal of an Urgleichung. Those attempts were encouraged by the success of general relativity, which embraced (...) classical mechanics and Newtonian gravity as well defined limits. A decade later quantum mechanics was given its final shape, which allowed the explanation of all atomic phenomena known up to then and contained classical mechanics as its macroscopic limit at least in the stochastic interpretation, i.e. comparing both as theories of measurement. After the success of gauge theories in elementary particle physics, the search for a fundamental simple equation was replaced by the search for a basic symmetry group that described all fundamental interactions apart from gravity. It resulted in the famous gauge group of the Standard Model SU × SU L × U , which comprises the strong, the weak and the electromagnetic interaction. But the fact that the Standard Model contains 18 parameters, which have to be introduced from outside, inspired the search for a larger unifying gauge group. These Grand Unified Theories tried to derive some of the parameters of the Standard Model from more fundamental gauge symmetries. With the rise of string theory, which intends to include gravity as well, a new term popped up to express the old claims: Theory of Everything. (shrink)

According to the BSM- Supergravitation Unified Theory (BSM-SG), the energy is indispensable feature of matter, while the matter possesses hierarchical levels of organization from a simple to complex forms, with appearance of fields at some levels. Therefore, the energy also follows these levels. At the fundamental level, where the primary energy source exists, the matter is in its primordial form, where two super-dense fundamental particles (FP) exist in a classical pure empty space (not a physical vacuum). They are associated with (...) the Planck scale parameters of frequency and distance and interact by Supergravitational forces. These forces are inverse proportional to the cube of distance at pure empty space and they are based on frequency interactions. Since the two FPs have different intrinsic frequencies, the SG forces appear different for interactions between the like and unlike FPs and may change the sign. This primordial form of matter exists in the super-heavy black holes located in the center of each well formed galaxy. The next upper level of matter organization includes the underlying structure of the physical vacuum, called a Cosmic Lattice, and the structure of elementary particles. They have common substructure elements obtained by specific crystallization process preceding the formation of the observable galaxies. The Cosmic Lattice, forming a space known as a physical vacuum, is responsible for the existence and propagation of the physical fields: electrical, magnetic, Newtonian gravity and inertia. The energy of physical vacuum is in two forms: Static (enormous) and Dynamic (weak). The Static energy is directly related to the Newtonian mass by the Einstein equation E = mc^2 and it is a primary source of the nuclear energy. The Dynamic energy is responsible for the existence of the electric and magnetic fields, the constant speed of light and the quantum mechanical properties of the physical vacuum. The next upper energy level is the dynamical energy of excited atoms and molecules. At this level a hidden energy wells exit, such as the internal energy of the electron and the internal energy of atoms with more than one electron. The next upper energy level is at some organic molecules and particularly in the biomolecules that contain ring atomic structures. In such a structure, some quantum states are not emitted immediately, but rotating in the ring. While in organic molecules the energy stored in such a ring is released by a chemical process, in the long chain molecule of proteins in the living organism the stored energy can be released simultaneously by triggering. A huge number of atomic rings are contained in the DNA strands. The release of the energy stored in DNA, for example, is an avalanche process that causes an emission of entangled photons possessing a strong penetrating capability. A sequence of entangled photons emitted by DNA should carry the genetic information encoded by the cordons. This mechanism, predicted in BSM-SG theory, is very important for intercommunication between the cells of the living organism. The next upper level of energy organization may exist in the brain. The brain is an organ of a most abundant number of atomic rings, while its tissue environment might permit complex energy interactions. The human brain contains billions of atomic rings. The next hypothetical upper level of energy organization is an information field, physically existed outside, but connected with the living brain. It corresponds to a specific field known as aura, while the possibility of its existence is still not accepted by the main stream science. The problem is that this field could not be detected by the currently existing technical means used for EM communications. The BSM-SG predicts that this field might differ from the EM field we use for communication, but it is a subject of a further theoretical development that must be supported by experiments using specifically designed technical means. According to the BSM-SG theory, the energy conversion from the primary energy source to the complex levels of matter and field organization is a permanent syntropic process based on complex resonance interactions. (shrink)

The wavefunction is the central mathematical entity of quantum mechanics, but it still lacks a universally accepted interpretation. Much effort is spent on attempts to probe its fundamental nature. Here I investigate the consequences of a matter ontology applied to spherical masses of constant bulk density. The governing equation for the center-of-mass wavefunction is derived and solved numerically. The ground state wavefunctions and resulting matter densities are investigated. A lowering of the density from its bulk value is found for low (...) masses due to increased spatial spreading. A discussion of the possibility to experimentally observe these effects is given and the possible consequences for choosing an ontological interpretation for quantum mechanics are commented upon. (shrink)

Application of recently developed non-Archimedean algebra to a flat and finite universe of total mass M 0 and radius R 0 is described. In this universe, mass m of a body and distance R between two points are bounded from above, i.e., 0≤m≤M 0, 0≤R≤R 0. The universe is characterized by an event horizon at R 0 (there is nothing beyond it, not even space). The radial distance metric is compressed toward horizon, which is shown to cause the phenomenon of (...) red shift. The corresponding modified Minkowski's metric and Lorentz transforms are obtained. Applications to Newtonian gravity shows a weakening at large scales (R→R 0) and a regular behavior as R→0. (shrink)

Many condensed matter systems are such that their collective excitations at low energies can be described by fields satisfying equations of motion formally indistinguishable from those of relativistic field theory. The finite speed of propagation of the disturbances in the effective fields (in the simplest models, the speed of sound) plays here the role of the speed of light in fundamental physics. However, these apparently relativistic fields are immersed in an external Newtonian world (the condensed matter system itself and (...) the laboratory can be considered Newtonian, since all the velocities involved are much smaller than the velocity of light) which provides a privileged coordinate system and therefore seems to destroy the possibility of having a perfectly defined relativistic emergent world. In this essay we ask ourselves the following question: In a homogeneous condensed matter medium, is there a way for internal observers, dealing exclusively with the low-energy collective phenomena, to detect their state of uniform motion with respect to the medium? By proposing a thought experiment based on the construction of a Michelson-Morley interferometer made of quasi-particles, we show that a real Lorentz-FitzGerald contraction takes place, so that internal observers are unable to find out anything about their ‘absolute’ state of motion. Therefore, we also show that an effective but perfectly defined relativistic world can emerge in a fishbowl world situated inside a Newtonian (laboratory) system. This leads us to reflect on the various levels of description in physics, in particular regarding the quest towards a theory of quantum gravity. (shrink)

It is widely hoped that quantum gravity will shed light on the question of the origin of time in physics. The currently dominant approaches to a candidate quantum theory of gravity have naturally evolved from general relativity, on the one hand, and from particle physics, on the other hand. A third important branch of twentieth century ‘fundamental’ physics, condensed-matter physics, also offers an interesting perspective on quantum gravity, and thereby on the problem of time. The bottomline might (...) sound disappointing: to understand the origin of time, much more experimental input is needed than what is available today. Moreover it is far from obvious that we will ever find out the true origin of physical time, even if we become able to directly probe physics at the Planck scale. But we might learn some interesting lessons about time and the structure of our universe in the process. A first lesson is that there are probably several characteristic scales associated with “quantum gravity” effects, rather than the single Planck scale usually considered. These can differ by several orders of magnitude, and thereby conspire to hide certain effects expected from quantum gravity, rendering them undetectable even with Planck-scale experiments. A more tentative conclusion is that the hierarchy between general relativity, special relativity and Newtonian physics, usually taken for granted, might have to be interpreted with caution. (shrink)

We discuss the concepts of Weyl and Riemann frames in the context of metric theories of gravity and state the fact that they are completely equivalent as far as geodesic motion is concerned. We apply this result to conformally flat spacetimes and show that a new picture arises when a Riemannian spacetime is taken by means of geometrical gauge transformations into a Minkowskian flat spacetime. We find out that in the Weyl frame gravity is described by a scalar (...) field. We give some examples of how conformally flat spacetime configurations look when viewed from the standpoint of a Weyl frame. We show that in the non-relativistic and weak field regime the Weyl scalar field may be identified with the Newtonian gravitational potential. We suggest an equation for the scalar field by varying the Einstein-Hilbert action restricted to the class of conformally-flat spacetimes. We revisit Einstein and Fokker’s interpretation of Nordström scalar gravity theory and draw an analogy between this approach and the Weyl gauge formalism. We briefly take a look at two-dimensional gravity as viewed in the Weyl frame and address the question of quantizing a conformally flat spacetime by going to the Weyl frame. (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)