Newtonian mechanics is more than just an empirically successful theory of matter in motion: it is an account of what knowledge of the physical world should look like. But what is this account? What is distinctive about it? To answer these questions, I begin by introducing the laws of motion, the relations among them, and the spatio-temporal framework that is implicit in them. Then I turn to the question of their methodological character. This has been the locus of philosophical discussion (...) from Newton’s time to the present, and I survey the views of some of the major contributors. I show that while Newtonian mechanics motivates a number of philosophical ideas about force, mass, motion, and causality – and through this, ideas about space and time – the laws are themselves the outcome of a philosophical or critical conceptual analysis. (shrink)

The equivalence principle has constituted one of the cornerstones of discussions in the foundations of spacetime theories over the past century. However, up to this point the principle has been considered overwhelmingly only within the context of relativistic physics. In this article, we demonstrate that the principle has much broader, super-theoretic significance: to do so, we present a unified framework for understanding the principle in its various guises, applicable to both relativistic and Newtonian contexts. We thereby deepen significantly our understanding (...) of the role played by the equivalence principle in a broad class of spacetime theories. (shrink)

Newtonian forces are pushes and pulls, possessing magnitude and direction, that are exerted (in the first instance) by objects, and which cause (in particular) motions. I defend Newtonian forces against the four best reasons for denying or doubting their existence. A running theme in my defense of forces will be the suggestion that Newtonian Mechanics is a special science, and as such has certain prima facie ontological rights and privileges, that may be maintained against various challenges.

Newtonian physics is based on Newtonian calculus applied to Newtonian dynamics. New paradigms such as ‘modified Newtonian dynamics’ change the dynamics, but do not alter the calculus. However, calculus is dependent on arithmetic, that is the ways we add and multiply numbers. For example, in special relativity we add and subtract velocities by means of addition β1⊕β2=tanh+tanh-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _1\oplus \beta _2=\tanh \big +\tanh ^{-1}\big )$$\end{document}, although multiplication β1⊙β2=tanh·tanh-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} (...) \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _1\odot \beta _2=\tanh \big \cdot \tanh ^{-1}\big )$$\end{document}, and division β1⊘β2=tanh/tanh-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _1\oslash \beta _2=\tanh \big /\tanh ^{-1}\big )$$\end{document} do not seem to appear in the literature. The map fX=tanh-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_{\mathbb{X}}=\tanh ^{-1}$$\end{document} defines an isomorphism of the arithmetic in X=\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}=$$\end{document} with the standard one in R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}}$$\end{document}. The new arithmetic is projective and non-Diophantine in the sense of Burgin, 1977), while ultrarelativistic velocities are super-large in the sense of Kolmogorov, 1961). Velocity of light plays a role of non-Diophantine infinity. The new arithmetic allows us to define the corresponding derivative and integral, and thus a new calculus which is non-Newtonian in the sense of Grossman and Katz. Treating the above example as a paradigm, we ask what can be said about the set X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}$$\end{document} of ‘real numbers’, and the isomorphism fX:X→R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_{{\mathbb{X}}}:{\mathbb{X}}\rightarrow {\mathbb{R}}$$\end{document}, if we assume the standard form of Newtonian mechanics and general relativity but demand agreement with astrophysical observations. It turns out that the observable accelerated expansion of the Universe can be reconstructed with zero cosmological constant if fX≈0.8sinh/\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_{\mathbb{X}}\approx 0.8\sinh /$$\end{document}. The resulting non-Newtonian model is exactly equivalent to the standard Newtonian one with ΩΛ=0.7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega _\Lambda =0.7$$\end{document}, ΩM=0.3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega _M=0.3$$\end{document}. Asymptotically flat rotation curves are obtained if ‘zero’, the neutral element 0X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0_{{\mathbb{X}}}$$\end{document} of addition, is nonzero from the point of view of the standard arithmetic of R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}}$$\end{document}. This implies fX-1=0X>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f^{-1}_{{\mathbb{X}}}=0_{{\mathbb{X}}}>0$$\end{document}. The opposition Diophantine versus non-Diophantine, or Newtonian versus non-Newtonian, is an arithmetic analogue of Euclidean versus non-Euclidean in geometry. We do not yet know if the proposed generalization ultimately removes any need of dark matter, but it will certainly change estimates of its parameters. Physics of the dark universe seems to be both geometry and arithmetic. (shrink)

Newtonian gravitation is studied from a discrete point of view, in that the dynamical equation is an energy-conserving difference equation. Application is made to planetary-type, nondegenerate three-body problems and several computer examples of perturbed orbits are given.

The first two sections of this paper investigate what Newton could have meant in a now famous passage from “De Graviatione” (hereafter “DeGrav”) that “space is as it were an emanative effect of God.” First it offers a careful examination of the four key passages within DeGrav that bear on this. The paper shows that the internal logic of Newton’s argument permits several interpretations. In doing so, the paper calls attention to a Spinozistic strain in Newton’s thought. Second it sketches (...) four interpretive options: (i) one approach is generic neo-Platonic; (ii) another approach is associated with the Cambridge Platonist, Henry More; a variant on this (ii*) emphasizes that Newton mixes Platonist and Epicurean themes; (iii) a necessitarian approach; (iv) an approach connected with Bacon’s efforts to reformulate a useful notion of form and laws of nature. Hitherto only the second and third options have received scholarly attention in scholarship on DeGrav. The paper offers new arguments to treat Newtonian emanation as a species of Baconian formal causation as articulated, especially, in the first few aphorisms of part two of Bacon’s New Organon. If we treat Newtonian emanation as a species of formal causation then the necessitarian reading can be combined with most of the Platonist elements that others have discerned in DeGrav, especially Newton’s commitment to doctrines of different degrees of reality as well as the manner in which the first existing being ‘transfers’ its qualities to space (as a kind of causa-sui). This can clarify the conceptual relationship between space and its formal cause in Newton as well as Newton’s commitment to the spatial extended-ness of all existing beings. While the first two sections of this paper engage with existing scholarly controversies, in the final section the paper argues that the recent focus on emanation has obscured the importance of Newton’s very interesting claims about existence and measurement in “DeGrav”. The paper argues that according to Newton God and other entities have the same kind of quantities of existence; Newton is concerned with how measurement clarifies the way of being of entities. Newton is not claiming that measurement reveals all aspects of an entity. But if we measure something then it exists as a magnitude in space and as a magnitude in time. This is why in DeGrav Newton’s conception of existence really helps to “lay truer foundations of the mechanical sciences.”. (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)

Newton, along with a number of other seventeenth-century scientists, is frequently charged with having held an inconsistent view of nature and its operations, believing on the one hand in immutable laws of nature, and on the other in divine interventions into the natural order. In this paper I argue that Newton, William Whiston, and Samuel Clarke, came to understand miracles, not as violations of laws of nature, but rather as beneficent coincidences which were remarkable either because they were unusual, or (...) were beyond current understandings of nature. In this manner the Newtonians managed to reconcile their scientific pursuits with their religious convictions. (shrink)

This article concerns the problem of time pressures in higher education from the perspective of Newtonian (clock)time and pedagogical action. While most recent critiques of contemporary time pressures turn to alternative time theories in place of Newtonian temporality, the current paper outlines a way to conceive education from a Newtonian time perspective while also retaining theorizations of education as a form of cyclical and uncertain interaction. Time is theorized as changes in the immediate present which transform an uncertain and potential (...) future to an evident and permanent past in a Newtonian-linear temporal framework. Education, on the other hand, is defined as pedagogical influence to foster student’s human growth, demonstrated in a teaching–studying–learning relationship. Slow education theories and strategies are proposed as a way to reclaim time for education from the accelerative time policies of HE from within a linear time perspective instead of having to propose alternative time theories to ‘free’ education from its rootedness in the temporality of past, present, and future. (shrink)

Newtonian cosmology is logically inconsistent. I show its inconsistency in a rigorous but simple and qualitative demonstration. "Logic driven" and "content driven" methods of controlling logical anarchy are distinguished.

I argue that a criterion of theoretical equivalence due to Glymour :227–251, 1977) does not capture an important sense in which two theories may be equivalent. I then motivate and state an alternative criterion that does capture the sense of equivalence I have in mind. The principal claim of the paper is that relative to this second criterion, the answer to the question posed in the title is “yes”, at least on one natural understanding of Newtonian gravitation.

“Branching space-times” (BST) is intended as a representation of objective, event-based indeterminism. As such, BST exhibits both a spatio-temporal aspect and an indeterministic “modal” aspect of alternative possible historical courses of events. An essential feature of BST is that it can also represent spatial or space-like relationships as part of its (more or less) relativistic theory of spatio-temporal relations; this ability is essential for the representation of local (in contrast with “global”) indeterminism. This essay indicates how BST might be seen (...) to grow out of Newton’s deterministic and non-relativistic theory by two independent moves: (1) Taking account of indeterminism, and (2) attending to spatio-temporal relationships in a spirit derived from Einstein’s theory of special relativity. Since (1) and (2) are independent, one can see that there is room for four theories: Newtonian determinism, branching time indeterminism, relativistic determinism, and (finally) branching space-times indeterminism. (shrink)

John Norton has recently argued that Newtonian gravitation theory (at least as applied to cosmological contexts where one envisions the possibility of a homogeneous mass distribution throughout all of space) is inconsistent. I am not convinced. Traditional formulations of the theory may seem to break down in cases of the sort Norton considers. But the difficulties they face are only apparent. They are artifacts of the formulations themselves, and disappear if one passes to the so-called "geometrized" formulation of the theory.

The foundations of Statistical Mechanics can be recovered almost in their entirety from the principle of maximum entropy. In this work we show that its non-equilibrium generalization, the principle of maximum caliber (Jaynes, Phys Rev 106:620–630, 1957), when applied to the unknown trajectory followed by a particle, leads to Newton’s second law under two quite intuitive assumptions (both the expected square displacement in one step and the spatial probability distribution of the particle are known at all times). Our derivation explicitly (...) highlights the role of mass as an emergent measure of the fluctuations in velocity (inertia) and the origin of potential energy as a manifestation of spatial correlations. According to our findings, the application of Newton’s equations is not limited to mechanical systems, and therefore could be used in modelling ecological, financial and biological systems, among others. (shrink)

Sir Isaac Newton, writing in Latin, defined his celebrated laws of motion verbally. When the laws of motion are read as relating to his arithmetic and his calculus, division by zero is undefined so his physics fails at mathematical singularities. The situation is unchanged in modern real arithmetic and real calculus: division by zero is undefined so both Newtonian Physics and its modern developments fail at mathematical singularities. However, when Newton’s text is read as relating to transreal arithmetic and transreal (...) calculus, division by zero is defined and we show that the resulting Transreal Newtonian Physics does operate at mathematical singularities. We hold out the hope that the whole of modern physics may be similarly extended. We use the new physics to predict a convection current at the singularity in a black hole and suggest experiments in astronomy and high energy physics that might confirm or rebut our predictions. Thus our exegesis of Newton’s text extends mathematical physics and may, in future, extend experimental physics. (shrink)

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 argue that there is natural relationist interpretation of Newtonian and relativistic non-quantum physics. Although relationist, this interpretation does not fall prey to the traditional objections based on the existence of inertial effects.

The challenge of this work is to connect physics with the concept of intelligence. By intelligence we understand a capability to move from disorder to order without external resources, i.e., in violation of the second law of thermodynamics. The objective is to find such a mathematical object described by ODE that possesses such a capability. The proposed approach is based upon modification of the Madelung version of the Schrodinger equation by replacing the force following from quantum potential with non-conservative forces (...) that link to the concept of information. A mathematical formalism suggests that a hypothetical intelligent particle, besides the capability to move against the second law of thermodynamics, acquires such properties like self-image, self-awareness, self-supervision, etc. that are typical for Livings. However since this particle being a quantum-classical hybrid acquires non-Newtonian and non-quantum properties, it does not belong to the physics matter as we know it: the modern physics should be complemented with the concept of the information force that represents a bridge to intelligent particle. As a follow-up of the proposed concept, the following question is addressed: can artificial intelligence system composed only of physical components compete with a human? The answer is proven to be negative if the AI system is based only on simulations, and positive if digital devices are included. It has been demonstrated that there exists such a quantum neural net that performs simulations combined with digital punctuations. The universality of this quantum-classical hybrid is in capability to violate the second law of thermodynamics by moving from disorder to order without external resources. This advanced capability is illustrated by examples. In conclusion, a mathematical machinery of the perception that is the fundamental part of a cognition process as well as intelligence is introduced and discussed. (shrink)

For the last forty years, Hume's Newtonianism has been a debated topic in Hume scholarship. The crux of the matter can be formulated by the following question: Is Hume a Newtonian philosopher? Debates concerning this question have produced two lines of interpretation. I shall call them ‘traditional’ and ‘critical’ interpretations. The traditional interpretation asserts that there are many Newtonian elements in Hume, whereas the critical interpretation seriously questions this. In this article, I consider the main points made by both lines (...) of interpretations and offer further arguments that contribute to this debate. I shall first argue, in favor of the traditional interpretation, that Hume is sympathetic to many prominently Newtonian themes in natural philosophy such as experimentalism, criticality of hypotheses, inductive proof, and criticality of Leibnizian principles of sufficient reason and intelligibility. Second, I shall argue, in accordance with the critical interpretation, that in many cases Hume... (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 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)

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.

In two recent papers Perez Laraudogoitia has described a variety of supertasks involving elastic collisions in Newtonian systems containing a denumerably infinite set of particles. He maintains that these various supertasks give examples of systems in which energy is not conserved, particles at rest begin to move spontaneously, particles disappear from a system, and particles are created ex nihilo. An analysis of these supertasks suggests that they involve systems that do not satisfy the mathematical conditions required of Newtonian systems at (...) the time the supertask is due to be completed, or else they rely on the application of the time-reversal transformation to states which are not well-defined. Consequently, it is unjustified to conclude that the paradoxical results are arising from within the framework of Newtonian mechanics. In the last part of this article, we discuss various aspects of the physics of these supertasks. (shrink)

There has recently been a renewed interest in the “force” interpretation of evolutionary biology. In this article, I present the general structure of the arguments for the force interpretation and identify a problem in its overly permissive conditions for being a Newtonian force. I then attempt a solution that (1) helps to illuminate the difference between forces and other types of causes and (2) makes room for random genetic drift as a force. In particular, I argue that forces are not (...) different in kind from other types of causes but rather that forces are situated on a continuum of causes distinguished by their unifying power. †To contact the author, please write to: Department of Philosophy, University of Wisconsin–Madison, 5185 Helen C. White Hall, Madison, WI 53706; e‐mail: [email protected]. (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)

Physics is not just mathematics. This seems trivial, but poses difficult and interesting questions. In this paper we analyse a particular discrepancy between non-relativistic quantum mechanics and ‘classical’ space and time. We also suggest, but not discuss, the case of the relativistic QM. In this work, we are more concerned with the notion of space and its mathematical representation. The mathematics entails that any two spatially separated objects are necessarily different, which implies that they are discernible —we say that the (...) space is T2, or “Hausdorff”, or yet “separable”. But when enters QM, sometimes the systems need to be taken as completely indistinguishable, so that there is no way to tell which system is which, and this holds even in the case of fermions. But in the NST setting, it seems that we can always give an identity to them by means of their individuation, which seems to be contra the quantum physical situation, where individuation does not entail identity. Here we discuss this topic by considering a case study and conclude that, taking into account the quantum case, that is, when physics enter the discussion, even NST cannot be used to say that the systems do have identity. This case study seems to be relevant for a more detailed discussion on the interplay between physical theories and their underlying mathematics, in a simple way apparently never realized before. (shrink)

It is well-known that the conformal structure of a relativistic spacetime is of profound physical and conceptual interest. In this note, we consider the analogous structure for Newtonian theories. We show that the Newtonian Weyl tensor is an invariant of this structure.

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)

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)

This paper follows up a debate as to the consistency of Newtonian cosmology. Whereas Malament has shown that Newtonian cosmology *is* not inconsistent, to date there has been no analysis of Norton’s claim that Newtonian cosmology *was* inconsistent prior to certain advances in the 1930s, and in particular prior to Seeliger’s seminal paper of 1895. In this paper I agree that there are assumptions, Newtonian and cosmological in character, and relevant to the real history of science, which are inconsistent. But (...) there are some important corrections to make to Norton’s account. Here I display for the first time the inconsistencies—four in total—in all their detail. Although this extra detail shows there to be several different inconsistencies, it also goes some way towards explaining why they went unnoticed for two hundred years. (shrink)

We extend stit logic by adding a spatial dimension. This enables us to distinguish between powers and opportunities of agents. Powers are agent-specific and do not depend on an agent’s location. Opportunities do depend on locations, and are the same for every agent. The central idea is to define the real possibility to see to the truth of a condition in space and time as the combination of the power and the opportunity to do so. The focus on agent-relative powers (...) and space-relative opportunities firmly roots effectivity of an autonomous choice making agent in a space–time picture. Our space–time view will be classically Newtonian, since we will assume relativistic phenomena do not play a role in agentive effectivity. We show how our semantics naturally distinguishes between different kinds of histories; histories that reflect real possibilities and histories that reflect counterfactual possibilities. Furthermore, we discuss how the spatial picture sheds light on conceptual problems plaguing the central stit property of ‘independence of agency’. At several points in the article we will emphasise and defend the differences with Belnap’s theory of agency in relativistic branching space–times. (shrink)

The aim of this paper is to elucidate the question of whether Newtonian mechanics can be derived from relativity theory. Physicists agree that classical mechanics constitutes a limiting case of relativity theory. By contrast, philosophers of science like Kuhn and Feyerabend affirm that classical mechanics cannot be deduced from relativity theory because of the incommensurability between both theories; thus what we obtain when we take the limit c → ∞ in relativistic mechanics cannot be Newtonian mechanics sensu stricto. In this (...) paper I focus on the alleged change of reference of the term mass in the transition from one theory to the other. Contradicting Kuhn and Feyerabend, special relativity theory supports the view that the mass of an object is a characteristic property of the object, that it has the same value in whatever frame of reference it is measured, and that it does not depend on whether the object is in motion or at rest. Thus mass preserves the reference through the change of theory, and the existence of a Newtonian limit of relativity theory provides a good example of the rationality of theory change in mathematical physics. (shrink)

This book provides an introduction to Newtonian and relativistic mechanics. Unlike other books on the topic, which generally take a 'top-down' approach, it follows a novel system to show how the concepts of the 'science of motion' evolved through a veritable jungle of intermediate ideas and concepts. Starting with Aristotelian philosophy, the text gradually unravels how the human mind slowly progressed towards the fundamental ideas of inertia physics. The concepts that now appear so obvious to even a high school student (...) took great intellectuals more than a millennium to clarify. The book explores the evolution of these concepts through the history of science. After a comprehensive overview of the discovery of dynamics, it explores fundamental issues of the properties of space and time and their relation with the laws of motion. It also explores the concepts of spatio-temporal locality and fields, and offers a philosophical discussion of relative motion versus absolute motion, as well as the concept of an absolute space. Furthermore, it presents Galilean transformation and the principle of relativity, inadequacy of Galilean relativity and emergence of the spatial theory of relativity with an emphasis on physical understanding, as well as the debate over relative motion versus absolute motion and Mach's principle followed by the principle of equivalence. The natural follow-on to this section is the physical foundations of general theory of relativity. Lastly, the book ends with some new issues and possibilities regarding further modifications of the laws of motion leading to the solution of a number of fundamental issues closely connected with the characteristics of the cosmos. It is a valuable resource for undergraduate students of physics, engineering, mathematics, and related disciplines. It is also suitable for interdisciplinary coursework and introductory reading outside the classroom. (shrink)

The aim of this paper is to elucidate the question of whether Newtonian mechanics can be derived from relativity theory. Physicists agree that classical mechanics constitutes a limiting case of relativity theory. By contrast, philosophers of science like Kuhn and Feyerabend affirm that classical mechanics cannot be deduced from relativity theory because of the incommensurability between both theories; thus what we obtain when we take the limit c in relativistic mechanics cannot be Newtonian mechanics sensu stricto. In this paper I (...) focus on the alleged change of reference of the term mass in the transition from one theory to the other. Contradicting Kuhn and Feyerabend, special relativity theory supports the view that the mass of an object is a characteristic property of the object, that it has the same value in whatever frame of reference it is measured, and that it does not depend on whether the object is in motion or at rest. Thus mass preserves the reference through the change of theory, and the existence of a Newtonian limit of relativity theory provides a good example of the rationality of theory change in mathematical physics. (shrink)

As an example of a historical case study, some aspects of the post-Newtonian corrections in the Earth–Moon dynamics are described and discussed.

My argument owes much to two contemporary philosophical scholars of the development of modern physics beginning with Newton and extending through the late nineteenth and early twentieth centuries: George Smith and Howard Stein. From the former I take a conception of theory-mediated measurement, from the latter a conception of abstract structures in the phenomena. The relevant notion of phenomena, as we shall see, is closely related to Newtonian scientific methodology, a methodology that is clearly embraced by both philosophers. The conception (...) of abstract structures, however, is not so clear, and it is especially to be distinguished from the more recent conception of “structural realism.”. (shrink)

Based on our research regarding the relationship between physics and mathematics in HPS, and recently on Geneva Edition of Newton's Philosophiae Naturalis Principia Mathematica (1739–42) by Thomas Le Seur (1703–70) and François Jacquier (1711–88), in this paper we present some aspects of such Edition: a combination of editorial features and scientific aims. The proof of Proposition XLIII is presented and commented as a case study.

In my essay I look at the specifics of the dispute between the Scottish metaphysician Andrew Baxter and the mathematician Colin MacLaurin in an attempt to identify the source or sources of their contradictory, yet in both cases Newtonian, positions regarding occasionalism. After some general introductory remarks about each thinker, I examine the metaphysical implications that Baxter sees as following from Newton's concept of vis inertiæ. Following this, I look at MacLaurin's commitment to the role of sense experience in natural (...) philosophy. Finally, I discuss the different passages from Newton's Opticks on which the two thinkers focus. (shrink)

-/- Attempts to reduce irreversible processes to the scope of Newton’s mechanics are particularly challenging topics for both physical and philosophical research. Hollinger and Zenzen,1 for instance, claim that macroscopic irreversibility has a mechanical origin, and they explain this within the Newtonian framework. Newton’s Scientific and Philosophical Legacy Newton’s Scientific and Philosophical Legacy Look -/- .

According to Newton, the goals of natural philosophy comprise quantitative generalizations and causal knowledge, the latter being paramount. Quantitative generalizations are sometimes explanatory, in psychology as elsewhere . However, in psychology, they are not explanatory when the human subject is considered qua bearer of psychological states , but only when she is considered qua physical system. In the former case quantitative generalizations are, rather, to be causally explained. In this sense, psychology may be closer to the Newtonian methodological mark than (...) contemporary physics. (shrink)

Kant elaborated his dynamical theory of matter in two quite different systematic accounts, the first in the Monadologia physica, the second in the Dynamics chapter of the Metaphysische Anfangsgründe der Naturwissenschaft. In this paper I investigate the transition from the monadological to the “continuum” dynamical theory of matter, whose exact timing and motives are not explicitly clarified in Kant’s writings. I locate Kant’s turn around the middle 1760s, presenting Kant’s abandonment of his own physical monadology as a way out of (...) controversies about monads and materialism which characterized the German intellectual world of his time. Among the results of this crucial modification in matter theory stands out the new interpretation of Newtonian forces in the critical writings, which is not only relevant for Kant’s account of physics, but also plays a major exemplary role for his critical theory of knowledge. (shrink)

Around 3 decades ago, Jayant Narlikar & Halton Arp argued on possible variable mass hypothesis cosmology (VMH). In the meantime, the Earth expansion problem has attracted great interest, and recent study gives geodetic evidence that the Earth has been expanding, at least over the recent several decades. Therefore, in the present article discusses some interesting effects related to varying G, but here we argue that instead of varying G we can think of varying mass (M). Among other things we discuss (...) receding planets from the Sun, calculation of Pioneer spacecraft anomaly as proposed by B.G. Sidharth, and also possible slight change of LAGEOS Satellite. Further observation to verify or refute this conjecture is recommended, especially based on geological evidence of expanding earth. (shrink)