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)

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)

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 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)

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)

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)

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)

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)

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.

Defending Robert Rosen’s claim that in every confrontation between physics and biology it is physics that has always had to give ground, it is shown that many of the most important advances in mathematics and physics over the last two centuries have followed from Schelling’s demand for a new physics that could make the emergence of life intelligible. Consequently, while reductionism prevails in biology, many biophysicists are resolutely anti-reductionist. This history is used to identify and defend a fragmented but (...) progressive tradition of anti-reductionist biomathematics. It is shown that the mathematicoephysico echemical morphology research program, the biosemiotics movement, and the relational biology of Rosen, although they have developed independently of each other, are built on and advance this antireductionist tradition of thought. It is suggested that understanding this history and its relationship to the broader history of post-Newtonian science could provide guidance for and justify both the integration of these strands and radically new work in post-reductionist biomathematics. (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 -/- .

Reid was a Newtonian and a Theist, but did he found his Theism on Newton’s physics? In opposition to commonplace assumptions about the role of Theism in Reid’s philosophy, my answer is no. Reid prefers to found his Theism on a priori reasons, rather than on physics. Reid’s understanding of physics as an empirical science stops it from contributing in any clear and efficient way to issues of natural theology. In addition, Reid is highly sceptical of our ability to (...) discover the efficient and final causes of natural phenomena, knowledge of which is essential for natural theology. To bring out Reid’s differences with classical Newtonian Theists Richard Bentley and William Whiston, I examine their use of the law and force of general gravitation, and reconstruct what would be Reidian objections.Keywords: Thomas Reid; William Whiston; Richard Bentley; Physics; Theism; Isaac Newton. (shrink)

While "natural history" is practically synonymous with the name of Buffon, the term itself has been otherwise overlooked by historians of science. This essay attempts to address this omission by investigating the meanings of "physique," "natural philosophy," and "history," among other terms, with the purpose of understanding Buffon's actual objectives. It also shows that Buffon never claimed to be a Newtonian and should not be considered as such; the goal is to provide a historical analysis that resituates (...) Buffon's thought within his own era. This is done, primarily, by eschewing the often-studied question of time in Buffon. Instead, this study examines the nontemporal meanings of the word "history" within the naturalist's theory and method. The title of his Natural History is examined both as an indicator of the kind of science that Buffon was hoping to achieve and as a source of great misinterpretation among his peers. Unlike Buffon, many of his contemporaries actually envisioned the study of nature from a Baconian perspective where history was restricted to the mere collection of facts and where philosophy, which was the implicit and ultimate goal of studying nature, was seen, at least for the present, as unrealizable. Buffon confronts this tendency insofar as his Histoire naturelle claims to be the real physique that, along with describing nature, also sought to identify general laws and provide clear insight into what true knowledge of nature is or should be. According to Buffon, history (both natural and civil) is not analogous to mathematics; it is a nonmathematical method whose scope encompasses both nature and society. This methodological stance gives rise to the "physicization" of certain moral concepts--a gesture that was interpreted by his contemporaries as Epicurean and atheist. In addition, Buffon reduces a number of metaphysically tainted historical concepts (e.g., antediluvian monuments) to objects of physical analysis, thereby confronting the very foundation of natural theology. In Buffon, as this essay makes clear, natural history is paving the way for a new physique (science of natural beings), independent from mathematics and from God, that treats naturalia in a philosophical and "historical" manner that is not necessarily "temporal. ". (shrink)

The field of developmental psychology has typically traced its history to Darwin or to changes in views about the nature of childhood. What has been generally neglected is how the core assumptions of contemporary theories were forged in the early history of modern science. In particular, the rise of Newtonian mechanics precipitated similar perspectives in geology and then biology. They all converged on a shared set of assumptions about the nature of change in the physical world. Theology (...) also played a key role in this process, serving not only as a foil, but also as a source of important insights for the emerging scientific, and developmental, world view. The field of developmental psychology is a child of this complex and often stormy relationship between science and theology that has shaped Western thought. (shrink)

Pessimistic meta-induction is a powerful argument against scientific realism, so one of the major roles for advocates of scientific realism will be trying their best to give a sustained response to this argument. On the other hand, it is also alleged that structural realism is the most plausible form of scientific realism; therefore, the plausibility of scientific realism is threatened unless one is given the explicit form of a structural continuity and minimal structural preservation for all our current theories. This (...) essay aims to present what we call expansive structures, which are the structures that can be reconstructed from geometrized Newtonian gravitation and are capable of expanding into general relativity, explicitly. In this way, pessimistic meta-induction will be undermined. (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)

This paper explores the scientific sources behind Kant’s early dynamic theory of matter in 1755, with a focus on two main Kant’s writings: Universal Natural History and Theory of the Heavens and On Fire. The year 1755 has often been portrayed by Kantian scholars as a turning point in the intellectual career of the young Kant, with his much debated conversion to Newton. Via a careful analysis of some salient themes in the two aforementioned works, and a reconstruction of (...) the scientific sources behind them, this paper shows Kant’s debt to an often overlooked scientific tradition, i.e. speculative Newtonian experimentalism. The paper argues that more than the Principia, it was the speculative experimentalism that goes from Newton’s Opticks to Herman Boerhaave’s Elementa chemiae via Stephen Hales’ Vegetable Staticks that played a central role in the elaboration of Kant’s early dynamic theory of matter in 1755. (shrink)

This article explores and categorizes the belief of what awaited the soul after bodily death held by English divine Samuel Clarke, D.D. as compared to that held by his close friend Isaac Newton. Evidence taken from the corpus of Clarke's writings reveals both he and Newton to be mortalists, but of differing types and to different degrees. While it has long been known that Clarke and Newton were often of one mind in matters of theology, a comparative study of their (...) conceptions of soul reveals that the two friends held even more parallels than has been acknolwedged. (shrink)

I examine Popper’s claims about Newton’s use of induction in Principia with the actual contents of Principia and draw two conclusions. Firstly, in common with most other philosophers of his generation, it appears that Popper had very little acquaintance with the contents and methodological complexities of Principia beyond what was in the famous General Scholium. Secondly Popper’s ideas about induction were less sophisticated than those of Newton, who recognised that it did not provide logical proofs of the results obtained using (...) it, because of the possibilities of later, contrary evidence. I also trace the historical background to commonplace misconceptions about Newton’s method.Author Keywords: Newton; Popper; Induction; Principia; Kepler’s laws. (shrink)

Hume follows Newton in replacing the mechanical philosophy’s demonstrative ideal of science by the Principia’s ideal of inductive proof ; in this respect, Hume differs sharply from Locke. Hume is also guided by Newton’s own criticisms of the mechanical philosophers’ hypotheses. The first stage of Hume’s skeptical argument concerning causation targets central tenets of the mechanical philosophers’ conception of causation, all of which rely on the a priori postulation of a hidden configuration of primary qualities. The skeptical argument concerning the (...) causal inductive inference then raises doubts about what Hume himself regards as our very best inductive method. Hume’s own “Rules” further substantiate his reliance on Newton. Finally, Locke’s distinction between “Knowledge” and “Probability” does not leave room for Hume’s Newtonian notion of inductive proof. (shrink)

Worldviews affect human behavior, and how we behave affects the world around us. Animism and so-called higher religions remain influential world-views; but the scientific worldview is comparably significant, and has under-gone drastic change during the twentieth century. The physical science ideal of mathematical precision and predictability, as elaborated by Galileo, Newton, and their heirs, underwent an amazing transformation in the twentieth century when Big Bang cosmology substituted an expanding, unstable universe for the Newtonian world machine. As a result, a (...) grand convergence of the sciences seems to be emerging around an evolutionary vision of how new aspects of reality emerge locally from new levels of complexity, like the heavier atoms, forged in stellar furnaces, the living molecules that arose in earth's primordial seas, and the symbolic systems invented by human societies perhaps as recently as forty thousand years ago. History, once a hopelessly inexact laggard among the sciences, might even become something of a model for other disciplines, since it deals with the most complex levels of reality we are aware of, that is, the world of agreed-upon meanings that guides our interaction with one another and with the biological, chemical, and physical worlds around us. (shrink)

Hume’s arguments against the cosmological argument have, in the past century, often been highly praised by commentators such as H.D.Aiken and E.C. Mossner. While Hume’s argument often receives strong philosophical support, the four major objections raised against the cosmological argument in book IX of his Dialogues hinge upon a misunderstanding of Newtonian natural philosophy. Hence, when the proper historical context is considered, Hume’s objections are weak at best, for they assume an understanding of matter and physical necessity that are (...) inconsistent with Newtonian natural philosophy. This paper will outline Hume’s objections, and explore how the formulation of the cosmological argument put forth by the English philosopher Samuel Clarke was reliant upon the best available scientific evidence, i.e. Newtonian philosophy. Consequently, any contemporary supporter of Hume who believes that his argument was successful in quenching the enlightenment era reiteration of the cosmological argument does so anachronistically. (shrink)

In the history of science, the birth of classical chemistry and thermodynamics produced an anomaly within Newtonian mechanical paradigm: force and acceleration were no longer citizens of new cited sciences. Scholars tried to reintroduce them within mechanistic approaches, as the case of the kinetic gas theory. Nevertheless, Thermodynamics, in general, and its Second Law, in particular, gradually affirmed their role of dominant not-reducible cognitive paradigms for various scientific disciplines: more than twenty formulations of Second Law—a sort of indisputable (...) intellectual wealth—are conceived after 1824 Sadi Carnot’s original statement and a multitude of entropy functions are proposed after 1865 Clausius’ former definition. Furthermore, at the end of nineteenth century, thermodynamics extended its cognitive domain to chemistry. Mainly thanks to Gibbs, a brand new discipline—chemical thermodynamics or physical chemistry—gradually affirmed its role inside the scientific community. This paper reports the former results of collaborative research program in the History and Epistemology of Science as well as Nature of Science Teaching aimed at retracing the foundations of the physical chemistry. Specifically, the research is structured in three parts: historical-epistemic reflections on fundamental thermodynamic concepts and principles—such as reversible process, heat, temperature, thermal equilibrium and Clausius’ Second Law—that play a structural role inside modern physical chemistry; panoramic overview on the entropy, whose polysemy makes it one of the most demanding concepts for scholars, teachers and students while approaching thermodynamics; conceptualization of chemical equilibrium as complex entity according to the dual epistemological approach offered by Gibbs’ thermodynamic model and the kinetic standpoint by Guldberg and Waage. In particular, the present work details an original reading of thermodynamic principles with the aim of setting forth a rationalized multidisciplinary substrate whereon the foundational concepts of reversible process and thermal equilibrium can be set. (shrink)

Intertheoretic reduction in physics aspires to be both to be explanatory and perfectly general: it endeavors to explain why an older, simpler theory continues to be as successful as it is in terms of a newer, more sophisticated theory, and it aims to relate or otherwise account for as many features of the two theories as possible. Despite often being introduced as straightforward cases of intertheoretic reduction, candidate accounts of the reduction of general relativity to Newtonian gravitation have either (...) been insufficiently general or rigorous, or have not clearly been able to explain the empirical success of Newtonian gravitation. Building on work by Ehlers and others, I propose a different account of the reduction relation that is perfectly general and meets the explanatory demand one would make of it. In doing so, I highlight the role that a topology on the collection of all spacetimes plays in defining the relation, and how the selection of the topology corresponds with broader or narrower classes of observables that one demands be well-approximated in the limit. (shrink)

A theorem due to Bob Geroch and Pong Soo Jang ["Motion of a Body in General Relativity." Journal of Mathematical Physics 16, ] provides a sense in which the geodesic principle has the status of a theorem in General Relativity. I have recently shown that a similar theorem holds in the context of geometrized Newtonian gravitation [Weatherall, J. O. "The Motion of a Body in Newtonian Theories." Journal of Mathematical Physics 52, ]. Here I compare the interpretations of (...) these two theorems. I argue that despite some apparent differences between the theorems, the status of the geodesic principle in geometrized Newtonian gravitation is, mutatis mutandis, strikingly similar to the relativistic case. (shrink)