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 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)

William Whewell’s philosophy of scientific discovery is applied to the problem of understanding the nature of unification and explanation by the composition of causes in Newtonian mechanics. The essay attempts to demonstrate: the sense in which ”approximate’ laws successfully refer to real physical systems rather than to idealizations of them; why good theoretical constructs are not badly underdetermined by observation; and why, in particular, Newtonian forces are not conventional and how empiricist arguments against the existence of component (...) causes, and against the veracity of the fundamental laws, are flawed. (shrink)

This paper elaborates on the following correspondence theorem (which has been defended and formally proved elsewhere): if theory T has been empirically successful in a domain of applications A, but was superseded later on by a different theory T* which was likewise successful in A, then under natural conditions T contains theoretical expressions which were responsible for T’s success and correspond (in A) to certain theoretical expressions of T*. I illustrate this theorem at hand of the phlogiston versus oxygen theories (...) of combustion, and the classical versus relativistic theories of mass. The ontological consequences of the theorem are worked out in terms of the indirect reference and partial truth. The final section explains how the correspondence theorem may justify a weak version of scientific realism without presupposing the no-miracles argument. (shrink)

Modern agriculture is subject to a metaphysical as well as an ethical critique. As a casual review of the beliefs associated with food production in the past suggests, modern agriculture is embedded in and informed by the prevailing modern world view, Newtonian Mechanics, which is bankrupt as a scientific paradigm and unsustainable as an agricultural motif. A new holistic, organic world view is emerging from ecology and the new physics marked by four general conceptual features: Each level of (...) organization from atoms to ecosystems (1) exhibits emergent properties, (2) exerts downward causation from whole to part, (3) is a systemically integrated whole, (4) the parts of which are internally related. Organic agriculture has been favourably compared with industrial agriculture by the United States National Academy of Science's Board on Agriculture. Aldo Leopold was among the first to criticize industrial agriculture and to envision a new motif for agriculture informed by ecology. A future post-modern ecological agriculture will help to solve the ethical problems engendered by modern mechanical agriculture. (shrink)

Classical mechanics is presented so as to render the new formulation valid for an arbitrary temporal variable, as opposed to Newton’s Absolute Time only. Newton’s theory then becomes formally identical (in a precise sense) to relativity, albeit in a three-dimensional manifold. (The ultimate difference between the two dynamics is traced to the existence of the relativistic ‘mass-shell’ condition.) A classical Lagrangian is provided for our formulation of the equations of motion and it is related to one of the known (...) forms of the corresponding relativistic Lagrangian, which is the analogue of the Polyakov Lagrangian of string theory. (shrink)

Kant's account of Newtonian science in terms of a priori structures of the mind has been generally interpreted as too restrictive. If Newtonian science is an instantiation of the system of categories, then, in order to retain any value, they need to be dynamized in accordance with the development of science beyond Newton. This paper suggests that the restriction in best understood as Kant attempt to provide a primary matrix of sense for any possible natural science, inasmuch as (...) it reflects the "first idea" contained in the Copernican Revolution. (shrink)

Dirac's classical electrodynamics countenances "preaccelerations" of charged particles at a time t as mathematical functions of external forces applied after the time t. These preaccelerations have been interpreted as evidence for physical retrocausation upon assuming that, in electrodynamics no less than in Newton's second law, external forces sustain an asymmetric causal relation to accelerations. And this retrocausal interpretation has just been defended against the critiques in (Grunbaum 1976), (Grunbaum and Janis, 1977 and 1978) by appeal to the formal assimilation of (...) the electrodynamic laws of motion to Newton's second law. It is argued below that this latest defense of the retrocausal interpretation is even more ill-founded than the prior ones in the literature. (shrink)

This paper and its predecessor () are about the question: 'Are the events in the entire universe encoded in and predictable from any of its parts?' To approach a positive answer in classical physics, the following result is proved and commented on: in Newton's theory of gravitation, the entire trajectory of a particle can be predicted given any segment of it, regardless of how the other particles are moving-provided that there is only a finite number of particles and that their (...) speeds remain bounded. (It is this condition, together with a set of parameters characterising the motion of the other particles, which enables us to estimate the effect of the other particles on the trajectory of the given particle.) The extension of this result to other theories, in particular to special relativity, is discussed. (shrink)

can prevent non-contact interactions in Newtonian collision mechanics. The proposal is weakened by the apparent arbitrariness of what will be shown as the requirement of only an odd number of sets of some ex nihilo-created self-exciting particles. There is, however, an initial condition such that, without the ex nihilo self-exciting particles, either there is a contradictory outcome, or there is a non-contact configuration law, or there are odds versus evens indeterminacies. With the various odds versus evens arbitrarinesses and (...) other such difficulties, there seems to be an ontological unsatisfactoriness in the speed-unbounded Newtonian collision system. Introduction Taking self-excitations very seriously A problematic initial condition Another alternative. (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)

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)

Einstein’s 1905 paper on special relativity suggests that relativistic mechanics is simply a matter of adjusting Newton’s to make it Lorentz invariant. Einstein, for instance.

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)

The present note is intended to draw the reader's attention to the analysis of the relation between Newtonian Mechanics and Special Relativity Mechanics (henceforth to be referred to as NM and SRM), given by Philipp Frank, one of the classics of Logical Empiricism (in Frank [1938]). Frank's analysis of the relation between NM and SRM is interesting in many ways. Firstly, it shows clearly that problems of disruptive changes and of conceptual disparity were known to and discussed (...) by Logical Empiricists and that, therefore, some of them at least were not at all blinded to 'dynamic' problems of changes in actual science by their view of physical theories as interpreted axiomatic systems and did not deal with those theories as 'static, frozen in logical mold'. Secondly, it reveals some of the reasons for the Logical Empiricist rejection of what came to be known later as the incommensurability claim. (shrink)

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)

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 (...) class='Hi'>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)

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 (...) class='Hi'>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)

Supertasks recently discussed in the literature purport to display a failure ofenergy conservation and determinism in Newtonian mechanics. We debatewhether these supertasks are admissible as Newtonian systems, with Earmanand Norton defending the affirmative and Alper and Bridger the negative.

If the force on a particle fails to satisfy a Lipschitz condition at a point, it relaxes one of the conditions necessary for a locally unique solution to the particle’s equation of motion. I examine the most discussed example of this failure of determinism in classical mechanics—that of Norton’s dome—and the range of current objections against it. Finding there are many different conceptions of classical mechanics appropriate and useful for different purposes, I argue that no single conception is (...) preferred. Instead of arguing for or against determinism, I stress the wide variety of pragmatic considerations that, in a specific context, may lead one usefully and legitimately to adopt one conception over another in which determinism may or may not hold. (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)

The analysis of theory-confirmation generally takes the deductive form: show that a theory in conjunction with physical data and auxiliary hypotheses yield a prediction about phenomena; verify the prediction; provide a quantitative measure of the degree of theory-confirmation this yields. The issue of confirmation for an entire framework (e.g., Newtonian mechanics en bloc, as opposed, say, to Newton’s theory of gravitation) either does not arise, or is dismissed in so far as frameworks are thought not to be the (...) kind of thing that admits scientific confirmation. I argue that there is another form of scientific reasoning that has not received philosophical attention, what I call Newtonian abduction, that does provide confirmation for frameworks as a whole, and does so in two novel ways. (In particular, Newtonian abduction is not inference to the best explanation, but rather is closer to Peirce’s original idea of abduction.) I further argue that Newtonian abduction is at least as important a form of reasoning in science as standard deductive and inductive forms. The form is beautifully summed up by Maxwell (Proc Camb Philos Soc II:292–294, 1876): “The true method of physical reasoning is to begin with the phenomena and to deduce the forces from them by a direct application of the equations of motion.”. (shrink)

Recently philosophers of biology have argued over whether or not Newtonian mechanics provides a useful analogy for thinking about evolutionary theory. For philosophers, the canonical presentation of this analogy is Sober's. Matthen and Ariew and Walsh, Lewins, and Ariew argue that this analogy is deeply wrong-headed. Here I argue that the analogy is indeed useful, however, not in the way it is usually interpreted. The Newtonian analogy depends on having the proper analogue of Newton's First Law. That (...) analogue is what McShea and Brandon call the Zero Force Evolutionary Law. According to the ZFEL, change, not stasis, is the default state of evolutionary systems. (shrink)

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)

A number of recent papers have criticized what they call the dynamical interpretation of evolutionary theory found in Elliott Sober’s The Nature of Selection. Sober argues that we can think of evolutionary theory as a theory of forces analogous to Newtonian mechanics. These critics argue that there are several important disanalogies between evolutionary and Newtonian forces: Unlike evolutionary forces, Newtonian forces can be considered in isolation, they have source laws, they compose causally in a straightforward way, (...) and they are intermediate causes in causal chains. Here we defend and extend the forces analogy by arguing that each of these criticisms is based on a misunderstanding of Newtonian forces. Our discussion also has the interesting consequence that natural selection turns out to be more similar to forces such as friction and elastic forces rather than the more canonical gravitation. (shrink)

The INBIOSA project brings together a group of experts across many disciplines who believe that science requires a revolutionary transformative step in order to address many of the vexing challenges presented by the world. It is INBIOSA’s purpose to enable the focused collaboration of an interdisciplinary community of original thinkers. This paper sets out the case for support for this effort. The focus of the transformative research program proposal is biology-centric. We admit that biology to date has been more fact-oriented (...) and less theoretical than physics. However, the key leverageable idea is that careful extension of the science of living systems can be more effectively applied to some of our most vexing modern problems than the prevailing scheme, derived from abstractions in physics. While these have some universal application and demonstrate computational advantages, they are not theoretically mandated for the living. A new set of mathematical abstractions derived from biology can now be similarly extended. This is made possible by leveraging new formal tools to understand abstraction and enable computability. [The latter has a much expanded meaning in our context from the one known and used in computer science and biology today, that is "by rote algorithmic means", since it is not known if a living system is computable in this sense (Mossio et al., 2009).] Two major challenges constitute the effort. The first challenge is to design an original general system of abstractions within the biological domain. The initial issue is descriptive leading to the explanatory. There has not yet been a serious formal examination of the abstractions of the biological domain. What is used today is an amalgam; much is inherited from physics (via the bridging abstractions of chemistry) and there are many new abstractions from advances in mathematics (incentivized by the need for more capable computational analyses). Interspersed are abstractions, concepts and underlying assumptions “native” to biology and distinct from the mechanical language of physics and computation as we know them. A pressing agenda should be to single out the most concrete and at the same time the most fundamental process-units in biology and to recruit them into the descriptive domain. Therefore, the first challenge is to build a coherent formal system of abstractions and operations that is truly native to living systems. Nothing will be thrown away, but many common methods will be philosophically recast, just as in physics relativity subsumed and reinterpreted Newtonian mechanics. -/- This step is required because we need a comprehensible, formal system to apply in many domains. Emphasis should be placed on the distinction between multi-perspective analysis and synthesis and on what could be the basic terms or tools needed. The second challenge is relatively simple: the actual application of this set of biology-centric ways and means to cross-disciplinary problems. In its early stages, this will seem to be a “new science”. This White Paper sets out the case of continuing support of Information and Communication Technology (ICT) for transformative research in biology and information processing centered on paradigm changes in the epistemological, ontological, mathematical and computational bases of the science of living systems. Today, curiously, living systems cannot be said to be anything more than dissipative structures organized internally by genetic information. There is not anything substantially different from abiotic systems other than the empirical nature of their robustness. We believe that there are other new and unique properties and patterns comprehensible at this bio-logical level. The report lays out a fundamental set of approaches to articulate these properties and patterns, and is composed as follows. -/- Sections 1 through 4 (preamble, introduction, motivation and major biomathematical problems) are incipient. Section 5 describes the issues affecting Integral Biomathics and Section 6 -- the aspects of the Grand Challenge we face with this project. Section 7 contemplates the effort to formalize a General Theory of Living Systems (GTLS) from what we have today. The goal is to have a formal system, equivalent to that which exists in the physics community. Here we define how to perceive the role of time in biology. Section 8 describes the initial efforts to apply this general theory of living systems in many domains, with special emphasis on crossdisciplinary problems and multiple domains spanning both “hard” and “soft” sciences. The expected result is a coherent collection of integrated mathematical techniques. Section 9 discusses the first two test cases, project proposals, of our approach. They are designed to demonstrate the ability of our approach to address “wicked problems” which span across physics, chemistry, biology, societies and societal dynamics. The solutions require integrated measurable results at multiple levels known as “grand challenges” to existing methods. Finally, Section 10 adheres to an appeal for action, advocating the necessity for further long-term support of the INBIOSA program. -/- The report is concluded with preliminary non-exclusive list of challenging research themes to address, as well as required administrative actions. The efforts described in the ten sections of this White Paper will proceed concurrently. Collectively, they describe a program that can be managed and measured as it progresses. (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)

This article analyzes the view of evolutionary theory as a theory of forces. The analogy with Newtonian mechanics has been challenged due to the alleged mismatch between drift and the other evolutionary forces. Since genetic drift has no direction several authors tried to protect its status as a force: denying its lack of directionality, extending the notion of force and looking for a force in physics which also lacks of direction. I analyse these approaches, and although this strategy (...) finally succeeds, this discussion overlooks the crucial point on the debate between causalists and statisticalists: the causal status of evolutionary theory. (shrink)

In this paper, I critically assess different interpretations of Bohmian mechanics that are not committed to an ontology based on the wave function being an actual physical object that inhabits configuration space. More specifically, my aim is to explore the connection between the denial of configuration space realism and another interpretive debate that is specific to Bohmian mechanics: the quantum potential versus guidance approaches. Whereas defenders of the quantum potential approach to the theory claim that Bohmian mechanics (...) is better formulated as quasi-Newtonian, via the postulation of forces proportional to acceleration; advocates of the guidance approach defend the notion that the theory is essentially first-order and incorporates some concepts akin to those of Aristotelian physics. Here I analyze whether the desideratum of an interpretation of Bohmian mechanics that is both explanatorily adequate and not committed to configuration space realism favors one of these two approaches to the theory over the other. Contrary to some recent claims in the literature, I argue that the quasi-Newtonian approach based on the idea of a quantum potential does not come out the winner. (shrink)

These original essays explore the philosophical implications of Newton's work.

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)

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)

Bohmian mechanics is a quantum theory without observers. This means that neither the act of observation nor the notion of observer play any role in defining the theory, the theory is not about observers and observation, and it explains all non relativistic quantum phenomena. The theory is about something primitive', the basic ontology, and the laws for that are given. Bohmian mechanics is a deterministic theory of point particles. Like Newtonian mechanics it is invariant under Galilei (...) transformations, but unlike Newtonian mechanics it is a first-order theory, acceleration is not a concept entering the law of motion. Rather this law directly determines the velocities of the particles as follows. (shrink)

Here I explore a novel no-collapse interpretation of quantum mechanics that combines aspects of two familiar and well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. Despite reproducing the empirical predictions of quantum mechanics, the theory looks surprisingly classical. All there is at the fundamental level are particles interacting via Newtonian forces. There is no wave function. However, there are many worlds.