Classical Mechanics

We address a long-standing debate over whether classical magnetic forces can do work, ultimately answering the question in the affirmative. In detail, we couple a classical particle with intrinsic spin and elementary dipole moments to the electromagnetic field, derive the appropriate generalization of the Lorentz force law, show that the particle’s dipole moments must be collinear with its spin axis, and argue that the magnetic field does mechanical work on the particle’s elementary magnetic dipole moment. As consistency checks, we calculate (...) the overall system’s energy-momentum and angular momentum, and show that their local conservation equations lead to the same force law and therefore the same conclusions about magnetic forces and work. We also compute the system’s Belinfante–Rosenfeld energy–momentum tensor. (shrink)

Eleanor Knox has argued that our concept of spacetime applies to whichever structure plays a certain functional role in the laws (the role of determining local inertial structure). I raise two complications for this approach. First, our spacetime concept seems to have the structure of a cluster concept, which means that Knox's inertial criteria for spacetime cannot succeed with complete generality. Second, the notion of metaphysical fundamentality may feature in the spacetime concept, in which case spacetime functionalism may be uninformative (...) in the absence of answers to fundamental metaphysical questions like the substantivalist/relationist debate. (shrink)

In this paper, we review a general technique for converting the standard Lagrangian description of a classical system into a formulation that puts time on an equal footing with the system's degrees of freedom. We show how the resulting framework anticipates key features of special relativity, including the signature of the Minkowski metric tensor and the special role played by theories that are invariant under a generalized notion of Lorentz transformations. We then use this technique to revisit a classification of (...) classical particle-types that mirrors Wigner's classification of quantum particle-types in terms of irreducible representations of the Poincaré group, including the cases of massive particles, massless particles, and tachyons. Along the way, we see gauge invariance naturally emerge in the context of classical massless particles with nonzero spin, as well as study the massless limit of a massive particle and derive a classical-particle version of the Higgs mechanism. (shrink)

Standard lore holds that magnetic forces are incapable of doing mechanical work. More precisely, the claim is that whenever it appears that a magnetic force is doing work, the work is actually being done by another force, with the magnetic force serving only as an indirect mediator. On the other hand, the most familiar instances of magnetic forces acting in everyday life—bar magnets lifting other bar magnets—appear to present manifest evidence of magnetic forces doing work. These sorts of counterexamples are (...) often dismissed as arising from quantum effects that lie outside the classical regime. In this paper, however, we show that quantum theory is not needed to account for these phenomena, and that classical electromagnetism admits a model of elementary magnetic dipoles on which magnetic forces can indeed do work. In order to develop this model, we revisit the foundational principles of the classical theory of electromagnetism, showcase the importance of constraints from relativity, examine the structure of the multipole expansion, and study the connection between the Lorentz force law and conservation of energy and momentum. (shrink)

It is often contended that the special sciences, and even fundamental physics, make use of ceteris-paribus law-statements. Yet there are general concerns that such law-statements are vacuous or untestable or unscientific. I consider two main kinds of ceteris-paribus law-statement. I argue that neither kind is vacuous, that one of the kinds is untestable, that both kinds may count as scientific to the extent that they form parts of conjunctions that imply novel falsifiable statements which survive testing, but that one kind (...) has an affinity with ad hoc manoeuvres that are unsatisfactory from a scientific point of view. I show that the contemporary debate about ceteris-paribus law-statements is afflicted with error and confusion because of a general failure to disentangle the notions: non-vacuous, testable, scientific, verifiable, falsifiable, and ad hoc. (shrink)

Fundamental physics contains an important link between properties of elementary particles and continuous symmetries of particle systems. For example, properties such as mass and spin are said to be 'associated' with specific continuous symmetries. -/- These 'associations' have played a key role in the discovery of various new particle kinds, but more importantly: they are thought to provide a deep insight into the nature of physical reality. The link between properties and symmetries has been said to call for a radical (...) revision of perceived metaphysical orthodoxy. However, if we are to use claims about an 'association' between properties and symmetries in the articulation of metaphysical views, we first need to develop a sufficiently precise understanding of the content of these claims. The goal of this paper is to do just that. (shrink)

Una din cele mai disputate controverse privind prioritatea unor descoperiri științifice este cea privind legea gravitației universale, între Isaac Newton și Robert Hooke. În acest eseu extind o lucrare mai veche pe aceeași temă, ”Isaac Newton vs. Robert Hooke în legea gravitației universale”. Hooke l-a acuzat pe Newton de plagiat, preluându-i ideile exprimate în lucrările anterioare. În această lucrare încerc să arăt, pe baza unor analize anterioare, că ambii oameni de știință au greșit: Robert Hooke pentru că teoria sa nu (...) era în fond decât idei care nu s-ar fi materializat niciodată fără suportul matematic al lui Isaac Newton; iar acesta din urmă a greșit nerecunoscând niciun merit al lui Hooke în elaborarea teoriei gravitației. Mai mult, după moartea lui Hooke și preluarea prezidenției Societății Regale, Newton a înlăturat orice urmă din instituție a fostului președinte, Robert Hooke. De asemenea, La negarea contribuției lui Hooke a contribuit și statutul său social ”inferior”, fiind poreclit de contemporani ”mecanicul”, spre deosebire de Sir Isaac Newton cel nobil. Pentru aceasta detaliez acuzațiile și argumentele fiecăreia dintre părți, și cum a fost percepută această dispută de către contemporanii celor doi. Finalizez lucrarea cu concluziile desprinse din cuprins. (shrink)

The Kolmogorov-Sinai entropy is a fairly exotic mathematical concept which has recently aroused some interest on the philosophers’ part. The most salient trait of this concept is its working as a junction between such diverse ambits as statistical mechanics, information theory and algorithm theory. In this paper I argue that, in order to understand this very special feature of the Kolmogorov-Sinai entropy, is essential to reconstruct its genealogy. Somewhat surprisingly, this story takes us as far back as the beginning of (...) celestial mechanics and through some of the most exciting developments of mathematical physics of the 19th century. (shrink)

Shifts are a well-known feature of the literature on spacetime symmetries. Recently, discussions have focused on so-called dynamic shifts, which by analogy with static and kinematic shifts enact arbitrary linear accelerations of all matter (as well as a change in the gravitational potential). But in mathematical formulations of these shifts, the analogy breaks down: while static and kinematic shift act on the matter field, the dynamic shift acts on spacetime structure instead. I formulate a different, `active' version of the dynamic (...) shift which does act on matter. (shrink)

Although physical theories routinely posit absolute quantities, such as absolute position or intrinsic mass, it seems that only comparative quantities such as distance and mass ratio are observable. But even if there are in fact only distances and mass ratios, the success of absolutist theories means that the world looks just as if there are absolute positions and intrinsic masses. If comparativism is nevertheless true, there is a sense in which it is a cosmic conspiracy that the world looks just (...) as if there are absolute quantities: the comparative quantities satisfy certain relations that only absolutism can explain. I show that such cosmic conspiracies are a pervasive feature of comparativist theories. The argument is structurally similar to the well-known No Miracles Argument for scientific realism. Just as anti-realism cannot explain the empirical adequacy of our theories in general, so comparativism cannot explain the empirical adequacy of absolutist theories in particular. (shrink)

Physics presents us with a symphony of natural constants: G, h, c, etc. Up to this point, constants have received comparatively little philosophical attention. In this paper I provide an account of dimensionful constants, in particular the gravitational constant. I propose that they represent inter-quantity structure in the form of relations between quantities with different dimensions. I use this account of G to settle a debate over whether mass scalings are symmetries of Newtonian Gravitation. I argue that they are not, (...) but only if we interpret mass anti-quidditistically. This is analogous to anti-haecceitism in the presence of spacetime symmetries. (shrink)

Early modern foundations for mechanics came in two kinds, nomic and material. I examine here the dynamical laws and pictures of matter given respectively by Newton, Leibniz, and Kant. I argue that they fall short of their foundational task, viz. to represent enough kinematic behavior; or at least to explain it. In effect, for the true foundations of classical mechanics we must look beyond Newton, Leibniz, and Kant.

This book argues that the Enlightenment was a golden age for the philosophy of body, and for efforts to integrate coherently a philosophical concept of body with a mathematized theory of mechanics. Thereby, it articulates a new framing for the history of 18th-century philosophy and science. It explains why, more than a century after Newton, physics broke away from philosophy to become an autonomous domain. And, it casts fresh light on the structure and foundations of classical mechanics. Among the figures (...) studied are Malebranche, Leibniz, Du Châtelet, Boscovich, and Kant, alongside d’Alembert, Euler, Lagrange, Laplace and Cauchy. (shrink)

Newton’s First Law of Motion is typically understood to govern only the motion of force-free bodies. This paper argues on textual and conceptual grounds that it is in fact a stronger, more general principle. The First Law limits the extent to which any body can change its state of motion –– even if that body is subject to impressed forces. The misunderstanding can be traced back to an error in the first English translation of Newton’s Principia, which was published a (...) few years after Newton’s death. (shrink)

This is an essay review of Jill North’s book Physics, Structure, and Reality. It focuses on two of the main topics of the book. The first is North’s idea that we can use coordinates as a window into the structure that a theory posits; the second is North’s argument for the inequivalence of Lagrangian and Newtonian mechanics.

The concept of inertial frame of reference in classical physics and special theory of relativity is analysed. It has been shown that this fundamental concept of physics is not clear enough. A definition of inertial frame of reference is proposed which expresses its key inherent property. The definition is operational and powerful. Many other properties of inertial frames follow from the definition, or it makes them plausible. In particular, the definition shows why physical laws obey space and time symmetries and (...) the principle of relativity, it resolves the problem of clock synchronization and the role of light in it, as well as the problem of the geometry of inertial frames. (shrink)

Derived measurements involve problems of coordination. Conducting them often requires detailed theoretical assumptions about their target, while such assumptions can lack sources of evidence that are independent from these very measurements. In this paper, I defend two claims about problems of coordination. I motivate both by a novel case study on a central measurement problem in the history of physical geodesy: the determination of the earth's ellipticity. First, I argue that the severity of problems of coordination varies according to scientists' (...) predictive and experimental control over perturbations of the measurement process. Second, I identify a methodology by which scientists can solve hard problems of coordination and gradually increase their predictive control over perturbations. I dub this methodology ‘operational pluralism’ since it is driven by the introduction of alternative measurement operations that involve different physical indicators. (shrink)

Candidates for fundamental physical laws rarely, if ever, employ higher than second time derivatives. Easwaran sketches an enticing story that purports to explain away this puzzling fact and thereby provides indirect evidence for a particular set of metaphysical theses used in the explanation. I object to both the scope and coherence of Easwaran's account, before going on to defend an alternative, more metaphysically deflationary explanation: in interacting Lagrangian field theories, it is either impossible or very hard to incorporate higher than (...) second time derivatives without rendering the vacuum state unstable. The so-called Ostrogradski instability represents a powerful constraint on the construction of new field theories and supplies a novel, largely overlooked example of non-causal explanation in physics. (shrink)

One of the foremost goals of research in physics is to find the most basic and universal theories that describe our universe. Many theories assume the presence of absolute space and time in which the physical objects are located and physical processes take place. However, it is more fundamental to understand time as relative to the motion of another object, e.g., the number of swings of a pendulum, and the position of an object primarily relative to other objects. This paper (...) aims to explain how using the principle of relationalism, classical mechanics can be formulated on a most elementary space, which is freed from absolute entities: shape space. In shape space, only the relative orientation and length of subsystems are taken into account. A sufficient requirement for the validity of the principle of relationalism is that by changing a system’s scale variable, all the theory’s parameters that depend on the length, get changed accordingly. In particular, a direct implementation of the principle of relationalism introduces a proper transformation of the coupling constants of the interaction potentials in classical physics. This change leads consequently to a transformation in Planck’s measuring units, which enables us to derive a metric on shape space in a unique way. In order to find out the classical equations of motion on shape space, the method of “symplectic reduction of Hamiltonian systems” is extended to include scale transformations. In particular, we will give the derivation of the reduced Hamiltonian and symplectic form on shape space, and in this way, the reduction of a classical system with respect to the entire similarity group is achieved. (shrink)

Wigner’s quantum-mechanical classification of particle-types in terms of irreducible representations of the Poincaré group has a classical analogue, which we extend in this paper. We study the compactness properties of the resulting phase spaces at fixed energy, and show that in order for a classical massless particle to be physically sensible, its phase space must feature a classical-particle counterpart of electromagnetic gauge invariance. By examining the connection between massless and massive particles in the massless limit, we also derive a classical-particle (...) version of the Higgs mechanism. (shrink)

Some popular views of Ernst Mach cast him as a philosopher-scientist averse to imaginative practices in science. The aim of this analysis is to address the question of whether or not imagination is compatible with Machian philosophy of science. I conclude that imagination is not only compatible but essential to realizing the aim of science in Mach’s biologico-economical view. I raise the possible objection that my conclusion is undermined by Mach’s criticism of Isaac Newton’s famous “bucket experiment.” I conclude that (...) Mach’s issue lies not with thought experimentation, tout court, but with the improper use of thought experimentation as it relates to the aim of the biologico-economical development of science. (shrink)

Jill North offers answers to questions at the heart of the project of interpreting physics. How do we figure out the nature of the world from a mathematically formulated theory? What do we infer about the world when a physical theory can be mathematically formulated in different ways? The notion of structure is crucial to North's answers.

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)

While it is well known that Plutarch’s De facie in orbe lunae was a major source of inspiration for Galileo’s Sidereus nuncius, its influence on his Dialogo sopra i due massimi sistemi del mondo, and especially on his views on gravity, has not been sufficiently explored. This essay offers the first systematic comparison of Plutarch’s and Galileo’s accounts of gravity by focusing on four themes: the thought experiment of a stone falling in a tunnel passing through the center of the (...) Earth; the account of gravity as a tendency to unite with the whole; the view that the Moon is a separate center of attraction; and the impossibility of attraction by an incorporeal point. The essay analyzes the role that these themes play in De facie and in the Dialogo, trying to understand how Galileo appropriated, reworked, and expanded on Plutarch’s views. (shrink)

According to the principle of special relativity, the laws of nature are the same for systems at rest and for systems in uniform and rectilinear motion: for the formulation of the laws of nature, the body C and the body C´, which, relative to the former, is in uniform and rectilinear motion, are equivalent. Galileo, in the Dialogue on the Two Greatest Systems of the World, developed the following argument in favor of such a principle: two bodies C and C´, (...) which are in uniform and rectilinear motion in relation to a third body C´´, with the same direction and speed, are at rest in relation to one another; therefore, what is applicable to rest, is applicable to uniform and rectilinear motion. Einstein, in On the Influence of Gravity in the Propagation of Light, generalizes the principle of relativity: all reference bodies C, C´, etc., are equivalent for the formulation of the laws of nature, whatever their state of motion is. The argument is analogous to that of Galileo: two bodies in free fall are at rest in relation to each other; therefore, what is applicable to rest, is applicable to constant acceleration. I argue that those arguments are invalid: to say that rest is shared motion does not mean that rest is, simply, movement. Therefore, one can only conclude that the laws of nature are the same for systems at rest and for systems with shared motion. (shrink)

In his recent book Bananaworld. Quantum mechanics for primates, Jeff Bub revives and provides a mature version of his influential information-theoretic interpretation of Quantum Theory (QT). In this paper, I test Bub’s conjecture that QT should be interpreted as a theory about information, by examining whether his information-theoretic interpretation has the resources to explain (or explain away) quantum conundrums. The discussion of Bub’s theses will also serve to investigate, more in general, whether other approaches succeed in defending the claim that (...) QT is about quantum information. First of all, I argue that Bub’s interpretation of QT as a principle theory fails to fully explain quantum non-locality. Secondly, I argue that a constructive interpretation, where the quantum state is interpreted ontically as information, also fails at providing a full explanation of quantum correlations. Finally, while epistemic interpretations might succeed in this respect, I argue that such a success comes at the price of rejecting some in between the most basic scientific standards of physical theories. (shrink)

The notions of conservation and relativity lie at the heart of classical mechanics, and were critical to its early development. However, in Newton’s theory of mechanics, these symmetry principles were eclipsed by domain-specific laws. In view of the importance of symmetry principles in elucidating the structure of physical theories, it is natural to ask to what extent conservation and relativity determine the structure of mechanics. In this paper, we address this question by deriving classical mechanics—both nonrelativistic and relativistic—using relativity and (...) conservation as the primary guiding principles. The derivation proceeds in three distinct steps. First, conservation and relativity are used to derive the asymptotically conserved quantities of motion. Second, in order that energy and momentum be continuously conserved, the mechanical system is embedded in a larger energetic framework containing a massless component that is capable of bearing energy. Imposition of conservation and relativity then results, in the nonrelativistic case, in the conservation of mass and in the frame-invariance of massless energy; and, in the relativistic case, in the rules for transforming massless energy and momentum between frames. Third, a force framework for handling continuously interacting particles is established, wherein Newton’s second law is derived on the basis of relativity and a staccato model of motion-change. Finally, in light of the derivation, we elucidate the structure of mechanics by classifying the principles and assumptions that have been employed according to their explanatory role, distinguishing between symmetry principles and other types of principles that are needed to build up the theoretical edifice. (shrink)

The notions of conservation and relativity lie at the heart of classical mechanics, and were critical to its early development. However, in Newton’s theory of mechanics, these symmetry principles were eclipsed by domain-specific laws. In view of the importance of symmetry principles in elucidating the structure of physical theories, it is natural to ask to what extent conservation and relativity determine the structure of mechanics. In this paper, we address this question by deriving classical mechanics—both nonrelativistic and relativistic—using relativity and (...) conservation as the primary guiding principles. The derivation proceeds in three distinct steps. First, conservation and relativity are used to derive the asymptotically conserved quantities of motion. Second, in order that energy and momentum be continuously conserved, the mechanical system is embedded in a larger energetic framework containing a massless component that is capable of bearing energy. Imposition of conservation and relativity then results, in the nonrelativistic case, in the conservation of mass and in the frame-invariance of massless energy; and, in the relativistic case, in the rules for transforming massless energy and momentum between frames. Third, a force framework for handling continuously interacting particles is established, wherein Newton’s second law is derived on the basis of relativity and a staccato model of motion-change. Finally, in light of the derivation, we elucidate the structure of mechanics by classifying the principles and assumptions that have been employed according to their explanatory role, distinguishing between symmetry principles and other types of principles that are needed to build up the theoretical edifice. (shrink)

In 1907 Einstein had the insight that bodies in free fall do not “feel” their own weight. This has been formalized in what is called “the principle of equivalence.” The principle motivated a critical analysis of the Newtonian and special-relativistic concepts of inertia, and it was indispensable to Einstein’s development of his theory of gravitation. A great deal has been written about the principle. Nearly all of this work has focused on the content of the principle and whether it has (...) any content in Einsteinian gravitation, but more remains to be said about its methodological role in the development of the theory. I argue that the principle should be understood as a kind of foundational principle known as a criterion of identity. This work extends and substantiates a recent account of the notion of a criterion of identity by William Demopoulos. Demopoulos argues that the notion can be employed more widely than in the foundations of arithmetic and that we see this in the development of physical theories, in particular space–time theories. This new account forms the basis of a general framework for applying a number of mathematical theories and for distinguishing between applied mathematical theories that are and are not empirically constrained. (shrink)

Leibniz’s argument against Descartes’s conservation principle in the Brevis demonstratio (1686) has traditionally been read as passing from the premise that motive force must be conserved to the conclusion that motive force is not identical to quantity of motion and, finally, that quantity of motion is not conserved. In a lesser-known draft of the same year, Christiaan Huygens claimed that Descartes had in fact never held the view that Leibniz was attacking. Huygens is right as far as the traditional reading (...) is concerned. However, if the Brevis demonstratio is seen, as it should be, in the context of Leibniz’s attempt to ground mechanics in the foundational metaphysical axiom of the equivalence of full cause and entire effect, then Huygens’s objections can be answered. Leibniz may have committed Descartes to the foundational axiom because of the Traité de la méchanique, which was available to Leibniz at that time. Leibniz had used the equivalence of full cause and entire effect both in discovering the conservation of vis viva earlier and in various arguments for it later. Thus, the Brevis demonstratio should be viewed with Leibniz’s broader foundational mission in mind. (shrink)

The contemporary scientific and technological progress builds on the accomplishments of classical mechanics from the 19th century when the so-called ‘European scientific method and values’ were accepted practically by the whole educated world. Most scientific results and conclusions were reached based on the causal ontological approach proposed in principle already by Plato’s Socrates and developed further by Aristotle. Despite the late-modern paradigm shift in science, the topicality of the ontological approach proposed by Aristotle remains. On the other hand, 19th and (...) 20th century philosophers, mainly positivists such as Mach and Avenarius but also Schlick and Carnap, attempted to change this approach to unify scientific knowledge in accordance with an ideological, i.e. positivist outlook on reality. The authors place a special emphasis on the contribution of Rudolf Carnap and his interaction with Martin Heidegger. Three very different theories are applied to physical reality in the present: classical mechanics in the standard macroscopic realm, Copenhagen quantum mechanics in the microscopic realm, and special theory of reality in both realms in the case of systems consisting of objects having higher velocity values. Any explanation or description of transitions between different realms and theories had not been provided until now. Our paper describes the corresponding evolution in the modern period and identifies the underlying false philosophical assumptions and statements existing in today’s scientific systems. We will then demonstrate that one common theory for all realms of reality may exist; one that will be based fully on Hamilton equations. Only time change of particle impulse is to be determined by a corresponding force. All necessary characteristics of physical reality may be derived in such a case. Direct correlations of such physical approach to philosophy will be drawn. (shrink)

The principle of energy conservation is widely taken to be a se- rious difficulty for interactionist dualism (whether property or sub- stance). Interactionists often have therefore tried to make it satisfy energy conservation. This paper examines several such attempts, especially including E. J. Lowe’s varying constants proposal, show- ing how they all miss their goal due to lack of engagement with the physico-mathematical roots of energy conservation physics: the first Noether theorem (that symmetries imply conservation laws), its converse (that conservation (...) laws imply symmetries), and the locality of continuum/field physics. Thus the “conditionality re- sponse”, which sees conservation as (bi)conditional upon symme- tries and simply accepts energy non-conservation as an aspect of interactionist dualism, is seen to be, perhaps surprisingly, the one most in accord with contemporary physics (apart from quantum mechanics) by not conflicting with mathematical theorems basic to physics. A decent objection to interactionism should be a posteri- ori, based on empirically studying the brain. (shrink)

Wilson [Dialectica 63:525–554, 2009], Moore [Int Stud Philos Sci 26:359–380, 2012], and Massin [Br J Philos Sci 68:805–846, 2017] identify an overdetermination problem arising from the principle of composition in Newtonian physics. I argue that the principle of composition is a red herring: what’s really at issue are contrasting metaphysical views about how to interpret the science. One of these views—that real forces are to be tied to physical interactions like pushes and pulls—is a superior guide to real forces than (...) the alternative, which demands that real forces are tied to “realized” accelerations. Not only is the former view employed in the actual construction of Newtonian models, the latter is both unmotivated and inconsistent with the foundations and testing of the science. (shrink)

This volume offers a broad, philosophical discussion on mechanical explanations. Coverage ranges from historical approaches and general questions to physics and higher-level sciences. The contributors also consider the topics of complexity, emergence, and reduction. -/- Mechanistic explanations detail how certain properties of a whole stem from the causal activities of its parts. This kind of explanation is in particular employed in explanatory models of the behavior of complex systems. Often used in biology and neuroscience, mechanistic explanation models have been often (...) overlooked in the philosophy of physics. The authors correct this surprising neglect. They trace these models back to their origins in physics. The papers present a comprehensive historical, methodological, and problem-oriented investigation. The contributors also investigate the conditions for using models of mechanistic explanations in physics. The last papers make the bridge from physics to economics, the theory of complex systems and computer science . This book will appeal to graduate students and researchers with an interest in the philosophy of science, scientific explanation, complex systems, models of explanation in physics higher level sciences, and causal mechanisms in science. (shrink)

In this note, I apply Norton’s (Philos Sci 79(2):207–232, 2012) distinction between idealizations and approximations to argue that the epistemic and inferential advantages often taken to accrue to minimal models (Batterman in Br J Philos Sci 53:21–38, 2002) could apply equally to approximations, including “infinite” ones for which there is no consistent model. This shows that the strategy of capturing essential features through minimality extends beyond models, even though the techniques for justifying this extended strategy remain similar. As an application (...) I consider the justification and advantages of the approximation of a inertial reference frame in Norton’s dome scenario (Philos Sci 75(5):786–798, 2008), thereby answering a question raised by Laraudogoitia (Synthese 190(14):2925–2941, 2013). (shrink)

It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can’t contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is “random numbers”, as their series of bits are truly random. I propose an alternative classical mechanics, which is (...) empirically equivalent to classical mechanics, but uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic. Most physicists straightforwardly supplement classical theory with real numbers to which they attribute physical existence, while most physicists reject Bohmian mechanics as supplemented quantum theory, arguing that Bohmian positions have no physical reality. (shrink)

The concept of mechanistic philosophy dates back to the beginning of the early modern period. Among the commonalities that some of the conceptions of the main contemporary representatives share with those of the leading early modern exponents is their ontological classification: as regards their basic concepts, both contemporary and early modern versions of mechanism can be divided into monist and dualist types. Christiaan Huygens’ early modern mechanistic explanation of non- material forces and Stuart S. Glennan’s contemporary conception of mechanism will (...) serve as examples of monism. As examples of dualism, I will discuss Isaac Newton’s early modern mechanistic philosophy of nature and the contemporary conception of mechanism proposed by Peter Machamer, Lindley Darden, and Carl F. Craver. With the ontological commonalities are associated further characteristic features of the respective types that concern, among other things, the respective understandings of fundamental theories and evaluations of scientific practice. The ontological continuity Of the types does not play any role in contemporary discussions of the history of mechanistic philosophy. On my assessment the distinction between monism and dualism remains an unsolved problem and its persistence is an indication that this distinction is a fundamental one. (shrink)

In this paper I analyze the virtual debate between Locke and Leibniz on solidity as proposed in Leibniz’s chapter on solidity in his New Essays on Human Understanding. I first track the oddities of the dialogue presented in the New Essays’ chapter on solidity. In this virtual dialogue, Leibniz’s representative often digresses and sometimes overlooks or misrepresents some of Locke’s most important insights. I then argue that these oddities reflect Leibniz’s sentiment that a productive controversy on this issue cannot be (...) conducted due to his substantial differences with Locke regarding solidity and the nature of matter. These differences are at most indirectly implied in passing in Leibniz’s chapter on solidity and to see them one has to consider other texts presenting Leibniz’s theory of matter. (shrink)

I explore how the nature, scope, and limits of the knowledge obtained in orbital dynamics has changed in recent years. Innovations in the design of spacecraft trajectories, as well as in astronomy, have led to new logics of theory-testing—that is, new research methodologies—in orbital dynamics. These methodologies—which combine resonance overlap theories, numerical experiments, and the implementation of space missions—were developed in response to the discovery of chaotic dynamical systems in our solar system. In the past few decades, they have replaced (...) the methodology that dominated orbital research in the centuries following Newton's Principia. As a result, the kind of knowledge achieved by orbital research has changed: we can know how orbiting bodies in chaotic systems behave, but only over sufficiently short time scales; and we can reliably measure those temporal limitations, using Lyapunov time. (shrink)

Newton’s Regulae philosophandi—the rules for reasoning in natural philosophy—are maxims of causal reasoning and induction. This essay reviews their significance for Newton’s method of inquiry, as well as their application to particular propositions within the Principia. Two main claims emerge. First, the rules are not only interrelated, they defend various facets of the same core idea: that nature is simple and orderly by divine decree, and that, consequently, human beings can be justified in inferring universal causes from limited phenomena, if (...) only fallibly. Second, the rules make substantive ontological assumptions on which Newton’s argument in the Principia relies. (shrink)

In 1908, three years after Einstein first published his special theory of relativity, the mathematician Hermann Minkowski introduced his four-dimensional “spacetime” interpretation of the theory. Einstein initially dismissed Minkowski’s theory, remarking that “since the mathematicians have invaded the theory of relativity I do not understand it myself anymore.” Yet Minkowski’s theory soon found wide acceptance among physicists, including eventually Einstein himself, whose conversion to Minkowski’s way of thinking was engendered by the realization that he could profitably employ it for the (...) formulation of his new theory of gravity. The validity of Minkowski’s mathematical “merging” of space and time has rarely been questioned by either physicists or philosophers since Einstein incorporated it into his theory of gravity. Physicists often employ Minkowski spacetime with little regard to the whether it provides a true account of the physical world as opposed to a useful mathematical tool in the theory of relativity. Philosophers sometimes treat the philosophy of space and time as if it were a mere appendix to Minkowski’s theory. In this critical study, Joseph Cosgrove subjects the concept of spacetime to a comprehensive examination and concludes that Einstein’s initial assessment of Minkowksi was essentially correct. (shrink)

The impetus theory of motion states that to be in motion is to have a non-zero velocity. The at-at theory of motion states that to be in motion is to be at different places at different times, which in classical physics is naturally understood as the reduction of velocities to position developments. I first defend the at-at theory against the criticism raised by Arntzenius that it renders determinism impossible. I then develop a novel impetus theory of motion that reduces positions (...) to velocity developments. As this impetus theory of motion is by construction a mirror image of the at-at theory of motion, I claim that the two theories of motion are in fact epistemically on par—despite the unfamiliar metaphysical picture of the world furnished by the impetus version. (shrink)

I examine two claims that arise in Brown’s account of inertial motion. Brown claims there is something objectionable about the way in which the motions of free particles in Newtonian theory and special relativity are coordinated. Brown also claims that since a geodesic principle can be derived in Einsteinian gravitation, the objectionable feature is explained away. I argue that there is nothing objectionable about inertia and that while the theorems that motivate Brown’s second claim can be said to figure in (...) a deductive-nomological explanation, their main contribution lies in their explication rather than their explanation of inertial motion. (shrink)

Previzualizare carte -/- O privire de ansamblu asupra mecanicii clasice, care intenționează să ofere o acoperire a principiilor și tehnicilor fundamentale, un domeniu vechi dar care se află la baza întregii fizicii, și care în ultimii ani a cunoscut o dezvoltare rapidă. Se subliniază principiile de bază fenomenologice, fără a insista pe un formalism excesiv. Cartea începe cu o introducere în mecanică cu conceptele de bază, urmată de cele trei legi de mișcare ale lui Newton (inerția, forța, și acțiunea și (...) reacțiunea), mecanica unidimensională (liniară - viteza, accelerația, căderea liberă, masa inerțială și gravitaţională, forțe și interacțiuni, noțiuni de statică și dinamică, impulsul, coliziuni), energia (lucrul mecanic, puterea, energia potențială și cinetică, surse de energie) și un capitol special pentru mecanica mașinilor. Mișcarea de rotație este detaliată prin mișcarea circulară (momentul unghiular, forța centripetă, forța centrifugă, gravitația artificială). Sunt dedicate capitole speciale gravitației (legea universală a gravitației, câmpul gravitațional, teoria gravitației a lui Tesla și teoriile moderne ale gravitației) și mișcarea proiectilelor și sateliților (balistica - proiectile, sateliți artificiali, orbite circulare și eliptice). O carte pentru studiul personal, concisă și ușor de citit, care clarifică aceste teorii și profunzimea mecanicii newtoniene, cel mai important domeniu al fizicii pe care se bazează toate celelalte abordări teoretice și explicații ale fenomenelor fizice. -/- CUPRINS: -/- Mecanica - Istoria - Concepte de bază - - Poziția și derivații săi - - Viteza vectorială și scalară - - Accelerația - - Cadre de referință - Dincolo de legile lui Newton Prima lege de mișcare a lui Newton - Inerția - Aristotel despre mișcare - - Aristotel - Sistemul heliocentric - Galileo și turnul înclinat - - Galileo Galilei - - Experimentele lui Galileo Galilei cu planul înclinat - - - Plan înclinat de la Muzeul Galileo - Prima lege de mișcare a lui Newton - - Prima lege a lui Newton - Forța netă - - Forța totală - - Regula paralelogramului pentru însumarea forțelor - - Translație și rotire datorită unei forțe - - - Forțe punctuale - - - Corpuri rigide - - Forța rezultantă - - Folosire Mișcarea liniară - Mișcarea este relativă (Invarianța galileiană) - Dimensiuni - - Timpul - - - Măsurarea timpului - - - Timpul în inginerie şi fizica aplicată - - - Timpul în filosofie şi fizica teoretică - - Spaţiu-timp - - - Cadrul de referinţă - - - Câteva fapte generale despre spaţiu-timp - - - Este spaţiul-timp cuantificat? - Viteza - - Viteza instantanee - - Viteza medie - - Viteza vectorială - - - Viteza vectorială constantă vs. accelerație - - - Distincția dintre viteză și viteza vectorială - - - Viteza vectorială medie - - Viteza vectorială variabilă - - - Viteza vectorială instantanee - - - Relația cu accelerația - - - Accelerație constantă - - - Cantități care depind de viteza vectorială - Accelerația - - Definiție și proprietăți - - Accelerația medie - - Accelerația instantanee - - Unități - - Alte forme - Căderea liberă - - Exemple - - Câmpul gravitațional uniform fără rezistență la aer - - Ecuațiile căderii libere A doua lege de mișcare a lui Newton - Forța - Forța - Frecarea - - Frecarea uscată - - - Legi ale frecării uscate - - Reducerea frecării - Masa și greutatea - - Prezentare generală - - Masa se opune accelerației (Masa și inerția) - - - Masa inerțială - - - Masa gravitaţională - - - Echivalenţa maselor inerţială şi gravitaţională - - - Consecinţele relativităţii - A doua lege de mișcare a lui Newton - - Variația de impuls - - - Sisteme cu masă variabilă A treia lege de mișcare a lui Newton - Acțiunea și reacțiunea - Forțe și interacțiuni - - Descrieri - - Interacțiunea - A treia lege de mișcare a lui Newton - Acțiunea și reacțiunea - - Interacțiunea cu solul - - Forțele gravitaționale - - Masa sprijinită - - Masa pe un arc - - Interpretări cauzale greșite - - "Egal și opus" - - Forța centripetă și forța centrifugă - Sumarul legilor de mișcare ale lui Newton - - Prezentare generală - Statica - - Vectori - - Forţa - - - Momentul forţei - - Ecuaţiile de echilibru - - Momentul de inerţie - - Solide - - Fluide - Dinamica - - Principii - - Dinamica liniară şi de rotaţie Impulsul - Istoria conceptului - Impulsul newtonian - - Impulsul unei particule - - Mai multe particule - - Relația cu forța - - Dependența de cadrul de referință - Variația de impuls - Conservarea impulsului - Coliziuni - - Prezentare generală - - Tipuri de coliziuni - - Coliziunea inelastică - - - Formula - - - Coliziune perfect inelastică - - - Coliziuni parțial inelastice Energia - Istorie - Lucru mecanic - - Calculul lucrului mecanic - Puterea - - Unități - - Ecuații pentru putere - - Puterea medie - Energia mecanică - - Ecuații - - Conservarea energiei mecanice - - - Pendul oscilant - - - Ireversibilitatea - - - Sateliți - Energia potențială - - Prezentare generală - - Energia potențială gravitațională - - Energia potențială chimică - - Energia potențială electrică - - Energia potențială nucleară - Energia cinetică - - Prezentare generală - - Energia cinetică newtoniană - - - Energia cinetică a corpurilor rigide - - - Energia cinetică a sistemelor - - - Rotația în sisteme - Principiul lucru mecanic-energie - - Lucrul mecanic și energia potențială - - - Dependența de cale - - - Independența căii - - - Principiul lucru mecanic-energie - Conservarea energiei - - Istorie - - Echivalentul mecanic al căldurii - - Teorema lui Noether - Mașini - - Sisteme mecanice - - Surse de putere - - Mecanica - - - Dinamica mașinilor - - - Cinematica mașinilor - Eficiența conversiei energiei - - Prezentare generală - - Valorile și eficiența încălzirii cu combustibil - Surse de energie - - Clasificarea resurselor - - Combustibili fosili - - Nuclear - - - Fisiune - - Surse regenerabile - - - Hidroelectricitatea - - - Vânt - - - Solar - - - Biocombustibili - - - Geotermal - - - Oceanic - - Transmisie - - Depozitare Mișcarea de rotație - Mișcarea circulară - - Mișcarea circulară uniformă - - - Formule - - Mișcarea circulară neuniformă - Inerția rotațională (Momentul de inerție) - - Introducere - - Definiție - Cuplul (Momentul forței) - - Definirea terminologiei - - Definiție - - Unități - Centrul de masă și centrul de greutate - - Istorie - - Definiție - - Un sistem de particule - - Centrul de greutate - - Localizarea centrului de masă - - - În două dimensiuni - - - În trei dimensiuni - - Aplicații - - - Automobile - - - Aeronautică - - - Astronomie - - - Mișcarea corpurilor umane - Echilibrul mecanic - Stabilitatea - - Stabilitatea - - - Test de stabilitate a energiei potențiale - - - Derivata de ordinul doi < 0 - - - Derivata de ordinul doi > 0 - - - Derivata de ordinul doi = 0 sau nu există - - - Sistem static nedeterminat - Forța centripetă - - Formula - - Surse - Forța centrifugă - - Introducere - - Exemple - - - Vehicul în o curbă - - - Mărgea pe un șirag - - - Pământ - - - - Greutatea unui obiect la poli și la ecuator - - - - Căile ferate la ecuator - - Forța centrifugă în cadru de referință în rotație - - - Forțe fictive - - - Forța centrifugă - - - - Derivatele timpului într-un cadru rotativ - - - - Accelerația - - - - Forța - Gravitația artificială - - Centrifugal - - - Mecanism - - - Zborul în spațiu cu echipaj uman - - - Centrifuge - Momentul unghiular - - Momentul scalar – unghiular în două dimensiuni - - Discuţie - - Momentul unghiular (definiție modernă) - - Conservarea momentului unghiular Gravitația - Istoria teoriei gravitației - - Antichitate - - Era modernă - - - Teoria lui Newton despre gravitație - - - Explicații mecanice ale gravitației - Legea universală a gravitației - - Istorie - - Forma modernă - Constanta gravitațională universală, G - Legea inversului pătratului în gravitație - - Formula - - Justificare - - Gravitația - Greutatea și imponderabilitatea - - Greutatea în mecanica newtoniană - - Istorie - - - Newton - - - Relativitatea - Maree - - Caracteristici - - Constituienți - - Istoria fizicii mareelor - - Forțe - - Ecuațiile de maree ale lui Laplace - - Mareele oceanelor - - - Amplitudine și ciclu - - - Batimetrie - - Mareea Pământului - - - Forța fluxului - - - Mareea corporală - - - Ceilalți contribuabili ai mareelor Pământului - - Mareea atmosferei Pământului - - - Caracteristici generale - - Mareele lunare - - - Componenta principală lunară semi-diurnă - Câmpul gravitațional - - Mecanica clasică - Gravitația în interiorul unei planete (Teorema carcasei) - - Dovezile lui Newton - - - Forța pe un punct în interiorul unei sfere goale - - Modelul preliminar de referință al pământului (PREM) - Tesla şi Teoria dinamică a gravitaţiei - Teoria gravitației lui Einstein - - Gravitația și accelerația - - De la accelerație la geometrie - - Găuri negre - - - Istorie - - - Proprietăți și structură - - - Formarea și evoluția - - - Dovezi observaționale - Gravitația în Univers - - Gravitația și astronomia - - Radiații gravitaționale - - Viteza gravitației - Anti-gravitaţia - - Efecte convenţionale care imită efectele anti-gravitaţiei - - Soluţii ipotetice - - - Scuturi gravitaţionale - - - Cercetări în relativitatea generală în anii 1950 - - - A cincea forţă - - - "Unităţi distorsionate" în relativitatea generală - - - Breakthrough Propulsion Physics Program - - Încercări experimentale şi comerciale - - - Dispozitive giroscopice - - - Gravitatorul lui Thomas Townsend Brown - - - Cuplarea gravitoelectrică - - Premiul Göde Mișcarea proiectilelor și sateliților (Balistica) - Istorie - Proiectile - Sateliți - Mișcarea proiectilelor - - Proiectile lansate orizontal - - Proiectile lansate sub un anumit unghi - - - Intervalul unui proiectil - - - Mișcarea proiectilului - - - - Viteza inițială - - - Valori cinematice - - - - Accelerația - - - - Viteza - - - - Deplasarea - - - Timpul de zbor sau timpul total al întregii deplasări - - - Înălțimea maximă a proiectilului - - - Relația dintre deplasarea orizontală și înălțimea maximă - - - Distanța maximă a proiectilului - - - Aplicarea teoremei lucrului mecanic - - - Unghiul de acoperire - - - Unghiul θ necesar să se atingă coordonatele (x, y) - Sateliți artificiali - - Zborul orbital - - Lansarea pe orbită - - Stabilitate - - Orbite - - Manevre orbitale - - Deorbitarea și reintrarea - Orbite circulare ale sateliților - - Accelerația circulară - - Viteza vectorială - - Ecuația mișcării - - Viteza unghiulară și perioada orbitală - - Energia - - Delta-v pentru a atinge o orbită circulară - Orbite eliptice - - Viteza vectorială - - Perioada orbitală - - Energia - - - Energia în termeni de axa semi-majoră - - - Derivare - - Unghiul căii de zbor - - Parametrii orbitali - - Sistemul solar - - Traiectorie eliptică radială - Legile lui Kepler - - Comparație cu Copernic - - Accelerația planetară - Energia sateliților - - Energia orbitală specifică - - Ecuația vis-viva - - Energia pentru orbite eliptice - Viteza de scăpare - - Prezentare generală - - Traiectoria Referințe Despre autor - Nicolae Sfetcu - - De același autor - - Contact Editura - MultiMedia Publishing. (shrink)

Interpretarea textelor lui Isaac Newton a suscitat numeroase controverse, până în zilele noastre. Una din cele mai aprinse dezbateri este legată de acțiunea între două corpuri aflate la distanță unul de celălalt (atracția gravitațională), și în ce măsură Newton a implicat pe Dumnezeu în acest caz. Practic, majoritatea lucrărilor discută patru tipuri de atracții gravitaționale în cazul corpurilor aflate la distanță: acțiunea la distanță directă ca proprietate intrinsecă a corpurilor în sens epicurian; acțiunea la distanță directă mediată divin, de Dumnezeu; (...) acțiunea la distanță mediată printr-un eter material; sau acțiunea la distanță mediată printr-un eter imaterial. Scopul acestei lucrări este argumentarea opiniei proprii conform căreia Newton a refuzat categoric tipurile de acțiune directă ca proprietate intrinsecă a corpurilor, și acțiunea la distanță mediată printr-un eter material. În ceea ce privește celelalte două tipuri de acțiune, directă prin intervenție divină și mediată printr-un mediu imaterial, Newton a declarat în mai multe rânduri că nu cunoaște cauza exactă a gravitației, dar în amândouă cazuri a implicat pe Dumnezeu, în mod direct în primul caz și ca fiind cauza primară (mediul/eterul fiind cauza secundară) în acțiunea mediată imaterial. Însă, întrucât o recunoaștere a acțiunii directe la distanță ar fi putut da oarecare credit celor care considerau că gravitația poate fi esențială pentru materie, și în consecință ateismului, Newton nu a recunoscut niciodată în mod deschis acceptarea posibilității unei astfel de idei. Spre finele vieții, Newton a înclinat mai mult spre o acțiune la distanță mediată de un eter imaterial. -/- DOI: 10.58679/TW52523. (shrink)