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Three Payoffs of My Account

Marc Lange

in Laws and Lawmakers Science, Metaphysics, and the Laws of Nature

After examining several unsuccessful explanations of the laws' immutability, this chapter argues that the account (given in earlier chapters) in terms of stability explains nicely how a temporary law ... More

After examining several unsuccessful explanations of the laws' immutability, this chapter argues that the account (given in earlier chapters) in terms of stability explains nicely how a temporary law (for instance, a law that expires at a given moment) differs from an eternal but time-dependent law (a law that remains in force at all times, but treats different moments differently). This account explains why temporary laws are metaphysically impossible. In contrast, the laws' immutability is inserted “by hand” in David Lewis's and David Armstrong's accounts. Next, it is argued that meta-laws, such as symmetry principles, differ from regularities to which all laws governing sub-nomic facts just happen to conform. The account of lawhood in terms of stability extends naturally to cover meta-laws. Finally, it is shown that the laws' relation to objective chances falls naturally out of the account of lawhood in terms of stability, whereas Lewis must insert this relation by hand.Less

“There sweep great general principles which all the laws seem to follow”

Marc Lange

in Oxford Studies in Metaphysics volume 7

This chapter argues that science recognizes an important distinction: between conservation laws as constraints on the fundamental forces there could be, on the one hand, and conservation laws as ... More

This chapter argues that science recognizes an important distinction: between conservation laws as constraints on the fundamental forces there could be, on the one hand, and conservation laws as coincidences of the fundamental forces there happen to be, on the other hand. Whether they are constraints or coincidences would make an important difference to their role in scientific explanations. The distinction between constraints and coincidences applies to other laws besides the conservation laws; this chapter discusses examples from Hertz and Planck. The distinction between constraints and coincidences is ultimately elaborated in terms of the truth of various counterfactual conditionals. Dispositional essentialism (as advocated recently by Bird, Ellis, and Mumford) must portray all conservation laws as coincidences. It thus forecloses options that science has (with good reason) taken seriously ‐‐ which is a serious count against dispositional essentialism.Less

Concluding Remarks

Alexander Bird

in Nature's Metaphysics: Laws and Properties

This chapter reviews the central arguments of this book and charts the directions for future work on dispositional essentialism, identifying the need for an account of natural kinds and for responses ... More

This chapter reviews the central arguments of this book and charts the directions for future work on dispositional essentialism, identifying the need for an account of natural kinds and for responses to certain problems from physics, concerning fundamental constants, least-action principles, and conservation laws. Responses to these problems are sketched.Less

Nature Conservation in Legal Context

Christopher P. Rodgers

in The Law of Nature Conservation

This chapter introduces the principal themes of the work. It considers the scope and definition of ‘nature conservation law’, the different legal techniques used to promote the conservation of ... More

This chapter introduces the principal themes of the work. It considers the scope and definition of ‘nature conservation law’, the different legal techniques used to promote the conservation of natural habitats and species of rare or endangered bird plant and animal. It traces the historical development of legislation on the conservation of nature and the voluntary and partnership principles on which UK policy for the conservation of nature has been based since 1945. It considers the significance of different models of property rights and their importance in understanding how environmental regulation operates, and in particular how (acting through the medium of property rights) the law adjusts and modifies access to natural resources in order to pursue key public policy objectives for promoting biodiversity and conserving living natural resources.Less

“There Sweep Great General Principles Which All the Laws Seem to Follow”

Marc Lange

in Because Without Cause: Non-Causal Explanations in Science and Mathematics

This chapter concerns scientific explanations that appeal to symmetry principles and conservation laws (such as energy conservation and momentum conservation). It is argued that these laws (along ... More

This chapter concerns scientific explanations that appeal to symmetry principles and conservation laws (such as energy conservation and momentum conservation). It is argued that these laws (along with others, such as the principle of virtual work and Newton’s second law of motion) may transcend the hurly-burly of causal relations. They would then constitute constraints rather than coincidences and thus be able to figure in “explanations by constraint.” Examples of explanations by constraint proposed by Heinrich Hertz and J. Willard Gibbs are also given. An account is given of what it would be for a law of nature or for one of the symmetries of spacetime to qualify as a constraint. This account uses counterfactual conditionals to identify what it takes for a law of nature to possess a stronger variety of necessity than ordinary natural laws possess. Dispositional essentialist and manipulationist accounts of explanation cannot accommodate explanations by constraint; unfortunately, they must portray all conservation laws as coincidences.Less

Lagrangian and Hamiltonian mechanics

D. Violeau

in Fluid Mechanics and the SPH Method: Theory and Applications

This chapter details the basics of Lagrangian and Hamiltonian mechanics. From the basic principles of mechanics (Galilean invariance, least action principle), the chapter builds the fundamental ... More

This chapter details the basics of Lagrangian and Hamiltonian mechanics. From the basic principles of mechanics (Galilean invariance, least action principle), the chapter builds the fundamental equations of motion of a set of points named ‘particles’ (Lagrange and Hamilton equations), and introduces the conservation laws in connection with the symmetry of space–time. It also brings in the concept of internal energy for systems composed of several individual beings, and make the distinction between internal and external forces. Rigid body motion is rapidly treated for the needs of Chapters 5 and 6. Lastly, the concept of pressure is introduced.Less

Harmonic mappings between Riemannian manifolds

Paul Baird and John C. Wood

in Harmonic Morphisms Between Riemannian Manifolds

A harmonic morphism between arbitrary Riemannian manifolds is a type of harmonic map. This chapter is devoted to the description of those properties of harmonic maps, which are essential to the ... More

A harmonic morphism between arbitrary Riemannian manifolds is a type of harmonic map. This chapter is devoted to the description of those properties of harmonic maps, which are essential to the development. Harmonic maps are extremals of a natural energy integral; they can be characterized as maps whose tension field vanishes, where the tension field is a natural generalization of the Laplacian. The first three sections in this chapter give the necessary formalism, the basic definitions, examples, and properties of harmonic maps. In Section 3.4, a conservation law involving the stress-energy is given. Harmonic maps from surfaces have special properties and include (branched) minimal immersions, which are discussed in Section 3.5. The chapter ends with a treatment of the second variation.Less

Setting the stage

A. J. Leggett

in The Problems of Physics

This chapter traces the history of physics as we know it from its beginnings in the astronomy and mechanics of the 17th century, through the development of electromagnetism, optics, and mechanics in ... More

This chapter traces the history of physics as we know it from its beginnings in the astronomy and mechanics of the 17th century, through the development of electromagnetism, optics, and mechanics in the 18th, and the unification of optics with electromagnetism and thermodynamics with molecular theory in the 19th century, up to the two great revolutions of the early 20th century: the special theory of relativity, and quantum mechanics. It ends with a discussion of the relationship of physics to mathematics and philosophy, and of the nature of the fundamental assumptions about the world which underpin the subject.Less

THE CAUCHY PROBLEM FOR QUASILINEAR SYSTEMS

Sylvie Benzoni-Gavage and Denis Serre

in Multi-dimensional hyperbolic partial differential equations: First-order systems and applications

This chapter obtains local solutions for Hs -data when this space is contained in the differentiable functions. The proof proceeds from a contraction mapping principle. The ... More

This chapter obtains local solutions for Hs -data when this space is contained in the differentiable functions. The proof proceeds from a contraction mapping principle. The stability is obtained in Hs , thanks to the linear estimates of Chapter 2 and to Moser estimates, while the contraction is established in the L2 -norm. The Hs regularity is a little bit elaborate. Smooth solutions usually blow-up in finite time. The chapter recalls blow-up or continuation criteria. The analysis beyond blow-up requires the system to be given in the form of conservation laws. The chapter then recalls the notions of weak entropy solution, shock waves, and the Rankine-Hugoniot relations.Less

SYMMETRIES AND INVARIANCES

M. S. Sozzi

in Discrete Symmetries and CP Violation: From Experiment to Theory

This chapter reviews the general theory of transformations in quantum theory. Topics covered include symmetry and invariance, transformations and symmetries in quantum theory, symmetries and ... More

This chapter reviews the general theory of transformations in quantum theory. Topics covered include symmetry and invariance, transformations and symmetries in quantum theory, symmetries and conservation laws, discrete transformations and inversions, and symmetry violations. Suggested further reading and exercise problems are provided at the end of the chapter.Less

Determinism

Bas C. van Fraassen

in Quantum Mechanics: An Empiricist View

A sustained discussion of the relation between the concepts of determinism, symmetry, invariance, time, and conservation laws, in general terms.

Transport equations for the one-body density

Helmut Hofmann

in The Physics of Warm Nuclei: with Analogies to Mesoscopic Systems

This chapter begins by calculating the Wigner transform for the von Neumann equation for the one-body density operator. It shows how the Liouville equation follows in leading order in an expansion to ... More

This chapter begins by calculating the Wigner transform for the von Neumann equation for the one-body density operator. It shows how the Liouville equation follows in leading order in an expansion to ℏ. Properties of this expansion and of the resulting equation are discussed with respect to their physical and practical importance. Semi-classical approximations to the collision term are described and interpreted in terms of relevant transition rates. In Born approximation, equations of Boltzmann-Uehling-Uhlenbeck (BUU)- or Landau-Vlasov-type are obtained. The relevance of the conservation laws for particle number, energy, and momentum is discussed. For relaxation processes to equilibrium, self-energies are introduced and the relaxation-time approximation to the collision term is presented. The physical meaning of self-energies is discussed, together with the formula for the leading-order dependence of their imaginary part on energy, chemical potential, and temperature.Less

First-Generation Laws: Creating Use Interests in Natural Resources

Jan G. Laitos

in The Right of Nonuse

This chapter discusses how resource use initially dominated the creation of first-generation legal rights, including laws that were eventually adopted to curb resource use in order to conserve ... More

This chapter discusses how resource use initially dominated the creation of first-generation legal rights, including laws that were eventually adopted to curb resource use in order to conserve natural resources for future use. During the twentieth century, the world's total urban population grew 13-fold, and its industrial output increased roughly 40-fold. The world's population and its industrial base needed natural resources. These resources were extracted, developed, depleted, and otherwise used at an unprecedented rate. The resulting accelerated exploitation of natural resources began to exhaust, or make unsustainable, stock and renewable commodity resources. When humans realized that stock and even renewable resources necessary for twentieth-century human societies were being exhausted, with no easy substitutes available, so-called “conservation laws” were enacted, which restricted otherwise unlimited use in order to perpetrate future use. In other words, we sought to address the first consequence of overuse by adopting laws requiring some conservation of the resource base so that future use was not impaired.Less

The Annotated Manuscript

Hanoch Gutfreund and Jürgen Renn

in The Road to Relativity: The History and Meaning of Einstein's "The Foundation of General Relativity", Featuring the Original Manuscript of Einstein's Masterpiece

This section presents annotations of the manuscript of Albert Einstein's canonical 1916 paper on the general theory of relativity. It begins with a discussion of the foundation of the general theory ... More

This section presents annotations of the manuscript of Albert Einstein's canonical 1916 paper on the general theory of relativity. It begins with a discussion of the foundation of the general theory of relativity, taking into account Einstein's fundamental considerations on the postulate of relativity, and more specifically why he went beyond the special theory of relativity. It then considers the spacetime continuum, explaining the role of coordinates in the new theory of gravitation. It also describes tensors of the second and higher ranks, multiplication of tensors, the equation of the geodetic line, the formation of tensors by differentiation, equations of motion of a material point in the gravitational field, the general form of the field equations of gravitation, and the laws of conservation in the general case. Finally, the behavior of rods and clocks in the static gravitational field is examined.Less

Symmetries and Conservation Laws

Yemima Ben-Menahem

in Causation in Science

This chapter examines how symmetry principles—despite their a priori appearance—function as causal constraints through their conceptual relation with conservation laws. It first provides an overview ... More

This chapter examines how symmetry principles—despite their a priori appearance—function as causal constraints through their conceptual relation with conservation laws. It first provides an overview of how symmetries are linked to causation by focusing on some of their interconnections with other members of the causal family. It then considers an excellent illustration of the causal function of symmetries in physics, Pauli's exclusion principle, before discussing conservation laws in relation to symmetries. The chapter then explains the distinction between active and passive symmetries, and between global and local symmetries (or geometric versus dynamic symmetries, respectively), as well as gauge theories and the notion of gauge freedom. The chapter concludes with an analysis of Curie's principle and how it is intertwined with symmetries.Less

An Introduction to the History of Law and Natural Resources

Jan G. Laitos

in The Right of Nonuse

Laws initially encouraged and protected resource use. Contract law permitted one user to make enforceable, credible marketplace deals with other potential users of resources so that the resource ... More

Laws initially encouraged and protected resource use. Contract law permitted one user to make enforceable, credible marketplace deals with other potential users of resources so that the resource would wind up with the user most willing to pay for it. Property law allowed users to own the resource, and to exercise the right to control, develop, and exploit it to enhance the owner's selfish interests. Gradual resource exhaustion and depletion caused lawmakers to adopt another category of “first generation” resource use laws designed to slow unchecked resource extraction, and create a more sustainable resource base for future generations of resource use. These conservation laws still had as their primary purpose the long-term use of resources, albeit use that was now somewhat regulated to moderate the unchecked exploitation that had threatened the long-term viability of both exhaustible and renewable resources. But by the middle of the twentieth century, both categories of resource use laws had not prevented the depletion of the stock and renewable resource base. Moreover, such use had begun to pollute public environmental foods, such as the air, the water, and the soils. The heretofore dominant “use” component of natural uses was now threatening the critical “nonuse” component.Less

Wright’s Adaptive Landscape Versus Fisher’s Fundamental Theorem

Steven A. Frank

in The Adaptive Landscape in Evolutionary Biology

Two giants of evolutionary theory, Sewall Wright and R. A. Fisher, fought bitterly for over thirty years. The Wright–Fisher controversy forms a cornerstone of the history and philosophy of biology. ... More

Two giants of evolutionary theory, Sewall Wright and R. A. Fisher, fought bitterly for over thirty years. The Wright–Fisher controversy forms a cornerstone of the history and philosophy of biology. The chapter argues that the standard interpretations of the Wright–Fisher controversy do not accurately represent the ideas and arguments of these two key historical figures. The usual account contrasts the major slogans attached to each name: Wright's adaptive landscape and shifting balance theory of evolution versus Fisher's fundamental theorem of natural selection. These alternative theories are in fact incommensurable. Wright's theory is a detailed dynamical model of evolutionary change in actual populations. Fisher's theory is an abstract invariance and conservation law that, like all physical laws, captures essential features of a system but does not account for all aspects of dynamics in real examples. This key contrast between embodied theories of real cases and abstract laws is missing from prior analyses of Wright versus Fisher. They never argued about this contrast. Instead, the issue at stake in their arguments concerned the actual dynamics of real populations. Both agreed that fluctuations of nonadditive (epistatic) gene combinations play a central role in evolution. Wright emphasized stochastic fluctuations of gene combinations in small, isolated populations. By contrast, Fisher believed that fluctuating selection in large populations was the main cause of fluctuation in nonadditive gene combinations. Close reading shows that widely cited views attributed to Fisher mostly come from what Wright said about Fisher, whereas Fisher's own writings clearly do not support such views.Less

The Basic Theory of Quantum Mechanics

Bas C. van Fraassen

in Quantum Mechanics: An Empiricist View

Covered are Hilbert space, vector, and operator representations of pure and mixed states, measurable physical quantities (observables), Gleason's theorem, Lueders’ Rule, unitary operators, and ... More

Covered are Hilbert space, vector, and operator representations of pure and mixed states, measurable physical quantities (observables), Gleason's theorem, Lueders’ Rule, unitary operators, and Schroedinger's Equation, symmetries of the Hamiltonian and the corresponding conservation laws, and superselection rules.Less

Mathematical and computational modelling tools

Baltazar D. Aguda and Avner Friedman

in Models of Cellular Regulation

This chapter reviews chemical kinetics to illustrate the formulation of model equations for a given reaction mechanism. For spatially uniform systems, these model equations are usually ordinary ... More

This chapter reviews chemical kinetics to illustrate the formulation of model equations for a given reaction mechanism. For spatially uniform systems, these model equations are usually ordinary differential equations; but coupling of chemical reactions to physical processes such as diffusion requires the formulation of partial differential equations to describe the spatiotemporal evolution of the system. Mathematical analysis of the dynamical models involves basic concepts from ordinary and partial differential equations. Computational methods, including stochastic simulations and sources of computer software programs available free on the internet are also summarized.Less