Concentrating upon applications that are most relevant to modern physics, this valuable book surveys variational principles and examines their relationship to dynamics and quantum theory. Stressing the history and theory of these mathematical concepts rather than the mechanics, the authors provide many insights into the development of quantum mechanics and present much hard-to-find material in a remarkably lucid, compact form. After summarizing the historical background from Pythagoras to Francis Bacon, Professors Yourgrau and Mandelstram cover Fermat's principle of least time, the (...) principle of least action of Maupertuis, development of this principle by Euler and Lagrange, and the equations of Lagrange and Hamilton. Equipped by this thorough preparation to treat variational principles in general, they proceed to derive Hamilton's principle, the Hamilton-Jacobi equation, and Hamilton's canonical equations. An investigation of electrodynamics in Hamiltonian form covers next, followed by a resume of variational principles in classical dynamics. The authors then launch into an analysis of their most significant topics: the relation between variational principles and wave mechanics, and the principles of Feynman and Schwinger in quantum mechanics. Two concluding chapters extend the discussion to hydrodynamics and natural philosophy. Professional physicists, mathematicians, and advanced students with a strong mathematical background will find this stimulating volume invaluable reading. Extremely popular in its hardcover edition, this volume will find even wider appreciation in its first fine inexpensive paperbound edition. (shrink)

Some time ago, Joel Katzav and Brian Ellis debated the compatibility of dispositional essentialism with the principle of least action. Surprisingly, very little has been said on the matter since, even by the most naturalistically inclined metaphysicians. Here, we revisit the Katzav–Ellis arguments of 2004–05. We outline the two problems for the dispositionalist identified Katzav in his 2004 , and claim they are not as problematic for the dispositional essentialist at it first seems – but not for the reasons espoused (...) by Ellis. (shrink)

An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the (...) stage for a discussion of the physical principles that underlie the fundamental interactions of elementary particle physics and their description by gauge field theories. (shrink)

Scientific Essentialism defends the view that the fundamental laws of nature depend on the essential properties of the things on which they are said to operate, and are therefore not independent of them. These laws are not imposed upon the world by God, the forces of nature, or anything else, but rather are immanent in the world. Ellis argues that ours is a dynamic world consisting of more or less transient objects that are constantly interacting with each other, and whose (...) identities depend on their roles in these processes. The laws of nature are metaphysically necessary, and consequently, there are necessary connections between events. (shrink)

We argue that the inference from dispositional essentialism about a property (in the broadest sense) to the metaphysical necessity of laws involving it is invalid. Let strict dispositional essentialism be any view according to which any given property’s dispositional character is precisely the same across all possible worlds. Clearly, any version of strict dispositional essentialism rules out worlds with different laws involving that property. Permissive dispositional essentialism is committed to a property’s identity being tied to its dispositional profile or causal (...) role, yet is compatible with moderate interworld variation in a property’s dispositional profile. We provide such a model of dispositional essentialism about a property and metaphysical contingency of the laws involving it. (shrink)

This book outlines a major new theory of natural laws. The book begins with the question of whether there are any genuinely law-like phenomena in nature. The discussion addresses questions currently being debated by metaphysicians such as whether the laws of nature are necessary or contingent and whether a property can be identified independently of its causal role.

In this paper, I explore the feasibility of a realistic interpretation of the quantum mechanical path integral - that is, an interpretation according to which the particle actually follows the paths that contribute to the integral. I argue that an interpretation of this sort requires spacetime to have a branching structure similar to the structures of the branching spacetimes proposed by previous authors. I point out one possible way to construct branching spacetimes of the required sort, and I ask whether (...) the resulting interpretation of quantum mechanics is empirically testable. (shrink)

This paper discusses some of the modal involvements of analytical mechanics. I first review the elementary aspects of the Lagrangian, Hamiltonian and Hamilton-Jacobi approaches. I then discuss two modal involvements; both are related to David Lewis' work on modality, especially on counterfactuals. The first is the way Hamilton-Jacobi theory uses ensembles, i.e. sets of possible initial conditions. The structure of this set of ensembles remains to be explored by philosophers. The second is the way the Lagrangian and Hamiltonian approaches' variational (...) principles state the law of motion by mentioning contralegal dynamical evolutions. This threatens to contravene the principle that any actual truth, in particular an actual law, is made true by actual facts. Though this threat can be avoided, at least for simple mechanical systems, it repays scrutiny; not least because it leads to some open questions. (shrink)

This paper distinguishes two kinds of realist issue -- the issue of whether the propositions of a given domain are factual and the issue of whether they are fundamental. It criticizes previous accounts of what these issues come to and suggests that they are to be understood in terms of a basic metaphysical concept of reality. This leaves open the question of how such issues are to be resolved; and it is argued that this may be done through consideration of (...) what grounds the facts of a given domain, when fundamentality is in question, and what grounds our engagement with the putative facts, when factuality is in question. (shrink)

Given its importance in modern physics, philosophers of science have paid surprisingly little attention to the subject of symmetries and invariances, and they have largely neglected the subtopic of symmetry breaking. I illustrate how the topic of laws and symmetries brings into fruitful interaction technical issues in physics and mathematics with both methodological issues in philosophy of science, such as the status of laws of physics, and metaphysical issues, such as the nature of objectivity.

Scientific Essentialism defends the view that the fundamental laws of nature depend on the essential properties of the things on which they are said to operate, and are therefore not independent of them. These laws are not imposed upon the world by God, the forces of nature or anything else, but rather are immanent in the world. Ellis argues that ours is a dynamic world consisting of more or less transient objects which are constantly interacting with each other, and whose (...) identities depend on their roles in these processes. Natural objects must behave as they do, because to do otherwise would be contrary to their natures. The laws of nature are, therefore, metaphysically necessary, and consequently, there are necessary connections between events. Brian Ellis calls for the rejection of the theory of Humean Supervenience and an implementation of a new kind of realism in philosophical analysis. (shrink)

Professional philosophers and advanced students working in metaphysics and the philosophy of science will find this book both provocative and stimulating.

This paper forms part of a wider campaign: to deny pointillisme, the doctrine that a physical theory's fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or point-sized objects located there; so that properties of spatial or spatiotemporal regions and their material contents are determined by the point-by-point facts. More specifically, this paper argues against pointillisme about the concept of velocity in classical mechanics; especially against proposals by Tooley, Robinson and Lewis. (...) A companion paper argues against pointillisme about -geometry, as proposed by Bricker. To avoid technicalities, I conduct the argument almost entirely in the context of "Newtonian" ideas about space and time, and the classical mechanics of point-particles, i.e. extensionless particles moving in a void. But both the debate and my arguments carry over to relativistic physics. Introduction The wider campaign 2.1 Connecting physics and metaphysics 2.1.1 Avoiding controversy about the intrinsic–extrinsic distinction 2.1.2 Distinction from three mathematical distinctions 2.2 Classical mechanics is not pointilliste, and can be perdurantist 2.2.1 Two versions of pointillisme 2.2.2 Two common claims 2.2.3 My contrary claims 2.3 In more detail... 2.3.1 Four violations of pointillisme 2.3.2 For perdurantism Velocity as intrinsic? 3.1 Can properties represented by vectors be intrinsic to a point? 3.2 Orthodox velocity is extrinsic but local 3.2.1 A question and a debate 3.2.2 The verdict 3.3 Against intrinsic velocity 3.3.1 A common view—and a common problem 3.3.2 Tooley's proposal and his arguments 3.3.3 Tooley's further discussion "Shadow velocities": Lewis and Robinson 4.1 The proposal 4.2 Criticism: the vector field remains unspecified 4.3 Avoiding the presupposition of persistence, using Hilbert's symbol 4.4 Comparison with Robinson and Lewis. (shrink)

FIRST PARAGRAPH I have argued that dispositionalism is incompatible with the Principle of Least Action (PLA) (Katzav 2004). In ‘Katzav on the Limitations of Dispositionalism,’ Brian Ellis responds, arguing that while naïve dispositionalism is incompatible with the PLA, sophisticated dispositionalism is not. Naive dispositionalism, according to Ellis, is the view that the world is ultimately something like a conglomerate of objects and their dispositions, and that, therefore, dispositions are the ultimate ontological units that explain events. Sophisticated dispositionalism, according to Ellis, (...) supposes that, how things are disposed to behave depends also on what kinds of things they are, what kinds of property they have, and how these kinds of things and properties are placed in the natural kinds hierarchies to which they belong (Ellis 2005). Further, it supposes that at the top of each hierarchy of natural kinds there is a global kind. For example, ‘[t]he global natural kind in the category of substance is that of the physical system’ (Ellis 2005). Ellis continues, claiming that the PLA is of the essence of the global kind in the category of objects or substances. If this is so, then, of course, every continuing object must be Lagrangian, i.e. disposed to evolve in accordance with the principle of least action (Ellis 2005). Ellis concludes that, therefore, a sophisticated dispositionalist can accommodate the PLA and its metaphysical necessity. (shrink)

My aim is to argue for the incompatibility of one of the central principles of physics, namely the principle of least action (PLA), with the increasingly popular view that the world is, ultimately, merely something like a con- glomerate of objects and irreducible dispositions. First, I argue that the essentialist implications many suppose this view has are not compatible with the PLA. Second, I argue that, irrespective of whether this view has any essentialist implications, it is not compatible with the (...) kind of explanation that the PLA affords. (shrink)