In a recent article in this journal, Barbara Lariviere offers a very useful distinction between two ways of understanding the claims that Leibniz, or relational theorists in general, might wish to make about the nature of motion and the structure of space and time; viz.,

and

Citing the authority of Weyl, the author argues that L1 is untenable; indeed, the argument purports to show that if L1 were true, then there would be no coherent basis for a theory of motion, not even a relational theory. My main goal in this note is to point out why this argument is mistaken while at the same time sketching the real reason why the relational conception of motion is untenable. In addition I will offer a few remarks about the relevance of L2 to the absolute-relational controvery.

Various fault modes of determinism in classical physics are outlined. It is shown how quantum mechanics can cure some forms of classical indeterminism.

A number of arguments have been given to show that the modal interpretation of ordinary nonrelativistic quantum mechanics cannot be consistently extended to the relativistic setting. We find these arguments inconclusive. However, there is a prima facie reason to think that a tension exists between the modal interpretation and relativistic invariance; namely, the best candidate for a modal interpretation adapted to relativistic quantum field theory, a prescription due to Rob Clifton (2000), comes out trivial when applied to a number of systems of physical interest. However, it is far from clear whether this difficulty for the modal interpretation is traceable to relativistic invariance per se or to the infinite number of degrees of freedom involved. In any case, the proponents of the modal interpretation have work to do.

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.

We discuss the intertwined topics of Fulling non-uniqueness and the Unruh effect. The Fulling quantization, which is in some sense the natural one for an observer uniformly accelerated through Minkowski spacetime to adopt, is often heralded as a quantization of the Klein-Gordon field which is both physically relevant and unitarily inequivalent to the standard Minkowski quantization. We argue that the Fulling and Minkowski quantizations do not constitute a satisfactory example of physically relevant, unitarily inequivalent quantizations, and indicate what it would take to settle the open question of whether a satisfactory example exists. A popular gloss on the Unruh effect has it that an observer uniformly accelerated through the Minkowski vacuum experiences a thermal flux of Rindler quanta. Taking the Unruh effect, so glossed, to establish that the notion of particle must be relativized to a reference frame, some would use it to demote the particle concept from fundamental status. We explain why technical results do not support the popular gloss and why the attempted demotion of the particle concept is both unsuccessful and unnecessary. Fulling non-uniqueness and the Unruh effect merit attention despite these negative verdicts because they provide excellent vehicles for illustrating key concepts of quantum field theory and for probing foundational issues of considerable philosophical interest.

The constrained Hamiltonian formalism is recommended as a means for getting a grip on the concepts of gauge and gauge transformation. This formalism makes it clear how the gauge concept is relevant to understanding Newtonian and classical relativistic theories as well as the theories of elementary particle physics; it provides an explication of the vague notions of “local” and “global” gauge transformations; it explains how and why a fibre bundle structure emerges for theories which do not wear their bundle structure on their sleeves; it illuminates the connections of the gauge concept to issues of determinism and what counts as a genuine “observable”; and it calls attention to problems which arise in attempting to quantize gauge theories. Some of the limitations and problematic aspects of the formalism are also discussed.

Inflationary cosmology won a large following on the basis of the claim that it solves various problems that beset the standard big bang model. We argue that these problems concern not the empirical adequacy of the standard model but rather the nature of the explanations it offers. Furthermore, inflationary cosmology has not been able to deliver on its proposed solutions without offering models which are increasingly complicated and contrived, which depart more and more from the standard model it was supposed to improve upon, and which sever the connection between cosmology and particle physics that initially made the inflationary paradigm so attractive. Nevertheless, inflationary cosmology remains a promising research program, not least because it offers an explanation of the origin of the density perturbations that seeded the formation of galaxies and other cosmic structures. Tests of this explanation are underway and may settle the issue of whether inflation played an important role in the early universe.

The standard theory of computation excludes computations whose completion requires an infinite number of steps. Malament-Hogarth spacetimes admit observers whose pasts contain entire future-directed, timelike half-curves of infinite proper length. We investigate the physical properties of these spacetimes and ask whether they and other spacetimes allow the observer to know the outcome of a computation with infinitely many steps.

The nature and basis of irreversibility has been intensively investigated over the last 100 years by physicists, mathematicians, and philosophers. But if progress is measured by convergence of opinion among the “experts” then it is hard to detect; in fact the field is a virtual Tower of Babel. J.L. Lebowitz, one of the leading mathematical physicists in the field put it this way:

Einstein himself had a few words to say about the writing of the history of science. From the first of his famous conversations with Einstein, Robert Shankland relates: “Then he gave me his ideas on historical writing of science. ‘Nearly all historians of science are philologists and do not comprehend what physicists were aiming at, how they thought and wrestled with their problems… .’ The struggle with their:problems, their trying everything to find a solution which came at last often by very indirect means, is the correct picture.” (Shankland 1963, p. 50).

Why should we take these words seriously? After all, Einstein was not an historian, and, unless we are to pose him as an authority on every topic, these comments represent but a personal opinion. This, however, is precisely why they should be taken seriously, if we are interested in the history of Einstein's own accomplishments.

Various senses in which laws of nature are supposed to be “universal” are distinguished. Conditions designed to capture the content of the more important of these senses are proposed and the relations among these conditions are examined. The status of universality requirements is briefly discussed.

Classical statistical mechanics has commanded a modest but steady amount of attention from philosophers of science. By contrast, there has been an almost total neglect of relativistic statistical mechanics, or more precisely, a neglect of the prospects and problems of producing a relativistic version of classical statistical mechanics. The neglect is undeserved, for this area offers a fascinating array of case studies for those concerned with the history and sociology of science, with the structure and dynamics of scientific theories, or with foundations problems in physics. This paper is dedicated to the goal of ending the neglect. Towards this end, I will survey some of the issues which arise in attempting to marry statistical-thermodynamics with relativity theory. The choice of the issues to be discussed and their treatment naturally reflect my own preferences and prejudices, and I cannot hope for the reader’s agreement on all points.

It is argued that the main problem with “the problem of the direction of time” is to figure out what the problem is or is supposed to be. Towards this end, an attempt is made to disentangle and to classify some of the many issues which have been discussed under the label of ‘the direction of time’. Secondly, some technical apparatus is introduced in the hope of producing a sharper formulation of the issues than they have received in the philosophical literature. Finally, some tentative suggestions about the central issues are offered. In particuar, it is suggested that entropy and irreversibility are much less crucial to the central issues than most philosophers would have us believe. This suggestion is not made because of any firm conviction of its correctness but rather because it helps to focus the discussion on some basic but long neglected assumptions which underlie traditional approaches.