John Earman

Like moths attracted to a bright light, philosophers are drawn to glitz. So in discussing the notions of ‘gauge’, ‘gauge freedom’, and ‘gauge theories’, they have tended to focus on examples such as Yang–Mills theories and on the mathematical apparatus of fibre bundles. But while Yang–Mills theories are crucial to modern elementary particle physics, they are only a special case of a much broader class of gauge theories. And while the fibre bundle apparatus turned out, in retrospect, to be the right formalism to illuminate the structure of Yang–Mills theories, the strength of this apparatus is also its weakness: the fibre bundle formalism is very flexible and general, and, as such, fibre bundles can be seen lurking under, over, and around every bush. What is needed is an explanation of what the relevant bundle structure is and how it arises, especially for theories that are not initially formulated in fibre bundle language. Here I will describe an approach that grows out of the conviction that, at least for theories that can be written in Lagrangian/Hamiltonian form, gauge freedom arises precisely when there are Lagrangian/Hamiltonian constraints of an appropriate character. This conviction is shared, if only tacitly, by that segment of the physics community that works on constrained Hamiltonian systems.

Except for a few brief periods, Einstein was uninterested in analysing the nature of the spacetime singularities that appeared in solutions to his gravitational field equations for general relativity. The existence of such monstrosities reinforced his conviction that general relativity was an incomplete theory which would be superseded by a singularity-free unified field theory. Nevertheless, on a number of occasions between 1916 and the end of his life, Einstein was forced to confront singularities. His reactions show a strange asymmetry: he tended to be more disturbed by merely apparent singularities and less disturbed by real singularities. Einstein had strong a priori ideas about what results a correct physical theory should deliver. In the process of searching through theoretical possibilities, he tended to push aside technical problems and jump over essential difficulties. Sometimes this method of working produced brilliant new ideas—such as the Einstein–Rosen bridge—and sometimes it lead him to miss important implications of his theory of gravity—such as gravitational collapse.

This is the first part of a two-part article in which we defend the thesis of Humean Supervenience about Laws of Nature (HS). According to this thesis, two possible worlds cannot differ on what is a law of nature unless they also differ on the Humean base. The Humean base is easy to characterize intuitively, but there is no consensus on how, precisely, it should be defined. Here in Part I, we present and motivate a characterization of the Humean base that, we argue, enables HS to capture what is really stake in the debate, without taking on extraneous commitments.

Although the philosophical literature on the foundations of quantum field theory recognizes the importance of Haag’s theorem, it does not provide a clear discussion of the meaning of this theorem. The goal of this paper is to make up for this deficit. In particular, it aims to set out the implications of Haag’s theorem for scattering theory, the interaction picture, the use of non-Fock representations in describing interacting fields, and the choice among the plethora of the unitarily inequivalent representations of the canonical commutation relations for free and interacting fields.

It is argued that seemingly “merely technical” issues about the existence and uniqueness of self-adjoint extensions of symmetric operators in quantum mechanics have interesting implications for foundations problems in classical and quantum physics. For example, pursuing these technical issues reveals a sense in which quantum mechanics can cure some of the forms of indeterminism that crop up in classical mechanics; and at the same time it reveals the possibility of a form of indeterminism in quantum mechanics that is quite distinct from the indeterminism of state vector collapse. More generally, the examples considered indicate that the classical–quantum correspondence is more intricate and delicate than is generally appreciated. The aim of the article is to give a series of examples that reveal why the technical issues about self-adjointness are relevant to the philosophy of science and that help to make the issues accessible to philosophers of science.

Leibniz vertrat auf der einen Seite die Überzeugung, es gebe Relationen weder als abstrakte Universalien noch als konkrete Akzidenzen. Auf der anderen Seite war er überzeugt, daß es relationale Eigenschaften von physischen Gegenständen, die nicht auf nicht-relationale Eigenschaften dieser Objekte reduziert werden können, gebe. Die wirklichen Einzeldinge haben jedoch keine nicht-formalen relationalen Eigenschaften. Sie stehen zwar in Beziehung oder sind miteinander verknüpft, aber nur durch Perzeptionen, so daß der Begriff Beziehung hier ein Begriff der zweiten Ordnung ist. Die physische Welt mit ihren relationalen Eigenschaften ist fundiert in den Monaden. Die Fundierung ist eine Reduktion, aber es ist ein Mißverständnis, wenn man diese Reduktion so beschreibt, als impliziere sie eine Reduktion von relationalen Eigenschaften physischer Gegenstände; denn ihre nicht relationalen Eigenschaften werden in gleicher Weise reduziert

The purpose of this paper is to give a brief survey the implications of the theories of modern physics for the doctrine of determinism. The survey will reveal a curious feature of determinism: in some respects it is fragile, requiring a number of enabling assumptions to give it a fighting chance; but in other respects it is quite robust and very difficult to kill. The survey will also aim to show that, apart from its own intrinsic interest, determinism is an excellent device for probing the foundations of classical, relativistic, and quantum physics. The survey is conducted under three major presuppositions. First, I take a realistic attitude towards scientific theories in that I assume that to give an interpretation of a theory is, at a minimum, to specify what the world would have to be like in order for the theory to be true. But we will see that the demand for a deterministic interpretation of a theory can force us to abandon a naively realistic reading of the theory. Second, I reject the “no laws” view of science and assume that the field equations or laws of motion of the most fundamental theories of current physics represent science’s best guesses as to the form of the basic laws of nature. Third, I take determinism to be an ontological doctrine, a doctrine about the temporal evolution of the world. This ontological doctrine must not be confused with predictability, which is an epistemological doctrine, the failure of which need not entail a failure of determinism. From time to time I will comment on ways in which predictability can fail in a deterministic setting. Finally, my survey will concentrate on the Laplacian variety of determinism according to which the instantaneous state of the world at any time uniquely determines the state at any other time. The plan of the survey is as follows. Section 2 illustrates the fragility of determinism by means of a Zeno type example. Then sections 3 and 4 survey successively the fortunes of determinism in the Newtonian and the special relativistic settings..

Philosophical accounts of quantum theory commonly suppose that the observables of a quantum system form a Type-I factor von Neumann algebra. Such algebras always have atoms, which are minimal projection operators in the case of quantum mechanics. However, relativistic quantum field theory and the thermodynamic limit of quantum statistical mechanics make extensive use of von Neumann algebras of more general types. This chapter addresses the question whether interpretations of quantum probability devised in the usual manner continue to apply in the more general setting. Features of non-type I factor von Neumann algebras are cataloged. It is shown that these novel features do not cause the familiar formalism of quantum probability to falter, since Gleason's Theorem and the Lüders Rule can be generalized. However, the features render the problem of the interpretation of quantum probability more intricate.

A criterion is proposed to ensure that classical relativistic fields do not propagate superluminally. If this criterion does indeed serve as a sufficient condition for no superluminal propagation it follows that various other criteria found in the physics literature cannot serve as necessary conditions since they can fail although the proffered condition holds. The rejected criteria rely on energy conditions that are believed to hold for most classical fields used in actual applications. But these energy conditions are known to fail at small scales for quantum fields. It is argued that such a failure is not necessarily a cause for concern about superluminal propagation in the quantum regime since the proffered criterion of no superluminal propagation for classical fields has a natural analog for quantum fields and, further, this quantum analog condition provably holds for some quantum fields despite the violation of energy conditions. The apparatus developed here also offers a different approach to treating the Reichenbach-Salmon cases of "pseudo-causal processes" and helps to clarify the issue of whether relativity theory is consistent with superluminal propagation.

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

Many have claimed that ceteris paribus (CP) laws are a quite legitimate feature of scientific theories, some even going so far as to claim that laws of all scientific theories currently on offer are merely CP. We argue here that one of the common props of such a thesis, that there are numerous examples of CP laws in physics, is false. Moreover, besides the absence of genuine examples from physics, we suggest that otherwise unproblematic claims are rendered untestable by the mere addition of the CP operator. Thus, “CP all Fs are Gs” when read as a straightforward statement of fact, cannot be the stuff of scientific theory. Rather, we suggest that when ``ceteris paribus'' appears in scientific works it plays a pragmatic role of pointing to more respectable claims.