Gauge symmetries play a central role, both in the mathematical foundations as well as the conceptual construction of modern (particle) physics theories. However, it is yet unclear whether they form a necessary component of theories, or whether they can be eliminated. It is also unclear whether they are merely an auxiliary tool to simplify (and possibly localize) calculations or whether they contain independent information. Therefore their status, both in physics and philosophy of physics, remains to be fully clarified. In this (...) overview we review the current state of affairs on both the philosophy and the physics side. In particular, we focus on the circumstances in which the restriction of gauge theories to gauge invariant information on an observable level is warranted, using the Brout-Englert-Higgs theory as an example of particular current importance. Finally, we determine a set of yet to be answered questions to clarify the status of gauge symmetries. (shrink)

This discussion provides a brief commentary on each of the papers presented in the symposium on the conceptual foundations of field theories in physics. In Section 2 I suggest an alternative to Paul Teller's reading of the gauge argument that may help to solve, or dissolve, its puzzling aspects. In Section 3 I contend that Sunny Auyang's arguments against substantivalism and for “objectivism” in the context of gauge field theories face serious worries. Finally, in Section 4 I claim that Gordon (...) Fleming's proposal for hyperplane-dependent Newton-Wigner fields differs importantly from his previous arguments about hyperplane-dependent properties in quantum mechanics. (shrink)

Philosophers of physics have spent much effort unpacking the structure of gauge theories. But surprisingly, little attention has been devoted to the question of why we should require our best theories to be locally gauge invariant in the first place. Drawing on Steven Weinberg's works in the mid-1960s, I argue that the principle of local gauge invariance follows from Lorentz invariance and other natural assumptions in the context of perturbative relativistic quantum field theory. On this view, gauge freedom is a (...) mere accidental feature of an already highly constrained set of quantities; the distinctive structure of our best gauge theories, in turn, traces back to the peculiar space-time transformation properties of particles like photons, gluons, and gravitons. I conclude by drawing a few interpretative lessons for the philosophy of gauge theories. (shrink)

After decades of neglect philosophers of physics have discovered gauge theories--arguably the paradigm of modern field physics--as a genuine topic for foundational and philosophical research. Incidentally, in the last couple of years interest from the philosophy of physics in structural realism--in the eyes of its proponents the best suited realist position towards modern physics--has also raised. This paper tries to connect both topics and aims to show that structural realism gains further credence from an ontological analysis of gauge theories--in particular (...) U(1) gauge theory. In the first part of the paper the framework of fiber bundle gauge theories is briefly presented and the interpretation of local gauge symmetry will be examined. In the second part, an ontological underdetermination of gauge theories is carved out by considering the various kinds of non-locality involved in such typical effects as the Aharonov-Bohm effect. The analysis shows that the peculiar form of non-separability figuring in gauge theories is a variant of spatiotemporal holism and can be distinguished from quantum theoretic holism. In the last part of the paper the arguments for a gauge theoretic support of structural realism are laid out and discussed. (shrink)

The aim of this paper is twofold: First, to present an examination of the principles underlying gauge field theories. I shall argue that there are two principles directly connected to the two well-known theorems of Emmy Noether concerning global and local symmetries of the free matter-field Lagrangian, in the following referred to as "conservation principle" and "gauge principle". Since both these express nothing but certain symmetry features of the free field theory, they are not sufficient to derive a true interaction (...) coupling to a new gauge field. For this purpose it is necessary to advocate a third, truly empirical principle which may be understood as a generalization of the equivalence principle. The second task of the paper is to deal with the ontological question concerning the reality status of gauge potentials in the light of the proposed logical structure of gauge theories. A nonlocal interpretation of topological effects in gauge theories and, thus, the non-reality of gauge potentials in accordance with the generalized equivalence principle will be favoured. (shrink)

Symmetry-based inferences have permeated many discussions in philosophy of physics and metaphysics of science. It is claimed that symmetries in our physical theories would allow us to draw metaphysical conclusions about the world, a view that I call ‘symmetry inferentialism’. This paper is critical to this view. I claim that (a) it assumes a philosophically questionable characterization of the relevant validity domain of physical symmetries, and (b) it overlooks a distinction between two opposing ways through which relevant physical symmetries become (...) established. My conclusion is that symmetry inferentialism loses persuasive force when these two points are taken into consideration. (shrink)

Physics seems to tell us that there are four fundamental force-fields in nature: the gravitational, the electromagnetic, the weak, and the strong (or interactions). But it also seems to tell us that gravity cannot possibly be a force-field, in the same sense as the other three are. And yet the search for a grand unification of all four force-fields is today one of the hottest pursuits. Is this the result of a simple confusion? This article aims at clarifying this situation (...) by (i) reviewing the gauge-field programme and its conception of unification of force-fields, (ii) examining the various attempts at a gauge theory of gravity, and (iii) articulating the nature of "gauging" and using it to explain the difference between gravity and the other force-fields. (shrink)

I examine the construction process of the “Higgs mechanism” and its subsequent use by Steven Weinberg to formulate the electroweak theory of elementary particle physics. I characterize the development of the Higgs mechanism as a historical process that was guided through analogies drawn to the theories of solid-state physics and that was progressive through diverse contributions in the sixties from a number of physicists working independently. I also offer a detailed comparative study of the similarities and the differences that exist (...) between the approaches taken in these contributions. (shrink)

In this paper, I try to decipher the role of internal symmetries in the ontological maze of particle physics. The relationship between internal symmetries and laws of nature is discussed within the framework of “Platonic realism.” The notion of physical “structure” is introduced as representing a deeper ontological layer behind the observable world. I argue that an internal symmetry is a structure encompassing laws of nature. The application of internal symmetry groups to particle physics came about in two revolutionary steps. (...) The first was the introduction of the internal symmetries of hadrons in the early 1960s. These global and approximate symmetries served as means of bypassing the dynamics. I argue that the realist could interpret these symmetries as ontologically prior to the hadrons. The second step was the gauge revolution in the 1970s, where symmetries became local and exact and were integrated with the dynamics. I argue that the symmetries of the second generation are fundamental in the following two respects: According to the so-called “gauge argument,” gauge symmetry dictates the existence of gauge bosons, which determine the nature of the forces. This view, which has been recently criticized by some philosophers, is widely accepted in particle physics at least as a heuristic principle. In view of grand unified theories, the new symmetries can be interpreted as ontologically prior to baryon matter. (shrink)

This paper formulates generalized versions of the general principle of relativity and of the principle of equivalence that can be applied to general abstract spaces. It is shown that when the principles are applied to the Hilbert space of a quantum particle, its law of coupling to electromagnetic fields is obtained. It is suggested to understand the Aharonov-Bohm effect in light of these principles, and the implications for some related foundational controversies are discussed.

This article suggests a fresh look at gauge symmetries, with the aim of drawing a clear line between the a priori theoretical considerations involved, and some methodological and empirical non-deductive aspects that are often overlooked. The gauge argument is primarily based on a general symmetry principle expressing the idea that a change of mathematical representation should not change the form of the dynamical law. In addition, the ampliative part of the argument is based on the introduction of new degrees of (...) freedom into the theory according to a methodological principle that is formulated here in terms of correspondence between passive and active transformations. To demonstrate how the two kinds of considerations work together in a concrete context, I begin by considering spatial symmetries in mechanics. I suggest understanding Mach's principle as a similar combination of theoretical, methodological and empirical considerations, and demonstrate the claim with a simple toy model. I then examine gauge symmetries as a manifestation of the two principles in a quantum context. I further show that in all of these cases the relational nature of physically significant quantities can explain the relevance of the symmetry principle and the way the methodology is applied. In the quantum context, the relevant relational variables are quantum phases. (shrink)

The standard $\mathbb{U}(1)$ “gauge principle” or “gauge argument” produces an exact potential A=dλ and a vanishing field F=d 2 λ=0. Weyl (in Z. Phys. 56:330–352, 1929; Rice Inst. Pam. 16:280–295, 1929) has his own gauge argument, which is sketchy, archaic and hard to follow; but at least it produces an inexact potential A and a nonvanishing field F=dA≠0. I attempt a reconstruction.

The ''gauge argument'' is often used to 'deduce' interactions from a symmetry requirement. A transition---whose justification can take some effort---from global to local transformations is typically made at the beginning of the argument. But one can spare the trouble by \emph{starting} with local transformations, as global ones do not exist in general. The resulting economy seems noteworthy.

The paper discusses major implications of high energy physics for the scientific realism debate. The first part analyses the ways in which aspects of the empirically well-confirmed standard model of particle physics are relevant for a reassessment of entity realism, ontological realism and structural realism. The second part looks at the implications of more far-reaching concepts like string theory. While those theories have not found empirical confirmation, if they turned out viable, their implications for the realism debate would be more (...) substantial than those of the standard model. (shrink)

Since its discovery in 1959 the Aharonov-Bohm effect has continuously been the cause for controversial discussions of various topics in modern physics, e.g. the reality of gauge potentials, topological effects and nonlocalities. In the present paper we juxtapose the two rival interpretations of the Aharonov-Bohm effect. We show that the conception of nonlocality encountered in the Aharonov-Bohm effect is closely related to the nonseparability which is common in quantum mechanics albeit distinct from it due to its topological nature. We propose (...) a third alternative interpretation based on the loop space of holonomies which serves to solve some of the problems and we trace back the topological nonlocality and thereby the Aharonov-Bohm effect to their quantum mechanical origin. All three discussed interpretations are, of course, empirically equivalent. In fact, they present us with an instructive case study for the thesis of theory underdetermination by empirical data. (shrink)

This paper is an analysis of the geometrical interpretation of local gauge symmetry for theories of the Yang-Mills type.