We analyze the geometric foundations of classical Yang-Mills theory by studying the relationships between internal relativity, locality, global/local invariance, and background independence. We argue that internal relativity and background independence are the two independent defining principles of Yang-Mills theory. We show that local gauge invariance -heuristically implemented by means of the gauge argument- is a direct consequence of internal relativity. Finally, we analyze the conceptual meaning of BRST symmetry in terms of the invariance of the gauge fixed theory under general (...) local gauge transformations. (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 logic of gauge theory is considered by tracing its development from general relativity to Yang-Mills theory, through Weyl's two gauge theories. A handful of elements---which for want of better terms can be called \emph{geometrical justice}, \emph{matter wave}, \emph{second clock effect}, \emph{twice too many energy levels}---are enough to produce Weyl's second theory; and from there, all that's needed to reach the Yang-Mills formalism is a \emph{non-Abelian structure group} (say $\mathbb{SU}\textrm{(}N\textrm{)}$).

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 paper looks at the nature of idealizations and representational structures appealed to in the context of the fractional quantum Hall effect, specifically, with respect to the emergence of anyons and fractional statistics. Drawing on an analogy with the Aharonov–Bohm effect, it is suggested that the standard approach to the effects— the topological approach to fractional statistics—relies essentially on problematic idealizations that need to be revised in order for the theory to be explanatory. An alternative geometric approach is outlined and (...) endorsed. Roles for idealizations in science, as well as consequences for the debate revolving around so-called essential idealizations, are discussed. (shrink)

In this essay, I provide an overview of the debate on infinite and essential idealizations in physics. I will first present two ostensible examples: phase transitions and the Aharonov– Bohm effect. Then, I will describe the literature on the topic as a debate between two positions: Essentialists claim that idealizations are essential or indispensable for scientific accounts of certain physical phenomena, while dispensabilists maintain that idealizations are dispensable from mature scientific theory. I will also identify some attempts at finding a (...) middle ground between the essentialists and dispensabilists camps. Finally, I will raise questions for future research on essential and infinite idealizations via the notion of exploration. (shrink)

Two approaches to understanding the idealizations that arise in the Aharonov–Bohm effect are presented. It is argued that a common topological approach, which takes the non-simply connected electron configuration space to be an essential element in the explanation and understanding of the effect, is flawed. An alternative approach is outlined. Consequently, it is shown that the existence and uniqueness of self-adjoint extensions of symmetric operators in quantum mechanics have important implications for philosophical issues. Also, the alleged indispensable explanatory role of (...) said idealizations is examined via a minimal model explanatory scheme. Last, the idealizations involved in the AB effect are placed in a wider philosophical context via a short survey of part of the literature on infinite and essential idealizations. (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)

The first part of this paper discusses Quine’s views on underdetermination of theory by evidence, and the indeterminacy of translation, or meaning, in relation to certain physical theories. The underdetermination thesis says different theories can be supported by the same evidence, and the indeterminacy thesis says the same component of a theory that is underdetermined by evidence is also meaning indeterminate. A few examples of underdetermination and meaning indeterminacy are given in the text. In the second part of the paper, (...) Quine’s scientific realism is discussed briefly, along with some of the difficulties encountered when considering the ‘truth’ of different empirically equivalent theories. It is concluded that the difference between underdetermination and indeterminacy, while significant, is not as great as Quine claims. It just means that after we have chosen a framework theory, from a number of empirically equivalent ones, we still have further choices along two different dimensions. (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)

Four empirically equivalent versions of general relativity, namely standard GR, Lorentz-invariant gravitational theory,and the gravitational gauge theories of the Lorentz and translation groups, are investigated in the form of a case study for theory underdetermination. The various ontological indeterminacies (both underdetermination and inscrutability of reference) inherent in gravitational theories are analyzed in a detailed comparative study. The concept of practical underdetermination is proposed, followed by a discussion of its adequacy to describe scientific progress.

This paper explores the argument structure of the concept of spontaneous symmetry breaking in the electroweak gauge theory of the Standard Model: the so-called Higgs mechanism. As commonly understood, the Higgs argument is designed to introduce the masses of the gauge bosons by a spontaneous breaking of the gauge symmetry of an additional field, the Higgs field. The technical derivation of the Higgs mechanism, however, consists in a mere reshuffling of degrees of freedom by transforming the Higgs Lagrangian in a (...) gauge-invariant manner. This already raises serious doubts about the adequacy of the entire manoeuvre. It will be shown that no straightforward ontic interpretation of the Higgs mechanism is tenable, since gauge transformations possess no real instantiations. In addition, the explanatory value of the Higgs argument will be critically examined. (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)

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.

Nella sua straordinaria opera scientifica, Franco Selleri si è sempre opposto alla rinuncia alla comprensione della struttura della realtà e della natura degli oggetti fisici, che egli considera come l’elemento caratterizzante delle principali teorie della fisica del Novecento e che è stata stigmatizzata da Karl Popper come tesi della “fine della strada in fisica”. Sin dalla fine degli anni ’60, egli ha sviluppato quella riflessione critica nei confronti delle teorie fondamentali della fisica moderna, in particolar modo della teoria delle particelle (...) elementari e della meccanica quantistica, e in un secondo tempo delle teorie relativistiche, che contraddistingue il suo programma di ricerca. Nel corso della sua intensa e infaticabile attività scientifica, Selleri è entrato in proficuo contatto con molti grandi fisici e filosofi della scienza, instaurando un intenso dialogo critico con Louis de Broglie, John Bell e Karl Popper. Le sue originali e non convenzionali ricerche lo hanno portato a risultati significativi non solo nell’ambito dei fondamenti della fisica, ma anche della storia e della filosofia della fisica. Per questo abbiamo voluto dedicare un numero speciale di Isonomia al nostro impareggiabile amico e collega, sia per la sua passione instancabile e la sua profonda conoscenza dei fondamenti formali, concettuali e filosofici delle teorie della fisica contemporanea, sia e forse ancor più come maestro di una prospettiva perennemente critica che egli ha sempre seguito e proposto con particolare rigore ed estrema determinazione. (shrink)

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.

Going from two dimensions to three can shed light on the Aharonov-Bohm debate. The three-dimensional analogy is misleading if taken too literally; it makes sense on a more abstract, formal level. A slight tweak is enough to produce gauge freedom in three dimensions.

In discussions of the Aharonov-Bohm effect, Healey and Lyre have attributed reality to loops $\sigma_0$ (or hoops $[\sigma_0]$), since the electromagnetic potential $A$ is currently unmeasurable and can therefore be transformed. I argue that $[A]=[A+d\lambda]_{\lambda}$ and the hoop $[\sigma_0]$ are related by a meaningful duality, so that however one feels about $[A]$ (or any potential $A\in[A]$), it is no worse than $[\sigma_0]$ (or any loop $\sigma_0\in[\sigma_0]$): no ontological firmness is gained by retreating to the loops, which are just as flimsy (...) as the potentials. And one wonders how the unmeasurability of one entity can invest another with physical reality; would an eventual observation of $A$ dissolve $\sigma_0$, consigning it to a realm of incorporeal mathematical abstractions? The reification of loops rests on the potential's ''gauge dependence''; which in turn rests on its unmeasurability; which is too shaky and arbitrary a notion to carry so much weight. (shrink)

In discussions of the Aharonov-Bohm effect, Healey and Lyre have attributed reality to loops $\sigma_0$ (or hoops $[\sigma_0]$), since the electromagnetic potential $A$ is currently unmeasurable and can therefore be transformed. I argue that $[A]=[A+d\lambda]_{\lambda}$ and the hoop $[\sigma_0]$ are related by a meaningful duality, so that however one feels about $[A]$ (or any potential $A\in[A]$), it is no worse than $[\sigma_0]$ (or any loop $\sigma_0\in[\sigma_0]$): no ontological firmness is gained by retreating to the loops, which are just as flimsy (...) as the potentials. And one wonders how the unmeasurability of one entity can invest another with physical reality; would an eventual observation of $A$ dissolve $\sigma_0$, consigning it to a realm of incorporeal mathematical abstractions? The reification of loops rests on the potential's ''gauge dependence''; which in turn rests on its unmeasurability; which is too shaky and arbitrary a notion to carry so much weight. (shrink)

The Aharonov-Bohm effect is typically called ``topological.'' But it seems no more topological than magnetostatics, electrostatics or Newton-Poisson gravity. I distinguish between two senses of ``topological.''.

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.