This paper examines the so-called "gauge argument" sometimes used by physicists to motivate the introduction of gauge fields, here facilitated by an informal exposition of the fiber bundle formalism. The discussion suggests some preliminary ways of understanding the connection between gauge fields and interactions.

Why is gauge symmetry so important in modern physics, given that one must eliminate it when interpreting what the theory represents? In this paper we discuss the sense in which gauge symmetry can be fruitfully applied to constrain the space of possible dynamical models in such a way that forces and charges are appropriately coupled. We review the most well-known application of this kind, known as the 'gauge argument' or 'gauge principle', discuss its difficulties, and (...) then reconstruct the gauge argument as a valid theorem in quantum theory. We then present what we take to be a better and more general gauge argument, based on Noether's second theorem in classical Lagrangian field theory, and argue that this provides a more appropriate framework for understanding how gauge symmetry helps to constrain the dynamics of physical theories. (shrink)

I consider the question of how literally one can construe the “gauge argument,” which is the canonical means of understanding the putatively central import of local gauge symmetry principles for fundamental physics. As I argue, the gauge argument must be afforded a heuristic reading. Claims to the effect that the argument reflects a deep “logic of nature” must, for numerous reasons I discuss, be taken with a grain of salt.

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.

[To be presented at PSA 2018] -/- The gauge/gravity duality and its relation to the possible emergence of gravity from quantum physics has been much discussed. Recently, however, Sebastian De Haro has argued that the very notion of a duality precludes emergence, given what he calls the internal view of dualities, on which the dual theories are physically equivalent. However, I argue that De Haro's argument for the internal view is not convincing, and we do not have good (...) reasons to adopt it. In turn, I propose we adopt the external view, on which dual theories are not physically equivalent, instead. (shrink)

In this paper I critically examine the most recent gauge-theoretic argument against the intrinsicality of fundamental properties formulated by French and McKenzie (2012). I show that it cannot achieve its intended goal (which is to undermine Lewis’s neo-Humean metaphysical project) but it can have a signifi cant infl uence to dispositional essentialists that hold that the fundamental physical properties are intrinsic features of their bearers.

In this paper, I argue that the Hole Argument can be formulated without using the notion of isomorphism, and for this reason it is not threatened by the criticism of Halvorson and Manchak (Br J Philos Sci, 2022. https://doi.org/10.1086/719193). Following Earman and Norton (Br J Philos Sci 38, pp. 515–525, 1987), I divide the Hole Argument into two steps: the proof of the Gauge Theorem and the transition from the Gauge Theorem to the conclusion of radical (...) indeterminism. In the analaysis of the first step, I argue that the Gauge Theorem does not rely on the notion of isomorphism but on the notion of the diffeomorphism-invariance of the equations of local spacetime theories; however, for this approach to work, the definition of local spacetime theories needs certain amendments with respect to Earman and Norton’s formulation. In the analysis of the second step, I postulate that we should use the notion of radical indeterminism instead of indeterminism simpliciter and that we should not decide in advance what kind of maps are to be used in comparing models. Instead, we can tentatively choose some kind of maps for this purpose and check whether a given choice leads to radical indeterminism involving empirically indistinguishable models. In this way, the use of the notion of isomorphism is also avoided in the second step of the Hole Argument. A general picture is that physical equivalence can be established by means of an iterative procedure in which we examine various candidate classes of maps, and, depending on the outcomes, we need to broaden or narrow these classes. The Hole Argument can be viewed as a particular instance of this procedure. (shrink)

Gauge symmetries provide one of the most puzzling examples of the applicability of mathematics in physics. The presented work focuses on the role of analogical reasoning in the gauge argument, motivated by Mark Steiner's claim that the application of the gauge principle relies on a Pythagorean analogy whose success undermines naturalist philosophy. In this paper, we present two different views concerning the analogy between gravity, electromagnetism, and nuclear interactions, each providing a different philosophical response to the (...) problem of the applicability of mathematics in the natural sciences. The first is based on an account of Weyl's original work, which first gave rise to the gauge principle. Drawing on his later philosophical writings, we develop an idelaist reading of the mathematical analogies in the gauge argument. On this view, mathematical analogies serve to ensure a conceptual harmony in our scientific account of nature. We further discuss the construction of Yang and Mills's gauge theory in light of this idealist reading. The second account presents a naturalist alternative, formulated in terms of John Norton's account of a material analogy, according to which the analogy succeeds in virtue of a physical similarity between the different interactions. This account is based on the methodological equivalence principle, a simple conceptual extension of the gauge principle that allows us to understand the relation between coordinate transformations and gravity as a manifestation of the same method. The physical similarity between the different cases is based on attributing the success of this method to the dependence of the coupling on relational physical quantities. We conclude by reflecting on the advantages and limits of the idealist, naturalist, and anthropocentric Pythagorean views, as three alternative ways to understand the puzzling relation between mathematics and physics. -/- . (shrink)

Einstein algebras have been suggested (Earman 1989) and rejected (Rynasiewicz 1992) as a way to avoid the hole argument against spacetime substantivalism. In this article, I debate their merits and faults. In particular, I suggest that a gauge‐invariant interpretation of Einstein algebras that avoids the hole argument can be associated with one approach to quantizing gravity, and, for this reason, is at least as well motivated as sophisticated substantivalist and relationalist interpretations of the standard tensor formalism.

Gauge symmetries provide one of the most puzzling examples of the applicability of mathematics in physics. The presented work focuses on the role of analogical reasoning in the gauge argument, motivated by Mark Steiner’s claim that the application of the gauge principle relies on a Pythagorean analogy whose success undermines naturalist philosophy. In this paper, we present two different views concerning the analogy between gravity, electromagnetism, and nuclear interactions, each providing a different philosophical response to the (...) problem of the applicability of mathematics in the natural sciences. The first is based on an account of Weyl’s original work, which first gave rise to the gauge principle. Drawing on his later philosophical writings, we develop an idealist reading of the mathematical analogies in the gauge argument. On this view, mathematical analogies serve to ensure a conceptual harmony in our scientific account of nature. We further discuss the construction of Yang and Mills’s gauge theory in light of this idealist reading. The second account presents a naturalist alternative, formulated in terms of John Norton’s account of a material analogy, according to which the analogy succeeds in virtue of a physical similarity between the different interactions. This account is based on the methodological equivalence principle, a simple conceptual extension of the gauge principle that allows us to understand the relation between coordinate transformations and gravity as a manifestation of the same method. The physical similarity between the different cases is based on attributing the success of this method to the dependence of the coupling on relational physical quantities. We conclude by reflecting on the advantages and limits of the idealist, naturalist, and anthropocentric Pythagorean views, as three alternative ways to understand the puzzling relation between mathematics and physics. (shrink)

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)

This paper deals with a number of technical achievements that are instrumental for a dis-solution of the so-called "Hole Argument" in general relativity. Such achievements include: 1) the analysis of the "Hole" phenomenology in strict connection with the Hamiltonian treatment of the initial value problem. The work is carried through in metric gravity for the class of Christoudoulou-Klainermann space-times, in which the temporal evolution is ruled by the "weak" ADM energy; 2) a re-interpretation of "active" diffeomorphisms as "passive and (...) metric-dependent" dynamical symmetries of Einstein's equations, a re-interpretation which enables to disclose their (up to now unknown) connection to gauge transformations on-shell; understanding such connection also enlightens the real content of the Hole Argument or, better, dis-solves it together with its alleged "indeterminism"; 3) the utilization of the Bergmann-Komar "intrinsic pseudo-coordinates", defined as suitable functionals of the Weyl curvature scalars, as tools for a peculiar gauge-fixing to the super-hamiltonian and super-momentum constraints; 4) the consequent construction of a "physical atlas" of 4-coordinate systems for the 4-dimensional "mathematical" manifold, in terms of the highly non-local degrees of freedom of the gravitational field (its four independent "Dirac observables"). Such construction embodies the "physical individuation" of the points of space-time as "point-events", independently of the presence of matter, and associates a "non-commutative structure" to each gauge fixing or four-dimensional coordinate system; 5) a clarification of the multiple definition given by Peter Bergmann of the concept of "(Bergmann) observable" in general relativity. This clarification leads to the proposal of a "main conjecture" asserting the existence of i) special Dirac's observables which are also Bergmann's observables, ii) gauge variables that are coordinate independent (namely they behave like the tetradic scalar fields of the Newman-Penrose formalism). A by-product of this achievements is the falsification of a recently advanced argument asserting the absence of (any kind of) "change" in the observable quantities of general relativity. 6) a clarification of the physical role of Dirac and gauge variables as their being related to "tidal-like" and "inertial-like" effects, respectively. This clarification is mainly due to the fact that, unlike the standard formulations of the equivalence principle, the Hamiltonian formalism allows to define notion of "force" in general relativity in a natural way; 7) a proposal showing how the physical individuation of point-events could in principle be implemented as an experimental setup and protocol leading to a "standard of space-time" more or less like atomic clocks define standards of time. We conclude that, besides being operationally essential for building measuring apparatuses for the gravitational field, the role of matter in the non-vacuum gravitational case is also that of "participating directly" in the individuation process, being involved in the determination of the Dirac observables. This circumstance leads naturally to a peculiar new kind of "structuralist" view of the general-relativistic concept of space-time, a view that embodies some elements of both the traditional "absolutist" and "relational" conceptions. In the end, space-time point-events maintain a "peculiar sort of objectivity". Some hints following from our approach for the quantum gravity programme are also given. (shrink)

The eliminative view of gauge degrees of freedom—the view that they arise solely from descriptive redundancy and are therefore eliminable from the theory—is a lively topic of debate in the philosophy of physics. Recent work attempts to leverage properties of the QCD $$\theta _{\text {YM}}$$ θ YM -term to provide a novel argument against the eliminative view. The argument is based on the claim that the QCD $$\theta _{\text {YM}}$$ θ YM -term changes under “large” gauge (...) transformations. Here we review geometrical propositions about fiber bundles that unequivocally falsify these claims: the $$\theta _{\text {YM}}$$ θ YM -term encodes topological features of the fiber bundle used to represent gauge degrees of freedom, but it is fully gauge-invariant. Nonetheless, within the essentially classical viewpoint pursued here, the physical role of the $$\theta _{\text {YM}}$$ θ YM -term shows the physical importance of bundle topology (or superpositions thereof) and thus counts against (a naive) eliminativism. (shrink)

Einstein's mass-energy equivalence law, argues de Broglie, by fixing the zero of the potential energy of a system,ipso facto selects a gauge in electromagnetism. We examine how this works in electrostatics and in magnetostatics and bring in, as a “trump card,” the familiar, but highly peculiar, system consisting of a toroidal magnet m and a current coil c, where none of the mutual energy W resides in the vacuum. We propose the principle of a crucial test for measuring the (...) fractions of W residing in m and in c; if the latter is nonzero, the (fieldless) vector potential has physicality. Also, using induction for transferring energy from the magnet to a superconducting current, we prove that W is equipartitioned between m and c. (shrink)

Hermann Weyl was one of the early contributors to the mathematics of general relativity. This article argues that in 1929, for the formulation of a general relativistic framework of the Dirac equation, he both abolished and preserved in modified form the conceptual perspective that he had developed earlier in his “analysis of the problem of space.” The ideas of infinitesimal congruence from the early 1920s were aufgehoben in the general relativistic framework for the Dirac equation. He preserved the central idea (...) of gauge as a “purely infinitesimal” aspect of symmetries in a group extension schema. With respect to methodology, however, Weyl gave up his earlier preferences for relatively a-priori arguments and tried to incorporate as much empiricism as he could. This signified a clearly expressed empirical turn for him. Moreover, in this step he emphasized that the mathematical objects used for the representation of matter structures stood at the center of the construction, rather than interaction fields which, in the early 1920s, he had considered as more or less derivable from geometrico-philosophical considerations. (shrink)

The concepts in the title refer to properties of physical theories and this paper investigates their nature and relations. The first three concepts, especially gauge invariance and indeterminism, have been widely discussed in connection to spacetime theories and the hole argument. Since the gauge invariance principle is at the crux of the issue, this paper aims at clarifying the nature of gauge invariance. I first explore the following chain of relations: gauge invariance $\Rightarrow $ the (...) conservation laws $\Rightarrow $ the Cauchy problem $\Rightarrow $ indeterminism. Then I discuss gauge invariance in light of our understanding of the above relations and the possibility of spontaneous symmetry breaking. (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, (...) class='Hi'>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)

As is well know from Einstein the choice of a criterion for distant simultaneity is equivalent to stipulating one-way speeds for the transit of light. It is shown that any choice of non-standard synchrony is equivalent to a Lorentz local time boost. From this and considerations from the hole argument, it follows that there is a non-trivial sense in which distant simultaneity is conventional, at least to the extent that the “gauge freedom” arising in the hole argument (...) is non-trivial. (shrink)

We develop some ideas about gauge symmetry in the context of Maxwell’s theory of electromagnetism in the Hamiltonian formalism. One great benefit of this formalism is that it pairs momentum and configurational degrees of freedom, so that a decomposition of one side into subsets can be translated into a decomposition of the other. In the case of electromagnetism, this enables us to pair degrees of freedom of the electric field with degrees of freedom of the vector potential. Another benefit (...) is that the formalism algorithmically identifies subsets of the equations of motion that represent time-dependent symmetries. For electromagnetism, these two benefits allow us to define gauge-fixing in parallel to special decompositions of the electric field. More specifically, we apply the Helmholtz decomposition theorem to split the electric field into its Coulombic and radiative parts, and show how this gives a special role to the Coulomb gauge (i.e. div \((\mathbf{A}) = 0\) ). We relate this argument to Maudlin’s (Entropy, 2018. https://doi.org/10.3390/e20060465 ) discussion, which advocated the Coulomb gauge. (shrink)

The equations of motion for a particle in a classical gauge field are derived from the invariance identities 2 and basic assumptions about the Lagrangian. They are found to be consistent with the equations of some other approaches to classical gauge-field theory, and are expressed in terms of a set of undetermined functions Eα. The functions Eα are found to satisfy a system of differential equations which has the same formal structure as a system of equations from Yang-Mills (...) theory. 3 These results are obtained by a new method which applies techniques from the theory of functional equations to deduce the way in which the arguments of the Lagrangian must combine. The method constitutes an aid for obtaining the equations of motion when a non-gauge-invariant Lagrangian is chosen, and it is assumed that the equations of motion can be written in a gauge-invariant manner. (shrink)

Those looking for holism in contemporary physics have focused their attention primarily on quantum entanglement. But some gauge theories arguably also manifest the related phenomenon of nonseparability. While the argument is strong for the classical gauge theory describing electromagnetic interactions with quantum “particles”, it fails in the case of general relativity even though that theory may also be formulated in terms of a connection on a principal fiber bundle. Anandan has highlighted the key difference in his analysis (...) of a supposed gravitational analog to the Aharonov-Bohm effect. By contrast with electromagnetism in the original Aharonov-Bohm effect, gravitation is separable and exhibits no novel holism in this case. Whether the nonseparability of classical gauge theories of non-gravitational interactions is associated with holism depends on what counts as the relevant part-whole relation. Loop representations of quantized gauge theories of non- gravitational interactions suggest that these conclusions about holism and nonseparability may extend also to quantum theories of the associated fields. (shrink)

Recently, Michael Redhead has argued that the grouping of particles into multiplets by grand unified gauge theories (GUT's) does not, by itself, imply an ontological reduction in the number of elementary particles. While sympathetic to Redhead's argument, in this note I argue that under certain conditions involving Kaluza-Klein theories, GUT's would provide such an ontological reduction.

This paper presents two interpretations of the fiber bundle formalism that is applicable to all gauge field theories. The constructionist interpretation yields a substantival spacetime. The analytic interpretation yields a structural spacetime, a third option besides the familiar substantivalism and relationalism. That the same mathematical formalism can be derived in two different ways leading to two different ontological interpretations reveals the inadequacy of pure formal arguments.

Recently two pairs of authors have aimed to vindicate the longstanding "orthodox" or conventional claim that a first-class constraint generates a gauge transformation in typical gauge theories such as electromagnetism, Yang-Mills and General Relativity, in response to the Lagrangian-equivalent reforming tradition, in particular Pitts, _Annals of Physics_ 2014. Both pairs emphasize the coherence of the extended Hamiltonian formalism against what they take to be core ideas in Pitts 2014, but both overlook Pitts 2014's sensitivity to ways that one (...) might rescue the claim in question, including an additive redefinition of the electrostatic potential. Hence the bulk of the paper is best interpreted as arguing that the longstanding claim about separate first-class constraints is _either false or trivial_---de-Ockhamization (using more when less suffices by splitting one quantity into the sum of two) being trivial. Unfortunately section 9 of Pitts 2014, a primarily verbal argument that plays no role in other works, is refuted. Pooley and Wallace's inverse Legendre transformation to de-Ockhamized electromagnetism with an additively redefined electrostatic potential, however, opens the door to a precisely analogous calculation introducing a photon mass, which shows that a _second-class primary_ constraint generates a 'gauge transformation' in the exactly same sense---a _reductio ad absurdum_ of the orthodox claim that a first-class constraint generates a gauge transformation _and a second-class constraint does not_. A _reductio_ using massive electromagnetism was presaged in Pitts 2014. Gauge freedom by de-Ockhamization does not require any constraints at all, first-class or second-class, because any dynamical variable in any Lagrangian can be de-Ockhamized into exhibiting trivial additive artificial gauge freedom by splitting one quantity into the sum of two. Physically interesting gauge freedom, however, is typically generated by a tuned sum of first-class constraints, not each first-class constraint alone. (shrink)

The Argument from Temporary Intrinsics is one of the canonical arguments against endurantism. I show that the two standard ways of presenting the argument have limited force. I then present a new version of the argument, which provides a more promising articulation of the underlying objection to endurantism. However, the premises of this argument conflict with the gauge theories of particle physics, and so this version of the argument is no more successful than its (...) predecessors. I conclude that no version of the Argument from Temporary Intrinsics gives us a compelling reason to favor one theory of persistence over another. (shrink)

Frege’s contribution to philosophical logic has been so overwhelming that little if any attention seems to have been paid to his remarks on epistemology. It is of course true that he never published a work exclusively concerned with epistemological issues. But his paper “The Thought” contains extensive treatment of matters concerning the theory of knowledge. Moreover the importance which he attributed to some of his remarks on specific epistemological problems can be gauged by the frequency with which he repeats them (...) throughout his writings. The introductions to the Foundations of Arithmetic and to the Basic Laws of Arithmetic contain much the same biting sarcastic onslaught upon idealism and psychologism. Similar points are repeated in his review of Husserl’s Philosophie der Arithmetik, in his paper “Negation”, and in other articles. His concern with epistemology is wholly determined by the bearing which it has upon philosophical logic. This is largely negative. Apart from the paper “The Thought” his remarks go only so far as is necessary in order for him to vindicate his doctrine of the purity of logic. Indeed even in that paper his motives are similar, but his treatment of the issues involved is more extensive and his own incompletely developed epistemological position shows through more clearly than elsewhere. An examination of his views is of value from two points of view, firstly it is of some intrinsic interest, secondly his position takes him to the threshold of Wittgenstein’s argument against the possibility of a private language. Moreover, as I shall try to show, the substance of his view is frequently the target of Wittgenstein’s critical discussion. (shrink)

Gary Gutting argues, in his recent book What Philosophers Know, that analytic philosophy provides a sizable collection of exemplary arguments that effectively yield a “disciplinary body of philosophical knowledge”—“metaphilosophy,” he names it—that is, specimens that define in a notably perspicuous way what we should understand as philosophical knowledge itself. He concedes weaknesses in the best-known specimens, and he admits that, generally, even the best specimens do not provide answers to the usual grand questions. I admire his treatment of the matter (...) but argue that the metaphilosophical issues are, normally, of a much grander gauge than that of his sort of specimen; that they require a much more open, informal sort of inquiry and exchange than that of the distinctive rigor of the classic specimens themselves; that analytic philosophy, not uncharacteristically, tends to ignore the metaphilosophical issue or takes the validity of its method of argument for granted; and that the issue itself invites an appraisal of competing second-order conceptions of how philosophical argument proves fruitful. I proceed by way of the examination of cases drawn from Quine and Kripke. (shrink)

In this paper I investigate, within the framework of realistic interpretations of the wave function in nonrelativistic quantum mechanics, the mathematical and physical nature of the wave function. I argue against the view that mathematically the wave function is a two-component scalar field on configuration space. First, I review how this view makes quantum mechanics non- Galilei invariant and yields the wrong classical limit. Moreover, I argue that interpreting the wave function as a ray, in agreement many physicists, Galilei invariance (...) is preserved. In addition, I discuss how the wave function behaves more similarly to a gauge potential than to a field. Finally I show how this favors a nomological rather than an ontological view of the wave function. (shrink)

Much recent philosophy of physics has investigated the process of symmetry breaking. Here, I critically assess the alleged symmetry restoration at the fundamental scale. I draw attention to the contingency that gauge symmetries exhibit, that is, the fact that they have been chosen from an infinite space of possibilities. I appeal to this feature of group theory to argue that any metaphysical account of fundamental laws that expects symmetry restoration up to the fundamental level is not fully satisfactory. This (...) is a symmetry argument in line with Curie’s first principle. Further, I argue that this same feature of group theory helps to explain the ‘unreasonable’ effectiveness of mathematics in physics, and that it reduces the philosophical significance that has been attributed to the objectivity of gauge symmetries. (shrink)

An academic division of labor resulted from the distinction between sex and gender. Sex remained a productive topic (excuse the pun) for biologists, who are interested in the genetic, developmental, and chemical pathways of male/female dimorphism. People in the social sciences and humanities, by contrast, made gender, not sex, the subject of their work. In gender studies, we learn about the ways that men and women “perform” their respective roles—people of male sex can perform as female gender, and vice versa, (...) by adopting modes of speech, dress, behavior, and even values. There is no talk of innate instincts or brain differences in gender studies. The French philosopher Michel Foucault set the agenda when he lamented, as early as 1976, that “the notion of sex made it possible to group together, in an artificial unity, anatomical elements, biological functions, conducts, sensations, and pleasures, and it enabled one to make use of this fictitious unity as a causal principle.” Following this approach, more-recent theorists like Anne Fausto-Sterling and Judith Butler have argued that even the biological categories of sex are just artificial inventions, designed to keep women and intersexed peoples down. Society, they suggest, decides which of us are males and which are females—pushing everyone into rigid binary categories. -/- There are two main arguments that are usually offered in defense of this controversial thesis that sexual dimorphism is political rather than ontological. One is based on a general critique of knowledge (an epistemological argument), and the other on a specific picture of reality (a metaphysical argument). I will offer counterarguments to both. (shrink)

I examine the relationship between \\)-dimensional Poincaré metrics and d-dimensional conformal manifolds, from both mathematical and physical perspectives. The results have a bearing on several conceptual issues relating to asymptotic symmetries in general relativity and in gauge–gravity duality, as follows: I draw from the remarkable work by Fefferman and Graham on conformal geometry, in order to prove two propositions and a theorem that characterise which classes of diffeomorphisms qualify as gravity-invisible. I define natural notions of gravity-invisibility that apply to (...) the diffeomorphisms of Poincaré metrics in any dimension. I apply the notions of invisibility, developed in, to gauge–gravity dualities: which, roughly, relate Poincaré metrics in \ dimensions to QFTs in d dimensions. I contrast QFT-visible versus QFT-invisible diffeomorphisms: those gravity diffeomorphisms that can, respectively cannot, be seen from the QFT. The QFT-invisible diffeomorphisms are the ones which are relevant to the hole argument in Einstein spaces. The results on dualities are surprising, because the class of QFT-visible diffeomorphisms is larger than expected, and the class of QFT-invisible ones is smaller than expected, or usually believed, i.e. larger than the PBH diffeomorphisms in Imbimbo et al. :1129, 2000, Eq. 2.6). I also give a general derivation of the asymptotic conformal Killing equation, which has not appeared in the literature before. (shrink)

The discovery that Einstein's celebrated argument for general covariance, the 'point-coincidence argument ', was actually a response to the ' hole argument ' has generated an intense philosophical debate in the last thirty years. Even if the philosophical consequences of Einstein's argument turned out to be highly controversial, the protagonists of such a debate seem to agree on considering Einstein's argument as an expression of 'Leibniz equivalence', a modern version of Leibniz's celebrated indiscernibility arguments against (...) Newton's absolute space. The paper attempts to show that the reference to Leibniz, however plausible at first sight, is actually in many respects misleading. In particular it is claimed that the Logical Empiricists offer a significant historical example of an attempt to interpret the point-coincidence argument as an indiscernibility argument in the sense of Leibniz, similar to those used in 19th century by Helmholtz, Hausdorff or Poincaré. However the logical empiricist account of General Relativity clearly failed to grasp the philosophical novelty of Einstein's theory. Thus, if Einstein's point coincidence/ hole argument can be regarded as an indiscernibility argument, it cannot be an indiscernibility argument in the sense of Leibniz. Einstein rather introduced a new form of indiscernibility argument, which might be better described as an expression of 'Einstein-equivalence'. Developing some ideas of Weyl it is argued that, whereas Leibniz's arguments introduced the notion of 'symmetry' in the history of science, Einstein's argument seems to anticipate what we now call 'gauge freedom'. If in the first case indiscernibility arises from a lack of mathematical structure, in the second case it is a consequence of a surplus of mathematical structure. _German_ Die Entdeckung, dass Einsteins berühmtes Punkt-Koinzidenz- Argument zur allgemeinen Kovarianz tatsächlich eine Reaktion auf die Lochbetrachtung war, hat in den vergangenen 30 Jahren zu einer intensiven philosophischen Debatte geführt. Auch wenn die philosophischen Konsequenzen äußerst kontrovers gesehen werden, stimmen die Protogonisten doch darin überein, das Argument als Ausdruck von Leibniz-Äquivalenz, mithin als eine moderne Version von Leibniz berühmten Ununterscheidbarkeitsargumenten gegen Newtons absoluten Raum aufzufassen. Ziel des Aufsatzes ist es zu zeigen, dass der Bezug zu Leibniz, wenn auch auf den ersten Blick plausibel, tatsächlich in vielerlei Hinsicht irreführend ist. Insbesondere wird dahingehend argumentiert, dass die Logischen Empiristen ein signifikantes historisches Beispiel für einen Versuch darstellen, das Punkt-Koinzidenz Argument als ein Ununterscheidbarkeitsargument im Sinne von Leibniz, ähnlich denen im 19. Jahrhundert von Helmholtz, Hausdorff und Poincaré vorgebrachten, zu deuten. Dieser Deutung der Allgemeinen Relativitätstheorie gelingt es aber nicht, das eigentlich philosophisch Neue von Einsteins Theorie plausibel zu interpretieren. Wenn Einsteins Punkt-Koinzidenz/Lochargument als ein Ununterscheidbarkeitsargument angesehen werden soll, kann dies kein Argument à la Leibniz sein. Vielmehr hat Einstein ein neuartiges Ununterscheidbarkeitsargument eingeführt, das vielleicht besser als,Einstein-Äquivalenz' charakterisiert werden sollte. Durch Aufnahme und Weiterentwicklung einiger Ideen von Weyl wird gezeigt, dass Leibniz' Argumente zwar das Konzept der,Symmetrie' in die Wissenschaftsgeschichte eingebracht haben, Einsteins Argument aber etwas antizipiert hat, was heute gewöhnlich,Eichfreiheit' genannt wird. Wird im ersten Fall die Ununterscheidbarkeit durch ein zu wenig an mathematischer Struktur erzeugt, so ist sie im zweiten Fall gerade die Folge eines Überschusses an mathematischer Struktur. (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)

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)

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)

After some background setting in which it is shown how Maudlin's (1989, 1990) response to the hole argument of Earman and Norton (1987) is related to that of Rynasiewicz (1994), it is argued that the syntactic proposals of Mundy (1992) and of Leeds (1995), which claim to dismiss the hole argument as an uninteresting blunder, are inadequate. This leads to a discussion of how the responses of Maudlin and Rynasiewicz relate to issues about gauge freedom and relativity (...) principles. (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)

It has long been a commonplace that there is a problem understanding the role of time when one tries to quantize the General Theory of Relativity (GTR). In his "Thoroughly Modern McTaggart" (Philosophers' Imprint Vol 2, No. 3), John Earman presents several arguments to the conclusion that there is a problem understanding change and the passage of time in the unadorned GTR, quite apart from quantization. His Young McTaggart argues that according to the GTR, no physical magnitude ever changes. A (...) close consideration of Young McTaggart's arguments show that they turn on either a bad choice of formalism or an unwarranted interpretation of the implications of the formalism. This suggests that the problems that arise in quantization may be founded in similar shortcomings. (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 (1999) reading of the gauge argument that may help to solve, or dissolve, its puzzling aspects. In Section 3 I contend that Sunny Auyang's (1999) 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 (1999) proposal for hyperplane-dependent Newton-Wigner fields differs importantly from his previous arguments about hyperplane-dependent properties in quantum mechanics. (shrink)

"Ever since the explosion in relationships of power during the 1960s, the humanities have become a battlefield. What had previously been thought of as merely academic concerns have spilled over academic boundaries and attracted the attention of politicians, government officials, members of the media, and, ultimately, the general public. As a way of addressing this turmoil, Karlis Racevskis considers the legacy of the Enlightenment and revaluates modernity's claims for objective knowledge and the traditional model of reason. How relevant, he asks, (...) are the Enlightenment ideals of freedom, democracy, and equality in today's attempts to understand society and gauge the prospects for civilization? What responsibility can or should intellectuals assume in promoting Enlightenment values? What, in the end, constitutes a humanistic education?" "Drawing largely on the work of Foucault, Racevskis elucidates the philosophical and political problems at issue in the debate and the changes taking place in our ways of seeing ourselves and our relations with others. He shows how the theme of enlightenment has been a central component in the conflicts that pit modernists against postmodernists, Marxists against post-Marxists, and liberals against conservatives, and he juxtaposes the arguments in such a way as to place reason and enlightened action in a new perspective. One result of the upheaval, argues Racevskis, is a sense of renewed purpose and intensity in the study of the humanities that constitutes a fundamental reorientation in our ways of understanding society. Viewing the tension between the chaos of current theories and the comfort of traditional values, not with horror but with excitement, he suggests how postmodern criticism can be seen as a dynamic and promising development in the renewal and expansion of the liberal arts." "This wide-ranging book should have general appeal across a broad spectrum of disciplines-among them, literature and the arts, philosophy, social and political theory, and intellectual history."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved. (shrink)

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)

Following the argument of Pusey et al. (in Nature Phys. 8:476, 2012), new interest has been raised on whether one can interpret state-vectors (pure states) in a statistical way (ψ-epistemic theories), or if each one of them corresponds to a different ontological entity. Each interpretation of quantum theory assumes different ontology and one could ask if the PBR argument carries over. Here we examine this question for histories formulations in general with particular attention to the co-event formulation. State-vectors (...) appear as the initial state that enters into the quantum measure. While the PBR argument goes through up to a point, the failure to meet some of the assumptions they made does not allow one to reach their conclusion. However, the author believes that the “statistical interpretation” is still impossible for co-events even if this is not proven by the PBR argument. (shrink)

ABSTRACT Despite the claim in Miroslav Imbrišević’s paper about differences between the positions of Jon Pike and myself, there are also significant overlaps. I endorsed the WR consultative process that Jon was part of, agreed that Jon had produced a compelling argument, and agreed with the lexical framework of the argument. Miroslav’s major contentions with my argument appears to be that it dresses up patriarchal outcomes in feminist clothes, and that it ignores the voices of women [athletes] (...) in coming to its conclusions. In this paper, I address the charges by suggesting that both emanate from Miroslav’s attempts to see gender critical feminism as the gauge against which all positions need to be judged. My position is that this school of feminism will lead to largely conservative outcomes in the discursive and organizational hierarchies in sport, so that any individual benefits that accrue to female athletes will be less substantial than the loss of transformational potential in women’s sport. (shrink)

In their modern classic ``What Price Substantivalism? The Hole Story'' Earman and Norton argued that substantivalism about spacetime points implies that general relativity is indeterministic and, for that reason, must be rejected as a candidate ontology for the theory. More recently, Earman has cottoned on to a related argument (in fact, related to a \emph{response} to the hole argument) that arises in the context of canonical general relativity, according to which the enforcing of determinism along standard lines---using the (...) machinery of gauge theory---leads to a `frozen universe' picture (grounded in an absence of changes in values of general relativity's observables). \emph{Prima facie} this would seem to land the anti-substantivalist in waters at least as deep as those that Earman and Norton argued troubled substantivalism. In this paper I introduce the argument in what I think are clearer terms than Earman's, and assess his treatment of the problem. For the most part I agree with Earman about the nature of the problem, but I find aspects of his discussion wanting, especially as regards his proposed ontology. I argue that ontological sense can be made of the changelessness if a structuralist stance is adopted with respect to a natural class of observables. (shrink)

When confronted with the question of which philosophical conception of religion to consider most adequate, many philosophers appeal to what I call the adequacy-argument: that we should prefer the one that looks most adequate from the perspective of religious believers. In this paper, I provide a critique of the adequacy-argument based on a pragmatic analysis of adequacy-judgments according to which reflective adequacy-judgments are forward-looking, and hence include considerations of the consequences of adopting different judgments as guides for conduct. (...) It is this forward-looking character that is virtually absent within the current adequacy-debate. The major advantage of a pragmatic analysis of adequacy is itself forward-looking: it would enable philosophers of religion to play a more critical and constructive role vis-à-vis religious practices than presently. (shrink)

The paper deals with an attempt to present an “abductive-transcendental” argument in favour of a particular version of structural realism (SR), dubbed Intermediate SR. In the first part of the paper the general structure of transcendental arguments is scrutinized with a close view on Kant’s original version and the prospect of their abductive variation. Then the role of symmetries in modern physics, especially symmetries without real instantiations and in particular gauge symmetries is discussed. This is combined with a (...) presentation of SR as a promising current version of scientific realism. The discussion is supported by various arguments form gauge theories in modern physics. Intermediate SR, a realist position about all and only structurally derivable entities located between the extremes of Epistemic and Ontic SR turns out as the best fit to our current fundamental gauge physics and this finally leads to an abductive-transcendental reasoning concerning this position. (shrink)

In this paper, I critically examine an important premise in theories of global distributive justice that, despite its widespread influence, has remained largely unexamined. This is the claim that state borders are morally arbitrary with respect to a just distribution of goods. I examine two common arguments for this claim, the argument that state borders are historically unjust and therefore morally arbitrary; and the argument first made by Charles Beitz that the conditions of a fair, hypothetical social contract (...) would not include knowledge of one's location with respect to the distribution of natural resources between state borders. I argue that there are good reasons to reject both arguments. Beitz's immense contribution to international justice can be gauged by the fact that it is difficult to find a contemporary work on global justice that does not reference his arguments in Political Theory and International Relations . Although some authors find Beitz's cosmopolitan theory objectionable, no author has, to my knowledge, criticized Beitz's pivotal arguments that our placement in the distribution of natural resources is morally arbitrary. The aim of this paper is to do just that. (shrink)

Assessing the scientific status of theories of consciousness is often a difficult task. In this paper, I explore the dialectic between the Integrated Information Theory, e1003588, 2014; Tononi et al. Nat Rev Neurosci, 17, 450-61, 2016) and a recently proposed criticism of that theory: the ‘unfolding argument’. I show that the phenomenology-first approach in consciousness research can lead to valid scientific theories of consciousness. I do this by highlighting the two reasons why the unfolding argument fails: first, phenomenology-first (...) theories are grounded, not circular. Second, falsificationism does not provide an adequate demarcation criterion in philosophy of science. I conclude that this specific debate has significance for how, in general, consciousness researchers test and criticize theories of consciousness, and how dismissing the phenomenology-first methodology in favour of a third person-based methodology means endorsing a position in philosophy of mind that has already been challenged. (shrink)

This dissertation is an attempt to examine the role of historical argument in political theory. Its main contention is that political theory, rather than relying on concepts of abstract right and timeless duty, often attempts to convince by giving its readers a particular sense of history. I argue that authors of political theory in many instances present to their readers a narrative, rather than a logic, of politics. Political theory persuades not simply by reason but by giving the reader (...) a more convincing account of history and of the particular role s/he is to play. Consequently, I maintain, we put our own powers of interpretation in a strait-jacket if we approach each book of political theory only in search of an everlasting argument. Our readings will be more fruitful if we consider the qualities of historical argument alongside those of abstract right. The project of political theory, I conclude, is not so much to reform our morals as it is to reform our memories. ;The weight of my argument falls on extended interpretations of three figures in the history of political thought: G. W. F. Hegel, John Locke, and Friedrich Nietzsche. My aim in each chapter is to show that these theorists are at their most persuasive when the historical element in their thought is brought to the forefront. Taken together, however, they do not provide a single 'historical' viewpoint; instead they offer markedly different narratives which rest on different notions of human experience: Locke's account stresses labor, both mental and physical. Hegel's story is rooted in his understanding of art and beauty. Nietzsche's history centers on matters of violence and pain. ;In the prologue and conclusion I consider how political debates can often appear as historical disputes . By reading political theory with an eye to history, I hope to restore it to a position from which it can contribute to such controversies and speak directly to some of our political concerns, even if it must remain, to some degree, persistently aloof from them. (shrink)