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.

Symmetries in physics are most commonly recognized and discussed in terms of their function in the mathematical formalism of the theories. Discussion of the observation of symmetries in nature is less common. This paper analyses the observation of particular symmetries such as Lorentz and gauge symmetries, distinguishing between direct observation of the symmetry itself and indirect evidence, the latter being the observation of some consequence of the symmetry are, in an important sense, directly observed, while local symmetries such as gauge (...) symmetry are not. (shrink)

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.

Vers 1918 Hermann Weyl abandonnait le logicisme et donc la tentative de réduire les mathématiques à la logique et la théorie des ensembles. Au niveau philosophique, ses points de référence furent ensuite Husserl et Fichte. Dans les années 1920 il distingua leurs positions, entre une direction intuitionniste-phénoménologique d’un côté, et formaliste-constructiviste de l’autre. Peu après Weyl, Oskar Becker adopta une distinction similaire. Mais à la différence du phénoménologue Becker, Weyl considérait l’approche active du constructivisme de Fichte comme supérieure à la (...) vision d’essences passive de Husserl. Dans cet essai, je montre ce développement dans la pensée de Weyl. Bien que certains points dans sa réception de Husserl et Fichte ne soient pas soutenables, je vais argumenter en faveur de la distinction fondamentale mentionnée ci-dessus. (shrink)

Vers 1918 Hermann Weyl abandonnait le logicisme et donc la tentative de réduire les mathématiques à la logique et la théorie des ensembles. Au niveau philosophique, ses points de référence furent ensuite Husserl et Fichte. Dans les années 1920 il distingua leurs positions, entre une direction intuitionniste-phénoménologique d’un côté, et formaliste-constructiviste de l’autre. Peu après Weyl, Oskar Becker adopta une distinction similaire. Mais à la différence du phénoménologue Becker, Weyl considérait l’approche active du constructivisme de Fichte comme supérieure à la (...) vision d’essences passive de Husserl. Dans cet essai, je montre ce développement dans la pensée de Weyl. Bien que certains points dans sa réception de Husserl et Fichte ne soient pas soutenables, je vais argumenter en faveur de la distinction fondamentale mentionnée ci-dessus. (shrink)

We propose a group-theoretical interpretation of the fact that the transition from classical to quantum mechanics entails a reduction in the number of observables needed to define a physical state and \ to \ or \ in the simplest case). We argue that, in analogy to gauge theories, such a reduction results from the action of a symmetry group. To do so, we propose a conceptual analysis of formal tools coming from symplectic geometry and group representation theory, notably Souriau’s moment (...) map, the Mardsen–Weinstein symplectic reduction, the symplectic “category” introduced by Weinstein, and the conjecture according to which “quantization commutes with reduction”. By using the generalization of this conjecture to the non-zero coadjoint orbits of an abelian Hamiltonian action, we argue that phase invariance in quantum mechanics and gauge invariance have a common geometric underpinning, namely the symplectic reduction formalism. This stance points towards a gauge-theoretical interpretation of Heisenberg indeterminacy principle. We revisit this principle in the light of the difference between the set-theoretic points of a phase space and its category-theoretic symplectic points. (shrink)

Dans cet article, nous entendons montrer que les principes d’invariance interviennent de manière essentielle pour caractériser les lois de la nature en physique. Pour ce faire, nous nous focaliserons sur les réflexions épistémologiques que Weyl et Wigner consacrent aux symétries. Nous proposerons une analyse conceptuelle de l’invariance en indiquant qu’elle permet de généraliser la première analogie de l’expérience de Kant (le principe de permanence de la substance). Nous analyserons de plus l’argument de Weyl selon lequel les principes d’invariance constituent des (...) connaissances a priori en un sens relativisé. Nous indiquerons pour finir qu’aux yeux de Wigner, les « symétries » constituent des conditions qui nous permettent de structurer notre compréhension de la réalité empirique. (shrink)

Dans cet article, nous entendons montrer que les principes d’invariance interviennent de manière essentielle pour caractériser les lois de la nature en physique. Pour ce faire, nous nous focaliserons sur les réflexions épistémologiques que Weyl et Wigner consacrent aux symétries. Nous proposerons une analyse conceptuelle de l’invariance en indiquant qu’elle permet de généraliser la première analogie de l’expérience de Kant (le principe de permanence de la substance). Nous analyserons de plus l’argument de Weyl selon lequel les principes d’invariance constituent des (...) connaissances a priori en un sens relativisé. Nous indiquerons pour finir qu’aux yeux de Wigner, les « symétries » constituent des conditions qui nous permettent de structurer notre compréhension de la réalité empirique. (shrink)

We propose a conceptual framework for understanding the relationship between observables and operators in mechanics. To do so, we introduce a postulate that establishes a correspondence between the objective properties permitting to identify physical states and the symmetry transformations that modify their gauge dependant properties. We show that the uncertainty principle results from a faithful—or equivariant—realization of this correspondence. It is a consequence of the proposed postulate that the quantum notion of objective physical states is not incomplete, but rather that (...) the classical notion is overdetermined. (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.

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)

In a recent paper in this journal, Kosso ([2000]) discussed the observational status of continuous symmetries of physics. While we are in broad agreement with his approach, we disagree with his analysis. In the discussion of the status of gauge symmetry, a set of examples offered by 't Hooft ([1980]) has influenced several philosophers, including Kosso; in all cases the interpretation of the examples is mistaken. In this paper, we present our preferred approach to the empirical significance of symmetries, re-analysing (...) the cases of gauge symmetry and general covariance. Direct and indirect empirical significance Global and local continuous symmetries Gauge symmetry 3.1 Local gauge symmetry 3.1.1 Discussion of the first claim 3.1.2 Discussion of the second claim 3.2 Global gauge symmetry Space-time symmetries Direct and indirect empirical significance again Conclusion. (shrink)

It is widely recognized that ‘global’ symmetries, such as the boost invariance of classical mechanics and special relativity, can give rise to direct empirical counterparts such as the Galileo-ship phenomenon. However, conventional wisdom holds that ‘local’ symmetries, such as the diffeomorphism invariance of general relativity and the gauge invariance of classical electromagnetism, have no such direct empirical counterparts. We argue against this conventional wisdom. We develop a framework for analysing the relationship between Galileo-ship empirical phenomena on the one hand, and (...) physical theories that model such phenomena on the other, that renders the relationship between theoretical and empirical symmetries transparent, and from which it follows that both global and local symmetries can give rise to Galileo-ship phenomena. In particular, we use this framework to exhibit an analogue of Galileo’s ship for the local gauge invariance of electromagnetism. 1 Introduction2 Analogues of Galileo’s Ship? Faraday’s Cage and t’Hooft’s Beam-Splitter2.1 Faraday’s cage2.2 t’Hooft’s beam-splitter3 A Framework for Symmetries I: Systems and Subsystems4 An Example: Coulombic Electrostatics5 A Framework for Symmetries II: The Relationship between Theoretical and Empirical Symmetries6 Newtonian Gravity7 Local Symmetries that Are Not Boundary-Preserving: Classical Electromagnetism and Faraday’s Cage8 Local Boundary-Preserving Symmetries: Klein-Gordon-Maxwell Gauge Theory and t’Hooft’s Beam-Splitter9 Summary10 Conclusions. (shrink)

Dans un discours prononcé à Zurich vers la fin des années 1940, Hermann Weyl a examiné l'épistémologie dialectique de Ferdinand Gonseth et l'a considérée comme trop strictement limitée aux aspects de changement historique. Son expérience de la philosophie diaclectique post-kantienne, en particulier la dérivation du concept de l'espace et de la matière chez Johann Gottlieb Fichte, avait constitué une base dialectique solide pour ses propres études de 1918 en une géométrie purement infinitésimale et la théorie antérieure d'un champ de matière (...) géométriquement unifié (en prolongement du programme Mie-Hilbert). Bien que Weyl se fût alors éloigné des aspects spéculatifs de la philosophie de sa jeunesse et eût montré, en particulier, moins d'enthousiasme qu'auparavant pour Fichte, il nourrissait encore de nombreux doutes sur la base culturelle de la science mathématique moderne et sur son rôle dans la culture matérielle du modernisme de pointe. Pour Weyl, la « réflexion » philosophique était une nécessité culturelle ; il se tourna alors vers lexistentialisme de Karl Jaspers et de Martin Heidegger pour trouver des raisons plus profondes, dans un mouvement comparable à son orientation vers la philosophie de Fichte après la Première Guerre mondiale. Le débat de la fin des années 1940 peut être compris comme une sorte de supplément postérieur à la Seconde Guerre mondiale par rapport à ses commentaires plus connus sur les mathématiques et les sciences naturelles publiés au milieu des années 1920. (shrink)

Eugene Wigner's several general discussions of symmetry and invariance principles are among the canonical texts of contemporary philosophy of physics. Wigner spoke from a position of authority, having pioneered for recognition of the importance of symmetry principles from nuclear to molecular physics. But perhaps recent commentators have not sufficiently stressed that Wigner always took care to situate the notion of invariance principles with respect to two others, initial conditions and laws of nature. Wigner's first such general consideration of invariance principles, (...) an address presented at Einstein's 70th birthday celebration, held in Princeton on 19 March 1949, began by laying out just this distinction, and in a way that seems to suggest that the three notions arise through abstraction in an analysis of the general problem of cognition in the natural sciences: The world is very complicated and it is clearly impossible for the human mind to understand it completely. Man has therefore devised an artifice which permits the complicated nature of the world to be blamed on something which is called accidental and thus permits him to abstract a domain in which simple laws can be found. The complications are called initial conditions; the domain of regularities, laws of nature. the underlying abstraction is probably one of the most fruitful the human mind has made. It has made the natural sciences possible. (shrink)