Gauge-invariance and the empirical significance of symmetries

Foundations of Physics, 2024

There is solid consensus among physicists and philosophers that, in gauge field theory, for a quantity to be physically meaningful or real, it must be gauge-invariant. Yet, every “elementary” field in the Standard Model of particle physics is actually gauge-variant. This has led a number of researchers to insist that new manifestly gauge-invariant approaches must be established. Indeed, in the foundational literature, dissatisfaction with standard methods for reducing gauge symmetries has been expressed: Spontaneous symmetry breaking is deemed conceptually dubious, while gauge fixing suffers the same limitations and is subject to the same criticisms as coordinate choices in General Relativity. An alternative gauge-invariant proposal was recently introduced in the literature, the so-called “dressing field method” (DFM). It is a mathematically subtle tool, and unfortunately prone to be confused with simple gauge transformations, hence with standard gauge fixings. As a matter of fact, in the physics literature the two are often conflated, and in the philosophy community some doubts have been raised about whether there is any substantial difference between them. Clarifying this issue is of special significance for anyone interested in both the foundational issues of gauge theories and their invariant formulation. It is thus our objective to establish as precisely as possible the technical and conceptual distinctions between the DFM and gauge fixing.

2010

We motivate the concept of emergent gauge symmetry and discuss ways that this concept can be tested. The key idea is that if a symmetry is emergent, one should look for small violations of this symmetry because the underlying fundamental theory does not contain the symmetry. We describe our recent work implementing this idea in the gravity sector. We also

Richard Healey's talk was divided in two parts. In the first part he argued that we are not justified in believing that localized gauge potential properties are there, but we are in believing that holonomy properties are. In the second part, he conceded that the holonomy interpretation offers an incomplete local and causal account, but he maintained that the onus is on QM.

Annales De La Fondation Louis De Broglie, 2005

"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The physically meaningful degrees of freedom then reemerge as being those invariant under a transformation connecting the variables (gauge transformation). Thus, one introduces extra variables to make the description more transparent and brings in at the same time a gauge symmetry to extract the physically relevant content. It is a remarkable occurrence that the road to progress has invariably been towards enlarging the number of variables and introducing a more powerful symmetry rather than conversely aiming at reducing the number of variables and eliminating the symmetry" [1]. We claim that the potentials of Classical Electromagnetism are not indetermined with respect to the so-called gauge transformations. Indeed, these transformations raise paradoxes that imply their rejection. Nevertheless, the potentials are still indetermined up to a constant.

2005

Symmetry considerations stand at the core of classical and quantum physics. No modern-and few older-physical theories forgo the immense services that these considerations offer. It is therefore only natural that philosophers of physics have increasingly started to study the motivations for, as well as the technical implementations and the interpretative implications of, symmetries in fundamental physics. Apart from the extraordinary foundational interest of symmetries, they provide a vehicle to study more general philosophical issues such as the relation between the physical world and its representations and between physics and mathematics. Moreover, traditional problems in metaphysics and philosophy of science such as the nature and status of laws of nature, scientific realism, and determinism naturally arise in, and enjoy substantial fertilisation from, the context of symmetries in physics. This volume, edited by Katherine Brading and Elena Castellani, which grew out of a workshop held at Oxford in 2001, thus fulfills the felt need to collect the current philosophical debates on different aspects of symmetries in physics. The editors declare at the outset that their intention was to offer a ''format that would provide a point of entry into the subject for non-experts, including students and philosophers of science in general.'' (p. ix) Indeed, some of the articles are clearly accessible (and relevant!) to this wider audience. A number of articles-among them some of the most interesting contributions-, however, presuppose at least a willingness on the part of the reader to engage with more technical material. Although this may partially undermine the editors' expressed intention, they need not worry, for these articles will stir the interest of the specialist. What is more, some of the contributions present splendid and truly didactical reviews of the core issues in the subject and will therefore be of great service in advanced courses in the foundations and philosophy of physics. Please join me in more extensively exploring the collection, which is divided into four parts. Part I concerns continuous symmetries and constitutes the most voluminous section of the collection. After brief selections of classic texts on the subject by Weyl and Wigner, Christopher Martin sets out to survey the role and significance of continuous symmetries in fundamental physics and to introduce the philosophical

2021

A fundamental tenet of gauge theory is that physical quantities should be gaugeinvariant. This prompts the question: can gauge symmetries have physical significance? On one hand, the Noether theorems relate conserved charges to symmetries, endowing the latter with physical significance, though this significance is sometimes taken as indirect. But for theories in spatially finite and bounded regions, the standard Noether charges are not gauge-invariant. I here argue that gauge-variance of charges is tied to the nature of the non-locality within gauge theories. I will flesh out these links by providing a chain of (local) implications: ‘local conservation laws ’⇒ ‘conserved regional charges ’ ⇔ ‘non-separability ’ ⇔ ‘direct empirical significance of symmetries ’.

arXiv: Logic, 2020

Quantum field theory has successfully generated a number of general conclusions. It seems meaningful to disclose the logical forms of these conclusions. The present paper reports two results. The first result shows the logic of local gauge symmetry and indefinability of mass. The second result shows the logic of Higgs mechanism and definability of mass. The results are obtained by integrating four components, namely, gauge symmetry and Higgs mechanism in quantum field theory, and incompleteness theorem and indefinability theorem in mathematical logic. Godel numbering is the key for arithmetic modeling applied in this paper.

Arxiv preprint arXiv:0911.5400, 2009

Einstein considered general covariance to characterize the novelty of his General Theory of Relativity (GTR), but Kretschmann thought it merely a formal feature that any theory could have. The claim that GTR is "already parametrized" suggests analyzing substantive general covariance as formal general covariance achieved without hiding preferred coordinates as scalar "clock fields," much as Einstein construed general covariance as the lack of preferred coordinates. Physicists often install gauge symmetries artificially with additional fields, as in the transition from Proca's to Stueckelberg's electromagnetism. Some post-positivist philosophers, due to realist sympathies, are committed to judging Stueckelberg's electromagnetism distinct from and inferior to Proca's. By contrast, physicists identify them, the differences being gauge-dependent and hence unreal. It is often useful to install gauge freedom in theories with broken gauge symmetries (second-class constraints) using a modified Batalin-Fradkin-Tyutin (BFT) procedure. Massive GTR, for which parametrization and a Lagrangian BFT-like procedure appear to coincide, mimics GTR's general covariance apart from telltale clock fields. A generalized procedure for installing artificial gauge freedom subsumes parametrization and BFT, while being more Lagrangian-friendly than BFT, leaving any primary constraints unchanged and using a non-BFT boundary condition. Artificial gauge freedom licenses a generalized Kretschmann objection. However, features of paradigm cases of artificial gauge freedom might help to demonstrate a principled distinction between substantive and merely formal gauge symmetry.

Journal of Student Research

The concept of symmetry is essential in understanding classical and quantum physics. Symmetry describes a system that remains unchanged in structure and behavior after undergoing a transformation. In this paper, I will describe the implications of symmetries (global and gauge) in Newton’s laws of mechanics, Maxwell’s electromagnetism equations, and quantum particle physics – in particular the Higgs mechanism – with the help of Noether’s Theorem. Purely based on symmetrical elements, this paper will then determine the isospin composition of pions given certain restraints. This solution will connect findings in preceding theories to current and future studies relevant to the subject of symmetry in physics.

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 (e.g. from q and p to q or p 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 (proposed by Guillemin and Sternberg) 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 (the extreme cases of) this principle in the light of the difference between the set-theoretic points of a phase space and its category-theoretic symplectic points.

2021

The following questions are germane to our understanding of gauge-(in)variant quantities and physical possibility: in which ways are gauge transformations and spacetime diffeomorphisms similar, and in which are they different? To what extent are we justified in endorsing different attitudes—sophistication, quidditism/haecceitism, or full elimination—towards each? In a companion paper, I assess new and old contrasts between the two types of symmetries. In this one, I propose a new contrast: whether the symmetry changes pointwise the dynamical properties of a given field. This contrast distinguishes states that are related by a gauge-symmetry from states related by generic spacetime diffeomorphisms, as being ‘pointwise dynamically indiscernible’. Only the rigid isometries of homogeneous spacetimes fall in the same category, but they are neither local nor modally robust, in the way that gauge transformations are. In spite of this difference, I argue that for both gauge transformations ...

European Journal for Philosophy of Science

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.

International Conference paper, 2002

We reconsider the role of Lorentz invariance in the dynamical generation of the observed internal symmetries. This invariance could only be imposed in the sense that all non-invariant effects caused by the spontaneous breakdown of Lorentz symmetry (SBLS) were physically unobservable. Remarkably, the application of this principle to the most general relativistically invariant Lagrangian, with arbitrary couplings for all the fields involved, leads by itself to the appearance of a symmetry and, what is more, to the massless vector fields gauging this symmetry in both Abelian and non-Abelian cases. In contrast, purely global symmetries are only emerged as accidental consequences of the gauge symmetry. A simple model for the SBLS based on massive vector and real scalar field interactions is considered; it is found that spontaneously broken gauge symmetries could also appear, when SBLS happens and is required to be physically unobservable. chkareuli˙MATINYAN*70:

Computers & mathematics with applications, 1989

The insights we have acquired about symmetries during the past 25 years have not only contributed to the construction of successful explanatory schemata in elementary particle physics, they have also modified the conceptual framework within which a series of philosophical and methodological issues of elementary physics are discussed. The atomistic paradigm of high energy physics cannot any more be dismissed because the proposed elementary particles are too many (and, hence, it is claimed, they do not provide a simple account of nature) or because it is not possible to observe quarks in an isolated manner. The developments in particle physics have brought about radical changes to our notions of simplicity and observability, and in this paper we elaborate on these changes. It is as a result of these changes that the present situation in elementary particle physics justify us to claim that we have indeed reached a level of explanation where the constituent particles (quarks, leptons, gluons and intermediate bosons) used for the explanation of the various phenomena considered to be delineating a particular level in the descriptive framework of the physical phenomena and a specific stratum in the organization of nature, can be regarded as elementary. "We call a piece of matter an elementary particle when it has no other kinds of particles inside of it and no subparts that can be identified--we think of it as a point particle." And as for the subject itself it is stated that: "The nature and purposes of elementary particle physics concern both the discovery of new phenomena exhibited by matter (and other forms of energy) under extreme conditions and the understanding of known phenomena."

PhDT, 2008

This dissertation updates the debate over the nontriviality of general covariance for Einstein's General Theory of Relativity (GTR) and considers particle physics in the debate over underdetermination and empirical equivalence. Both tasks are tied to the unexplored issue of artificial gauge freedom, a valuable form of descriptive redundancy. Whereas Einstein took general covariance to characterize GTR, Kretschmann thought it merely a formal feature that any theory could have. Anderson and Friedman analyzed substantive general covariance as the lack of absolute objects, fields the same in all models. Some extant counterexamples and a new one involving the electron spinor field are resolved. However, Geroch and Giulini diagnose an absolute object in GTR itself in the metric's volume element. One might instead analyze substantive general covariance as formal general covariance achieved without hiding preferred coordinates as scalar "clock fields," recalling Einstein's early views. Theories with no metric or multiple metrics make the age of the universe meaningless or ambiguous, respectively, so the ancient and medieval debate over the eternity of the world should be recast. Particle physics provides case studies for empirical equivalence. Proca's electromagnetism with some nonzero photon mass constitutes a family of rivals to