Merely approximate symmetry is mundane enough in physics that one rarely finds any explication of it. Among philosophers it has also received scant attention compared to exact symmetries. Herein I invite further consideration of this concept that is so essential to the practice of physics and interpretation of physical theory. After motivating why it deserves such scrutiny, I propose a minimal definition of approximate symmetry—that is, one that presupposes as little structure on a physical theory to which it is applied (...) as seems needed. Then I apply this definition to three topics: first, accounting for or explaining the symmetries of a theory emeritus in intertheoretic reduction; second, explicating and evaluating the Curie-Post principle; and third, a new account of accidental symmetry. (shrink)

Suppose that all non-qualitative facts are grounded in qualitative facts. I argue that this view naturally comes with a picture in which trans-world identity is indeterminate. But this in turn leads to either pervasive indeterminacy in the non-qualitative, or else contingency in what facts about modality and possible worlds are determinate.

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)

Pierre Curie claimed that a symmetry of a cause must be found in the produced effects. This paper shows why this principle works in Curie’s example of the electrostatics of central fields, but fails in many others. The failure of Curie’s claim is then shown to be of special empirical interest, in that this failure underpins the experimental discovery of parity violation and of CP violation in the twentieth century.

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 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)

The line of argument pursued in this paper is to proceed from Einstein’s fundamental problem situation to a consideration of scientific representation with respect to the Special theory of relativity (STR). Einstein’s fundamental problem situation, which is Kantian in spirit, is how the conceptual freedom of the scientist is compatible with the need for an objective representation of an independently given material world. To solve this philosophical issue Einstein employs a number of constraints, which are central to the STR. The (...) issue of scientific representation leads to a consideration of the notion of reality and to the realistic commitments implied in the STR. From this point of view, the paper concludes that Einstein was committed to a kind of ‘structural’ realism. (shrink)

The paper presents a historical-epistemological analysis of the notion of “spontaneous symmetry breaking”, which I believe today provides a template for conceiving the relationship between symmetry and asymmetry in physics as well as in other areas of the natural sciences. The central thesis of the paper is that spontaneous symmetry breaking represents an instance of “narrative knowing” in the sense developed by recent research in history and philosophy of science (Morgan and Wise (eds) SI narrative in science, Studies in history (...) and philosophy of science, 2017a). Spontaneous symmetry breaking is best understood as a hybrid narrative comprising formulas, verbal statements, images, and at times also other media. This flexible notion can be deployed in different variations, allowing to explain a broad range of non-symmetric phenomena or models as resulting from (not necessarily observable) processes of loss of symmetry. I will support this thesis by first analysing in detail the way in which spontaneous symmetry breaking, and in particular electroweak symmetry breakdown, are presented in today’s physics textbooks and reference works, and then by reconstructing the emergence of the hybrid construct from the late 1950s until the 1970s, when spontaneous symmetry breaking definitively established itself as a key physical notion. (shrink)

Quantum phenomena are notoriously difficult to grasp. The present paper first reviews the most important quantum concepts in a non-technical manner: superposition, uncertainty, collapse of the wave function, entanglement and non-locality. It then tries to clarify these concepts by examining their analogues in complex, self-organizing systems. These include bifurcations, attractors, emergent constraints, order parameters and non-local correlations. They are illustrated with concrete examples that include Rayleigh–Bénard convection, social self-organization and Gestalt perception of ambiguous figures. In both cases, quantum and self-organizing, (...) the core process appears to be a symmetry breaking that irreversibly and unpredictably “collapses” an ambiguous state into one of a number of initially equivalent “eigenstates” or “attractors”. Some speculations are proposed about the non-linear amplification of quantum fluctuations of the vacuum being ultimately responsible for such symmetry breaking. (shrink)

Curie’s principle asserts that every symmetry of a cause manifests as a symmetry of the effect. It can be formulated as a tautology that is vacuous until it is instantiated. However instantiation requires us to know the correct way to map causal terminology onto the terms of a science. Causal metaphysics has failed to provide a unique, correct way to carry out the mapping. Thus successful or unsuccessful instantiation merely reflects our freedom of choice in the mapping.

Despite remarkable efforts, it remains notoriously difficult to equip quantum theory with a coherent ontology. Hence, Healey (2017, 12) has recently suggested that ‘‘quantum theory has no physical ontology and states no facts about physical objects or events’’, and Fuchs et al. (2014, 752) similarly hold that ‘‘quantum mechanics itself does not deal directly with the objective world’’. While intriguing, these positions either raise the question of how talk of ‘physical reality’ can even remain meaningful, or they must ultimately embrace (...) a hidden variables-view, in tension with their original project. I here offer a neo-Kantian alternative. In particular, I will show how constitutive elements in the sense of Reichenbach (1920) and Friedman (1999, 2001) can be identified within quantum theory, through considerations of symmetries that allow the constitution of a ‘quantum reality’, without invoking any notion of a radically mind-independent reality. The resulting conception will inherit elements from pragmatist and ‘QBist’ approaches, but also differ from them in crucial respects. Furthermore, going beyond the Friedmanian program, I will show how non-fundamental and approximate symmetries can be relevant for identifying constitutive principles. (shrink)

Curie’s Principle says that any symmetry property of a cause must be found in its effect. In this article, I consider Curie’s Principle from the point of view of graphical causal models, and demonstrate that, under one definition of a symmetry transformation, the causal modeling framework does not require anything like Curie’s Principle to be true. On another definition of a symmetry transformation, the graphical causal modeling formalism does imply a version of Curie’s Principle. These results yield a better understanding (...) of the logical landscape with respect to the relationship between Curie’s Principle and graphical causal modeling. (shrink)

The orthodox characterization of spontaneous symmetry breaking in statistical mechanics appeals to novel properties of systems with infinite degrees of freedom, namely, the existence of multiple equilibrium states. This raises the same puzzles about the status of the thermodynamic limit fueling recent debates about phase transitions. I argue that there are prospects of explaining the success of the standard approach to SSB in terms of the properties of large finite systems. Consequently, despite initial appearances, the need to account for SSB (...) phenomena does not offer decisive support to claims about the explanatory and representational indispensability of the thermodynamic limit. (shrink)