and the ontology of symmetries in physics
3-4 Jul 2017 Louvain-la-Neuve (Belgium)

Chosen speakers

Chosen speakers


Below is the list of all confirmed conference speakers that were chosen via the CFA, as well as short versions of their abstracts.


Juliusz DOBOSZEWSKI (Jagiellonian University, Poland)

"Equivalent and inequivalent spacetimes"

Which transformations identify distinct mathematical representations of the same physical situation in a given theory? For classical general relativity a commonly given answer is that local diffeomorphisms which preserve metric are gauge symmetries of the theory, and hence spacetime metrics related by an isometry are physically equivalent: such spacetimes may be distinct mathematical objects, but they represent one and the same physical situation. This view is often taken for granted in metaphysical and physical contexts alike. But what about diffeomorphisms which do act non-trivially on a non-compact subset? I will discuss few examples of spacetimes which show that the question of physical equivalence in classical GR is not fully addressed by invariance under local diffeomorphisms, and suggest that in such cases there is no unique, context-independent characterization of physical equivalence. More precisely, there are (1) spacetimes which are related by an isometry, which intuitively are not physically equivalent; the examples come mostly from non-unique (up to certain transformation) spacetime extensions encountered in the context of the initial value problem; moreover, (2) there are spacetimes which are not related by an isometry, but in various theoretical contexts are treated as physically equivalent; use of universal covering spaces is one such case. Thus, using diffeomorphism invariance to characterize the notion of physical equivalence does not give a complete account of the equivalence of mathematical representations and notion of physical equivalence in classical general relativity and related theories.


Samuel FLETCHER (Ludwig-Maximilians-Universität München (Munich Center for Mathematical Philosophy), Germany & University of Minnesota - Twin Cities, USA)

"Approximate space-time symmetries"

Approximate symmetry is widely invoked in contexts from space-time geometry to effective field theories, but it is rarely fully explicated. Such an explication, in the case of space-time symmetries, is the goal of this presentation, which reveals a surprising number of complexities. The mathematics involved can be subtle, and requires conceptual input regarding which properties (directly observable or not) are relevant in comparing approximate symmetry-related space-times, how different those properties can be while still preserving approximate symmetry, and what it means, in the case of local space-time symmetries, for two symmetry transformations to be similar to one another. The first step in this is to develop the mathematical apparatus to represent approximate symmetry. To this end I will deploy methods from topology, and uniform spaces in particular, which are a sort of intermediate between topological and metric spaces in terms of structure. As a result, at least two interesting types of approximate symmetry can then be defined: approximate symmetry in the large, and approximate symmetry in the small, which arise when one is concerned with, respectively, all elements of the symmetry group, or only ones close to the identity. These in turn shed light on the direct empirical significance (DES) of space-time symmetries, for being approximable is certainly sufficient for DES and - under the right conditions - it may be necessary, too.


Simon FRIEDERICH (University of Groningen, the Netherlands)

"Direct empirical significance and physical identity"

Symmetries can be characterized as (or as inducing) mappings of a theory’s state space onto itself which connect states that are in some sense "physically equivalent". Philosophical debates about symmetries often start from recognizing that "physical equivalence" can have (at least) two different meanings in this context.

According to the first meaning of "physical equivalence", symmetries are descriptive redundancies in that any two states related by symmetry represent one and the same physical state in mathematically distinct ways. According to the second, symmetries operate between physically distinct states of affairs, but in such a way that there is no empirically detectable difference between states connected by symmetries for observers who can only make observations inside the region where the symmetry transformations operate. Symmetries which connect physically identical states are often said to not have any direct empirical significance, whereas those which operate between physically distinct states do.

The present contribution builds on a recently proposed framework by Hilary Greaves and David Wallace and combines it with a small number of plausible assumptions that allow to apply the notion of physical identity to subsystem states. Based on these assumptions, a result is derived according to which, contrary to the conclusions drawn by Greaves and Wallace, only global symmetries have direct empirical significance. Notably, states in gauge field theories that are related by local symmetry transformations correspond to the same physical state.


Leon LOVERIDGE (Utrecht University, the Netherlands), in collaboration with Paul Busch & Takayuki Miyadera

"Shadows of symmetry: Absolute and relative in quantum theory"

Classically, symmetry demands the invariance of observable quantities, with typical examples such as position and angle acquiring their meaning only through reference to a given frame: observables are relative. The use of non-invariant (hence, unobservable) quantities in the theoretical description and analysis of experiments is justified by the possibility of translating exactly between absolute and relative descriptions. The absolute quantities feature as shadows of their invariant selves, not represented in reality but yielding an adequate account of observation.

The connection between symmetry and observability persists in the quantum regime; observables and states are relative and all standard notions referring to individual systems - coherence, localisation, dynamics - must be appropriately adapted. Symmetry implies that ordinary quantum theory then refers not to quantum systems in themselves, but to the relation between quantum systems, one of which serves as a reference system through which the invariance of observable quantities is manifested. The relationship between absolute and relative descriptions is complicated by the presence of indeterminism and incompatibility; however, absolute and relative descriptions may still agree, contingent upon the possession of the reference of certain classical properties. From this observation follows the resolution of long-standing controversies surrounding the meaning of superpositions and coherence, and more generally the relational framework that arises adds physical impetus to Bohr's epistemology: the reference frame/experimental setting must be taken into account in interpreting quantum events and taken as part of the "individual" whole.


Joanna LUC (Jagiellonian University, Poland)

"Two divisions of symmetries and some of their consequences"

It seems that not much can be said about symmetries in general and the most important work in their analysis should be devoted to finding crucial differences between various types of symmetries. The first important distinction (Caulton 2015) is between analytic and synthetic symmetries. Analytic symmetries leave invariant all physically real properties of all states, synthetic - only some of them. The second important distinction (Kosso 2000) is between symmetries that have direct empirical significance (DES) and these that do not have it.

My first thesis is that under some plausible assumptions about being physically real and about observability, the two above distinctions coincide (that is, a symmetry is analytic iff it does not have DES and it is synthetic iff it has DES).

Analytic symmetries provide us information about what quantities are physically real. From the previous considerations it follows that their empirical significance is at best indirect. My second thesis is that to avoid this conclusion we should modify the definition of direct empirical significance.

My third thesis concerns the relationship between the above types of symmetries and other components of physical theories. A dominant approach is that symmetries are superior to laws of nature. However, their status is more complicated because it depends on the type of a given symmetry. Analytic symmetries encode the information about what is physically real. Synthetic symmetries can be treated as special cases of laws of nature if we understand laws as expressing relationships between physically real quantities.


Quentin RUYANT (Université catholique de Louvain, Belgium & University of Rennes 1, France)

"Symmetries and indexicals"

A symmetry is a transformation of a theoretical model that leaves some of its features invariant. It is generally considered that some symmetries, such as coordinate transformations, are not empirically significant, while others inform us on important aspects of nature. Following this consideration, some authors attempt to eliminate the "surplus structure" from our theories to derive ontological commitments. This can lead to deep metaphysical questions regarding, for example, the alleged inexistence of time and change. I wish to challenge this idea from an empiricist perspective, by arguing that all theoretical symmetries are empirically significant. My argument draws on an analogy between coordinate systems and indexicals in natural languages. Indexicals play an indispensable role for fixing the referential content of indexical propositions in context. Similarly, coordinate systems play an indispensable role in empirical confrontation for fixing the referential content of theoretical models. They can be associated with different operationalizations of measurements. Coordinate transformation symmetries are therefore empirically significant: they inform us on the invariance of some aspects of the observed phenomena under changes of operationalization. One could go further and question whether symmetries that are traditionally considered empirically significant differ in nature from these cases: if one still wants to maintain a distinction between different types of symmetries, one owes us non arbitrary criteria for distinguishing operational and non-operational aspects of experimental situations.


David SCHROEREN (Princeton University, USA)

"The metaphysics of invariance"

Transformations of a physical system generally leave certain features of the system invariant. For example, spatial rotations of a classical system do not change its mass or its magnitudes of linear and angular momentum. But some invariances seem have a significance that others lack. For example, the rotational invariance of the magnitude of angular momentum is significant in a way that the rotational invariance of mass or the magnitude of linear momentum is not: as opposed to mass and linear momentum, the magnitude of angular momentum can be characterized by the Casimir (or invariant) element of the Lie algebra of the rotation group SO(3).

The goal of this paper is to explain the metaphysical import of this mathematical characterization. On the proposed account, the rotational invariance of the magnitude of angular momentum is metaphysically privileged, in the sense that the invariance of this magnitude has a specific explanatory connection to rotations. In particular, the magnitude of angular momentum is invariant in virtue of what I refer to as the ‘constitutive component’ of the local structure of metaphysical orbits under rotations – orbits which are, roughly, the metaphysical analogues of mathematical orbits. By contrast, other rotational invariances obtain for altogether different reasons. I conclude by describing some potential applications of this proposal for the metaphysics of properties and the metaphysics of modality.


Ward STRUYVE (Ludwig-Maximilians-Universität München, Germany)

"Spontaneous symmetry breaking and the Higgs mechanism: Lifting the veil of gauge"

The Higgs mechanism gives mass to Yang-Mills gauge bosons. According to the conventional wisdom, this happens through the spontaneous breaking of gauge symmetry. Despite the empirical success of the theory (in the context of the electro-weak interaction), there have been some conceptual questions and concerns concerning the nature of the Higgs mechanism. The first to raise them was Earman, who asked in a series of papers: If gauge symmetry is an unphysical symmetry, which merely connects different mathematical representations of the same physical state, then what exactly does it mean to break it? And how can it have any physical consequences to break it? In the talk, I will show that the standard account of the Higgs mechanism can be done in a different way without invoking symmetry breaking. This alternative account is manifestly gauge invariant, by using a reformulation of the theory in terms of gauge invariant degrees of freedom. For simplicity, I will not consider the electro-weak theory but the case of the Abelian Higgs mechanism (in the context of classical field theory). I will discuss various notions of gauge that can be found in the literature. In particular, I will consider in detail one notion of gauge symmetry that is frequently used but that seems to be understandable only in the light of the distinction between empirical and non-empirical symmetries by Greaves and Wallace.

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