'The arrow of time' refers to the curious asymmetry that distinguishes the future from the past. Reversing the Arrow of Time argues that there is an intimate link between the symmetries of 'time itself' and time reversal symmetry in physical theories, which has wide-ranging implications for both physics and its philosophy. This link helps to clarify how we can learn about the symmetries of our world, how to understand the relationship between symmetries and what is real, and how to overcome (...) pervasive illusions about the direction of time. Roberts explains the significance of time reversal in a way that intertwines physics and philosophy, to establish what the arrow of time means and how we can come to know it. This book is both mathematically and philosophically rigorous yet remains accessible to advanced undergraduates in physics and the philosophy of physics. This title is also available as Open Access on Cambridge Core. (shrink)

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)

In recent years the quantum foundations community has seen increasing interest in the possibility of using retrocausality as a route to rejecting the conclusions of Bell’s theorem and restoring locality to quantum physics. On the other hand, it has also been argued that accepting nonlocality leads to a form of retrocausality. In this article we seek to elucidate the relationship between retrocausality and locality. We begin by providing a brief schema of the various ways in which violations of Bell’s inequalities (...) might lead us to consider some form of retrocausality. We then consider some possible motivations for using retrocausality to rescue locality, arguing that none of these motivations is sufficient to show that local retrocausal theories should always be preferred to nonlocal retrocausal theories, and therefore there is no clear reason to focus research efforts entirely on seeking local retrocausal models. Next, we examine several different conceptions of retrocausality, concluding that ‘all-at-once’ retrocausality is more coherent than the alternative dynamical picture. We then argue that since the ‘all-at-once’ approach requires probabilities to be assigned to entire histories, locality is not playing any crucial role within this picture. Thus we conclude that using retrocausality as a way to rescue locality may not be the right route to retrocausality. Finally, we demonstrate that accepting the existence of nonlocality and insisting on the nonexistence of preferred reference frames leads naturally to the acceptance of a form of retrocausality, albeit one which is not mediated by physical systems travelling backwards in time. We argue that this is the more natural way to motivate retrocausal models of quantum mechanics. (shrink)

It is now standard to interpret symmetry-related models of physical theories as representing the same state of affairs. Recently, a debate has sprung up around the question when this interpretational move is warranted. In particular, Møller-Nielsen :1253–1264, 2017) has argued that one is only allowed to interpret symmetry-related models as physically equivalent when one has a characterisation of their common content. I disambiguate two versions of this claim. On the first, a perspicuous interpretation is required: an account of the models’ (...) common ontology. On the second, stricter, version of this claim, a perspicuous formalism is required in addition: one whose mathematical structures ‘intrinsically’ represent the physical world, in the sense of Field. Using Dewar’s :485–521, 2019) distinction between internal and external sophistication as a case study, I argue that the second requirement is decisive. This clarifies the conditions under which it is warranted to interpret symmetry-related models as physically equivalent. (shrink)

In the recent philosophical literature, several counterexamples to the interpretative principle that symmetry-related models are physically equivalent have been suggested The Oxford handbook of philosophy of physics, Oxford University Press, Oxford, 2013, Noûs 52:946–981, 2018; Fletcher in Found Phys 50:228–249, 2020). Arguments based on these counterexamples can be understood as arguments from scientific practice of roughly the following form: because in scientific practice such-and-such symmetry-related models are treated as representing distinct physical situations, these models indeed represent distinct physical situations. In (...) this paper, a strategy for analysing arguments of this type is presented and applied to the examples that can be found in the literature. I argue that if we are exclusively interested in models understood as representing entire possible worlds, arguments from scientific practice should involve some additional assumptions to guarantee they are relevant for models understood in this way. However, none of the examples presented in the literature satisfy all these additional assumptions, which leads to the conclusion that arguments from scientific practice based on these examples do not undermine the interpretative principle that different symmetry-related models represent the same possible world. (shrink)

I critically examine the assumption that the theoretical structure that varies under theoretical symmetries is redundant and should be eliminated from a metaphysical picture of the universe, following a ‘symmetry to reality’ inference. I do so by analysing the status of coordinate change symmetries taking a pragmatic approach. I argue that coordinate systems function as indexical devices, and play an important pragmatic role for representing concrete physical systems. I examine the implications of considering this pragmatic role seriously, taking what I (...) call a perspectivist stance. My conclusion is that under a perspectivist stance, all symmetries (including local gauge symmetries) potentially have a direct empirical status: they point to dynamical aspects that are invariant under changes of operationalisation, and they constitute a guide not to reality, but to nomology and kinship. (shrink)

We make some remarks on the mathematics and metaphysics of the hole argument, in response to a recent article in this journal by Weatherall ([2018]). Broadly speaking, we defend the mainstream philosophical literature from the claim that correct usage of the mathematics of general relativity `blocks' the argument.

The presence of symmetries in physical theories implies a pernicious form of underdetermination. In order to avoid this theoretical vice, philosophers often espouse a principle called Leibniz Equivalence, which states that symmetry-related models represent the same state of affairs. Moreover, philosophers have claimed that the existence of non-trivial symmetries motivates us to accept the Invariance Principle, which states that quantities that vary under a theory’s symmetries aren’t physically real. Leibniz Equivalence and the Invariance Principle are often seen as part of (...) the same package. I argue that this is a mistake: Leibniz Equivalence and the Invariance Principle are orthogonal to each other. This means that it is possible to hold that symmetry-related models represent the same state of affairs whilst having a realist attitude towards variant quantities. Various arguments have been presented in favour of the Invariance Principle: a rejection of the Invariance Principle is inter alia supposed to cause indeterminism, undetectability or failure of reference. I respond that these arguments at best support Leibniz Equivalence. (shrink)

I advance a stipulational account of symmetry-to-reality inference, according to which symmetries are part of the content of theories. For a theory to have a certain symmetry is for the theory to stipulate that models related by the symmetry represent the same possibility. I show that the stipulational account compares positively with alternatives, including Dasgupta’s epistemic account of symmetry, Møller-Nielsen’s motivational account, and so-called formal and ontic accounts. In particular, the stipulational account avoids the problems Belot and Dasgupta have raised (...) against formal and ontic accounts of symmetry while retaining many of the advantages of these otherwise-attractive frameworks. (shrink)

In this paper, we put forward an alternative interpretation of time-reversal symmetry in philosophy of physics: Humean time-reversal symmetry. According to it, time-reversal symmetry is understood as a heuristic, epistemic virtue of the best system, not as a property of the Humean mosaic. One of the consequences of this view is that one of the main arguments against a primitive direction of time is rendered harmless, which paves the way for primitivism about the direction of time.

The laws of nature have come a long way since the time of Newton: quantum mechanics and relativity have given us good reasons to take seriously the possibility of laws which may be non-local, atemporal, ‘all-at-once,’ retrocausal, or in some other way not well-suited to the standard dynamical time evolution paradigm. Laws of this kind can be accommodated within a Humean approach to lawhood, but many extant non-Humean approaches face significant challenges when we try to apply them to laws outside (...) the time evolution picture. Thus for proponents of non-Humean approaches to lawhood there is a clear need for a novel non-Humean account which is capable of accommodating these sorts of laws. In this paper we propose such an account, characterizing lawhood in terms of constraints, which are understood as a form of modal structure. We demonstrate that our proposed realist account can indeed accommodate a large variety of laws outside the time evolution paradigm, and describe some possible applications to important philosophical problems. (shrink)

Symmetry fundamentalism claims that symmetries should be taken metaphysically seriously as part of the fundamental ontology. The main aim of this paper is to bring some novel objections against this view. I make two points. The first places symmetry fundamentalism within a broader network of philosophical commitments. I claim that symmetry fundamentalism entails idealization realism which, in turn, entails the reification of further theoretical structures. This might lead to an overloaded ontology as well as open the way to criticisms from (...) metaphysical frameworks that reject such reifications. The second point contrasts symmetry fundamentalism with the now common view that regards symmetries as stipulations guiding empirical research and theory construction. I claim that both views clash each other and cannot be held together. I finish the paper with a more positive prospect that will be developed in future work—symmetry deflationism. (shrink)

ABSTRACT In this journal, Middleton and Murgueitio Ramírez argue that absolute velocity is measurable, contrary to the received wisdom. Specifically, they claim that ‘there exists at least one reasonable analysis of measurement according to which the speedometer in [a world called “the Basic World”] measures the absolute velocity of the car.’ In this note, I critically respond to that claim: the analysis of measurement that Middleton and Murgueitio Ramírez propose is not reasonable; nor does it entail that absolute velocities are (...) measurable. (shrink)

In the recent philosophical debate about the relationship between symmetries and physical equivalence, two approaches have been distinguished: motivationalism and interpretationalism. In this paper, I point out that there are variants of interpretationalism that have not been taken into account by the proponents of motivationalism. I also argue that some of these overlooked variants of interpretationalism are not prone to the motivationalists’ criticism and overall are the most attractive positions available.

We study a long-recognised but under-appreciated symmetry called dynamical similarity and illustrate its relevance to many important conceptual problems in fundamental physics. Dynamical similarities are general transformations of a system where the unit of Hamilton’s principal function is rescaled, and therefore represent a kind of dynamical scaling symmetry with formal properties that differ from many standard symmetries. To study this symmetry, we develop a general framework for symmetries that distinguishes the observable and surplus structures of a theory by using the (...) minimal freely specifiable initial data for the theory that is necessary to achieve empirical adequacy. This framework is then applied to well-studied examples including Galilean invariance and the symmetries of the Kepler problem. We find that our framework gives a precise dynamical criterion for identifying the observables of those systems, and that those observables agree with epistemic expectations. We then apply our framework to dynamical similarity. First we give a general definition of dynamical similarity. Then we show, with the help of some previous results, how the dynamics of our observables leads to singularity resolution and the emergence of an arrow of time in cosmology. (shrink)