Symmetry in Physics

We address a long-standing debate over whether classical magnetic forces can do work, ultimately answering the question in the affirmative. In detail, we couple a classical particle with intrinsic spin and elementary dipole moments to the electromagnetic field, derive the appropriate generalization of the Lorentz force law, show that the particle’s dipole moments must be collinear with its spin axis, and argue that the magnetic field does mechanical work on the particle’s elementary magnetic dipole moment. As consistency checks, we calculate (...) the overall system’s energy-momentum and angular momentum, and show that their local conservation equations lead to the same force law and therefore the same conclusions about magnetic forces and work. We also compute the system’s Belinfante–Rosenfeld energy–momentum tensor. (shrink)

On one popular view, the general covariance of gravity implies that change is relational in a strong sense, such that all it is for a physical degree of freedom to change is for it to vary with regard to a second physical degree of freedom. At a quantum level, this view of change as relative variation leads to a fundamentally timeless formalism for quantum gravity. Here, we will show how one may avoid this acute ‘problem of time’. Under our view, (...) duration is still regarded as relative, but temporal succession is taken to be absolute. Following our approach, which is presented in more formal terms in, it is possible to conceive of a genuinely dynamical theory of quantum gravity within which time, in a substantive sense, remains. 1 Introduction1.1 The problem of time1.2 Our solution2 Understanding Symmetry2.1 Mechanics and representation2.2 Freedom by degrees2.3 Voluntary redundancy3 Understanding Time3.1 Change and order3.2 Quantization and succession4 Time and Gravitation4.1 The two faces of classical gravity4.2 Retaining succession in quantum gravity5 Discussion5.1 Related arguments5.2 Concluding remarks. (shrink)

We pose and resolve a puzzle about spontaneous symmetry breaking in the quantum theory of infinite systems. For a symmetry to be spontaneously broken, it must not be implementable by a unitary operator in a ground state's GNS representation. But Wigner's theorem guarantees that any symmetry's action on states is given by a unitary operator. How can this unitary operator fail to implement the symmetry in the GNS representation? We show how it is possible for a unitary operator of this (...) sort to connect the folia of unitarily inequivalent representations. This result undermines interpretations of quantum theory that hold unitary equivalence to be necessary for physical equivalence. (shrink)

Standard lore holds that magnetic forces are incapable of doing mechanical work. More precisely, the claim is that whenever it appears that a magnetic force is doing work, the work is actually being done by another force, with the magnetic force serving only as an indirect mediator. On the other hand, the most familiar instances of magnetic forces acting in everyday life—bar magnets lifting other bar magnets—appear to present manifest evidence of magnetic forces doing work. These sorts of counterexamples are (...) often dismissed as arising from quantum effects that lie outside the classical regime. In this paper, however, we show that quantum theory is not needed to account for these phenomena, and that classical electromagnetism admits a model of elementary magnetic dipoles on which magnetic forces can indeed do work. In order to develop this model, we revisit the foundational principles of the classical theory of electromagnetism, showcase the importance of constraints from relativity, examine the structure of the multipole expansion, and study the connection between the Lorentz force law and conservation of energy and momentum. (shrink)

In this paper, we review a general technique for converting the standard Lagrangian description of a classical system into a formulation that puts time on an equal footing with the system's degrees of freedom. We show how the resulting framework anticipates key features of special relativity, including the signature of the Minkowski metric tensor and the special role played by theories that are invariant under a generalized notion of Lorentz transformations. We then use this technique to revisit a classification of (...) classical particle-types that mirrors Wigner's classification of quantum particle-types in terms of irreducible representations of the Poincaré group, including the cases of massive particles, massless particles, and tachyons. Along the way, we see gauge invariance naturally emerge in the context of classical massless particles with nonzero spin, as well as study the massless limit of a massive particle and derive a classical-particle version of the Higgs mechanism. (shrink)

The concept of inertial frame of reference is analysed. It has been shown that this fundamental concept of physics is not clear enough. A definition of inertial frame of reference is proposed which expresses its key inherent property. The definition is operational and powerful. Many other properties of inertial frames follow from the definition or it makes them plausible. In particular, the definition shows why physical laws obey space and time symmetries and the principle of relativity, it resolves the problem (...) of clock synchronization and the role of light in it, as well as the problem of the geometry of inertial frames. (shrink)

In this chapter, we see one way that time flow may force us to develop our physical theory if we add it back into physics proper. Now of course this is speculative in this context, and should be thought of as a model. The two following extracts are from introductions a more complete unified theory. They explain the basic mathematical models that are required to illustrate the point that such models may be plausible. The second extract, ‘the parable of the (...) ants’, introduces us to the ideological-philosophical conflict that prevents such a development being considered in the present generation, which we will go on to next. (shrink)

This report offers a modern perspective on the question of time directionality as it arises in a classical and quantum mechanical context, based on key developments in the field of gravitational physics. Important clarifications are achieved regarding, in particular, the concepts of time reversal, negative energy and causality. From this analysis emerges an improved understanding of the general relativistic concept of stress-energy of matter as being a manifestation of local variations in the energy density of zero-point vacuum fluctuations. Based on (...) those developments a set of axioms is proposed from which are derived generalized gravitational field equations which actually constitute a simplification of relativity theory in the presence of negative energy matter and vacuum energy. Those results are then applied to provide original solutions to several long-standing problems in theoretical cosmology and concerning the foundations of quantum theory, including the problem of the nature of dark matter and dark energy, that of the origin of thermodynamic time asymmetry and several other issues traditionally approached using inflation theory. Significant new insights are also provided concerning gravitational entropy, the problem of quantum non-locality, that of the emergence of time in quantum cosmology as well as the problem of the persistence of quasiclassicality following decoherence. (shrink)

Following the 26th General Conference on Weights and Measures are fixed the numerical values of the 4 physical constants ($h, c, e, k_B$). This is premised on the independence of these constants. This article discusses a model of a mathematical electron from which can be defined the Planck units as geometrical objects (mass M=1, time T=2$\pi$ ...). In this model these objects are interrelated via this electron geometry such that once we have assigned values to 2 Planck units then we (...) have fixed the values for all Planck units. As all constants can then be defined using geometrical forms (in terms of 2 fixed mathematical constants, 2 unit-specific scalars and a defined relationship between the units $kg, m, s, A$), the least precise CODATA 2014 constants ($G, h, e, m_e, k_B$...) can then be solved via the most precise ($c, \mu_0, \alpha, R_\infty$), with numerical precision limited by the precision of the fine structure constant $\alpha$. In terms of this model we now for example have 2 separate values for elementary charge, calculated from ($c, \alpha, R_\infty$) and the 2017 revision. (shrink)

Fundamental physics contains an important link between properties of elementary particles and continuous symmetries of particle systems. For example, properties such as mass and spin are said to be 'associated' with specific continuous symmetries. -/- These 'associations' have played a key role in the discovery of various new particle kinds, but more importantly: they are thought to provide a deep insight into the nature of physical reality. The link between properties and symmetries has been said to call for a radical (...) revision of perceived metaphysical orthodoxy. However, if we are to use claims about an 'association' between properties and symmetries in the articulation of metaphysical views, we first need to develop a sufficiently precise understanding of the content of these claims. The goal of this paper is to do just that. (shrink)

Plato's theory of everything is an introduction to a Pythagorean natural philosophy that includes Egyptian sources. The Pythagorean Table and Pythagorean harmonics from the ancient geometry of the Cosmological Circle are related to symbolic associations of basic mathematical constants with the five elements of Plato's allegorical cosmology: Archimedes constant, Euler's number, the polygon circumscribing limit, the golden ratio, and Aristotle's quintessence. Quintessence is representative of the whole, or the one in four, extraneously considered a separate element or fifth force. This (...) relationship with four fundamental interactions or forces also involves the correlation of constants with the five Platonic solids: tetrahedron, hexahedron, octahedron, icosahedron, and dodecahedron. The values of several fundamental physical constants are also calculated, and a basic equation is given for a unified physical theory in the geometric universe of Plato's natural philosophy. (shrink)

The principle of Information Conservation or Determinism is a governing assumption of physical theory. Determinism has counterfactual consequences. It entails that if the present were different, then the future would be different. But determinism is temporally symmetric: it entails that if the present were different, the past would also have to be different. This runs contrary to our commonsense intuition that what has happened in the future depends on the past in a way the past does not depend on the (...) future. To understand how this can be so we observe that while the truth of some counterfactuals is guaranteed by the laws of logic or the laws of nature, some are not. It is among the latter contingent, counterfactuals that we find temporal asymmetry. It is this asymmetry that gives causation a temporal direction. The temporal asymmetry of these counterfactuals is explained by the fact that the dynamical laws of nature are logically irreversible functions from partial states of the world onto other partial states. (Logical reversibility is not to be confused, though it too often is, with time-reversal invariance). Though these irreversible laws are locally indeterministic, they can sum to give a globally deterministic description of the world. This combination of global determinism and local indeterminism gives rise to contingent counterfactual dependence and gives that dependence a direction. That direction is independent of the direction of entropy. The direction of contingent counterfactual dependence is time's arrow. (shrink)

In discussions of the Aharonov-Bohm effect, Healey and Lyre have attributed reality to loops $\sigma_0$ (or hoops $[\sigma_0]$), since the electromagnetic potential $A$ is currently unmeasurable and can therefore be transformed. I argue that $[A]=[A+d\lambda]_{\lambda}$ and the hoop $[\sigma_0]$ are related by a meaningful duality, so that however one feels about $[A]$ (or any potential $A\in[A]$), it is no worse than $[\sigma_0]$ (or any loop $\sigma_0\in[\sigma_0]$): no ontological firmness is gained by retreating to the loops, which are just as flimsy (...) as the potentials. And one wonders how the unmeasurability of one entity can invest another with physical reality; would an eventual observation of $A$ dissolve $\sigma_0$, consigning it to a realm of incorporeal mathematical abstractions? The reification of loops rests on the potential's ''gauge dependence''; which in turn rests on its unmeasurability; which is too shaky and arbitrary a notion to carry so much weight. (shrink)

Symmetry considerations dominate modern fundamental physics, both in quantum theory and in relativity. Philosophers are now beginning to devote increasing attention to such issues as the significance of gauge symmetry, quantum particle identity in the light of permutation symmetry, how to make sense of parity violation, the role of symmetry breaking, the empirical status of symmetry principles, and so forth. These issues relate directly to traditional problems in the philosophy of science, including the status of the laws of nature, the (...) relationships between mathematics, physical theory, and the world, and the extent to which mathematics suggests new physics.This entry begins with a brief description of the historical roots and emergence of the concept of symmetry that is at work in modern science. It then turns to the application of this concept to physics, distinguishing between two different uses of symmetry: symmetry principles versus symmetry arguments. It mentions the different varieties of physical symmetries, outlining the ways in which they were introduced into physics. Then, stepping back from the details of the various symmetries, it makes some remarks of a general nature concerning the status and significance of symmetries in physics. (shrink)

Symmetry principles are a central part of contemporary physics, yet there has been surprisingly little metaphysical work done on them. This paper develops the Wignerian treatment of symmetries as higher-order laws – metalaws – within a Humean framework of lawhood. Lange has raised two obstacles to Humean metalaws, and the paper shows that the account has the resources available to respond to both. It is argued that this framework for Humean metalaws stands as an example of naturalistic metaphysics, able to (...) bring Humeanism into contact with the practice of actual science without giving up on the central denial of necessary connections. (shrink)

Gauge symmetries provide one of the most puzzling examples of the applicability of mathematics in physics. The presented work focuses on the role of analogical reasoning in the gauge argument, motivated by Mark Steiner's claim that the application of the gauge principle relies on a Pythagorean analogy whose success undermines naturalist philosophy. In this paper, we present two different views concerning the analogy between gravity, electromagnetism, and nuclear interactions, each providing a different philosophical response to the problem of the applicability (...) of mathematics in the natural sciences. The first is based on an account of Weyl's original work, which first gave rise to the gauge principle. Drawing on his later philosophical writings, we develop an idelaist reading of the mathematical analogies in the gauge argument. On this view, mathematical analogies serve to ensure a conceptual harmony in our scientific account of nature. We further discuss the construction of Yang and Mills's gauge theory in light of this idealist reading. The second account presents a naturalist alternative, formulated in terms of John Norton's account of a material analogy, according to which the analogy succeeds in virtue of a physical similarity between the different interactions. This account is based on the methodological equivalence principle, a simple conceptual extension of the gauge principle that allows us to understand the relation between coordinate transformations and gravity as a manifestation of the same method. The physical similarity between the different cases is based on attributing the success of this method to the dependence of the coupling on relational physical quantities. We conclude by reflecting on the advantages and limits of the idealist, naturalist, and anthropocentric Pythagorean views, as three alternative ways to understand the puzzling relation between mathematics and physics. -/- . (shrink)

Science frequently gives us multiple, compatible ways of solving the same problem or formulating the same theory. These compatible formulations change our understanding of the world, despite providing the same explanations. According to what I call "conceptualism," reformulations change our understanding by clarifying the epistemic structure of theories. I illustrate conceptualism by analyzing a typical example of symmetry-based reformulation in chemical physics. This case study poses a problem for "explanationism," the rival thesis that differences in understanding require ontic explanatory differences. (...) To defend conceptualism, I consider how prominent accounts of explanation might accommodate this case study. I argue that either they do not succeed, or they generate a skeptical challenge. (shrink)

Ruetsche ([2011]) argues that the occurrence of unitarily inequivalent representations in quantum theories with infinitely many degrees of freedom poses a novel interpretational problem. According to Ruetsche, such theories compel us to reject the so-called ideal of pristine interpretation; she puts forward the ‘coalescence approach’ as an alternative. In this paper I offer a novel defence of the coalescence approach. The defence rests on the claim that the ideal of pristine interpretation already fails before one considers the peculiarities of QM∞: (...) there are pre-QM∞ parallels to coalescence. Despite this departure from pristinism, the ‘modest’ view that emerges poses no threat to scientific realism. (shrink)

The most part of the debates on Quantum Mechanics (QM) interpretation come out from the remains of a classical language based upon waves and particles. Such problems can find a decisive clarification in Quantum Field Theory (QFT), where the concept of “classical object” is replaced by an interaction networks. On the other hand, it is simpler to discuss about non-locality in QM than in QFT. We propose here the concept of transaction as a connection between theQM and QFT language as (...) well as the possibility to introduce quantum non-locality ab initio.We also mention the cosmological consequence of a non-local archaic vacuum here defined. (shrink)

In the last five years, the controversy about whether or not gauge transformations can be empirically significant has intensified. On the one hand, Greaves and Wallace (2014) developed a framework according to which, under some circumstances, gauge transformations can be empirically significant---and Teh (2015) further supported this result by using the Constrained Hamiltonian formalism. On the other hand, Friederich (2015, 2016) claims to have proved that gauge transformation can never be empirically significant. In this paper, I accomplish two tasks. First, (...) I argue that there are strong reasons to resist Friederich's proof because one of its assumptions is, at the very least, highly controversial. Second, I argue that, despite criticism by Brading and Brown (2004) and Friederich (2015), 't Hooft's Beam-Splitter experiment is indeed a concrete example of a case where a local gauge symmetry has empirical significance. By shedding light on these two points, this paper shows that recent arguments that claim gauge transformations cannot be empirically significant are not satisfactory. (shrink)

The recent debate about whether gauge symmetries can be empirically significant has focused on the possibility of 'Galileo's ship' types of scenarios, where the symmetries effect relational differences between a subsystem and the environment. However, it has gone largely unremarked that apart from such Galileo's ship scenarios, Greaves and Wallace (2014) proposed that gauge transformations can also be empirically significant in a 'non-relational' manner that is analogous to a Faraday-cage scenario, where the subsystem symmetry is related to a change in (...) a charged boundary state. In this paper, we investigate the question of whether such non-relational scenarios are possible for gauge theories. Remarkably, the answer to this question turns out to be closely related to a foundational puzzle that has driven a host of recent developments at the frontiers of theoretical physics. By drawing on these recent developments, we show that a very natural way of elaborating on Greaves and Wallace's claim of non-relational empirical significance for gauge symmetry is incoherent. However, we also argue that much of what they suggest is correct in spirit: one can indeed construct non-relational models of the kind they sketch, albeit ones where the empirical significance is not witnessed by a gauge symmetry but instead by a superficially similar boundary symmetry. Furthermore, the latter casts doubt on whether one really abandons Galileo's ship in such scenarios. (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)

Wigner’s quantum-mechanical classification of particle-types in terms of irreducible representations of the Poincaré group has a classical analogue, which we extend in this paper. We study the compactness properties of the resulting phase spaces at fixed energy, and show that in order for a classical massless particle to be physically sensible, its phase space must feature a classical-particle counterpart of electromagnetic gauge invariance. By examining the connection between massless and massive particles in the massless limit, we also derive a classical-particle (...) version of the Higgs mechanism. (shrink)

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)

According to the algebraic approach to spacetime, a thoroughgoing dynamicism, physical fields exist without an underlying manifold. This view is usually implemented by postulating an algebraic structure (e.g., commutative ring) of scalar-valued functions, which can be interpreted as representing a scalar field, and deriving other structures from it. In this work, we point out that this leads to the unjustified primacy of an undetermined scalar field. Instead, we propose to consider algebraic structures in which all (and only) physical fields are (...) primitive. We explain how the theory of natural operations in differential geometry—the modern formalism behind classifying diffeomorphism-invariant constructions—can be used to obtain concrete implementations of this idea for any given collection of fields. For concrete examples, we illustrate how our approach applies to a number of particular physical fields, including electrodynamics coupled to a Weyl spinor. (shrink)

This paper criticizes the traditional philosophical account of the quantization of gauge theories and offers an alternative. On the received view, gauge theories resist quantization because they feature distinct mathematical representatives of the same physical state of affairs. This resistance is overcome by a sequence of ad hoc modifications, justified in part by reference to semiclassical electrodynamics. Among other things, these modifications introduce "ghosts": particles with unphysical properties which do not appear in asymptotic states and which are said to be (...) purely a notational convenience. I argue that this sequence of modifications is unjustified and inadequate, making it a poor basis for the interpretation of ghosts. I then argue that gauge theories can be quantized by the same method as any other theory. On this account, ghosts are not purely notation: they are coordinates on the classical configuration space of the theory—specifically, on its gauge structure. This interpretation does not fall prey to the standard philosophical arguments against the significance of ghosts, due to Weingard. Weingard’s argumentative strategy, properly applied, in fact tells in favor of ghosts’ physical significance. (shrink)

It is often said that the world is explained by laws of nature together with initial conditions. But does that mean initial conditions don’t require further explanation? And does the explanatory role played by initial conditions entail or require that time has a preferred direction? This chapter looks at the use of the ‘initialness defence’ in physics, the idea that initial conditions are intrinsically special in that they don’t require further explanation, unlike the state of the world at other times. (...) Such defences commonly assume a primitive directionality of time to distinguish between initial and final conditions. Using the case study of the time-asymmetry of thermodynamics and the so-called ‘past hypothesis’ — the hypothesis that the early universe was in a state of very low entropy —, I outline and support a deflationary account of the initialness defence that does not pre- suppose a basic directionality of time, and argue that there is a relevant explanatory asymmetry between initial conditions and the state of systems at other times only if certain causal conditions are satisfied. Hence, the initialness defence is available to those who reject a fundamental direction of time. (shrink)

This article suggests a fresh look at gauge symmetries, with the aim of drawing a clear line between the a priori theoretical considerations involved, and some methodological and empirical non-deductive aspects that are often overlooked. The gauge argument is primarily based on a general symmetry principle expressing the idea that a change of mathematical representation should not change the form of the dynamical law. In addition, the ampliative part of the argument is based on the introduction of new degrees of (...) freedom into the theory according to a methodological principle that is formulated here in terms of correspondence between passive and active transformations. To demonstrate how the two kinds of considerations work together in a concrete context, I begin by considering spatial symmetries in mechanics. I suggest understanding Mach's principle as a similar combination of theoretical, methodological and empirical considerations, and demonstrate the claim with a simple toy model. I then examine gauge symmetries as a manifestation of the two principles in a quantum context. I further show that in all of these cases the relational nature of physically significant quantities can explain the relevance of the symmetry principle and the way the methodology is applied. In the quantum context, the relevant relational variables are quantum phases. (shrink)

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)

This book presents a thoroughly empiricist account of physics. By providing an overview of the development of empiricism from Ockham to van Fraassen the book lays the foundation for its own version of empiricism. Empiricism for the author consists of three ideas: nominalism, i.e. dismissing second order quantification as unnecessary, epistemological naturalism, and viewing classification of things in natural kinds as a human habit not in need for any justification. The book offers views on the realism-antirealism debate as well as (...) on the individuation of theories as a thoroughly neglected aspect of underdetermination. The book next discusses a broad range of topics, including the predicates body, spatial distance and time interval, the ontology of electromagnetism, propensities, the measurement problem and other philosophical issues in quantum theory. Discussions about the direction of time and about string theory make up the final part of the book. (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)

Jill North offers answers to questions at the heart of the project of interpreting physics. How do we figure out the nature of the world from a mathematically formulated theory? What do we infer about the world when a physical theory can be mathematically formulated in different ways? The notion of structure is crucial to North's answers.

According to the Standard Model of particle physics, some gauge transformations are physical symmetries. That is, they are mathematical transformations that relate representatives of distinct physical states of affairs. This is at odds with the standard philosophical position according to which gauge transformations are an eliminable redundancy in a gauge theory's representational framework. In this paper I defend the Standard Model's treatment of gauge from an objection due to Richard Healey. If we follow the Standard Model in taking some gauge (...) transformations to be physical symmetries then we face the “strong CP problem”, but if we adopt the standard philosophical position on gauge then the strong CP problem dissolves. Healey offers this as a reason in favor of the standard philosophical view. However, as I argue here, following Healey's recommendation gives a theory that makes bad empirical predictions. (shrink)

Elay Shech and John Earman have recently argued that the common topological interpretation of the Aharonov–Bohm (AB) effect is unsatisfactory because it fails to justify idealizations that it presupposes. In particular, they argue that an adequate account of the AB effect must address the role of boundary conditions in certain ideal cases of the effect. In this paper I defend the topological interpretation against their criticisms. I consider three types of idealization that might arise in treatments of the effect. First, (...) Shech takes the AB effect to involve an idealization in the form of a singular limit, analogous to the thermodynamic limit in statistical mechanics. But, I argue, the AB effect itself features no singular limits, so it doesn’t involve idealizations in this sense. Second, I argue that Shech and Earman’s emphasis on the role of boundary conditions in the AB effect is misplaced. The idealizations that are useful in connecting the theoretical description of the AB effect to experiment do interact with facts about boundary conditions, but none of these idealizations are presupposed by the topological interpretation of the effect. Indeed, the boundary conditions for which Shech and demands justification are incompatible with some instances of the AB effect, so the topological interpretation ought not justify them. Finally, I address the role of the non-relativistic approximation usually presumed in discussions of the AB effect. This approximation is essential if—as the topological interpretation supposes—the AB effect constrains and justifies a relativistic theory of the electromagnetic interaction. In this case the ends justify the means. So the topological view presupposes no unjustified idealizations. (shrink)

What would it be for a process to happen backwards in time? Would such a process involve different causal relations? It is common to understand the time-reversal invariance of a physical theory in causal terms, such that whatever can happen forwards in time can also happen backwards in time. This has led many to hold that time-reversal symmetry is incompatible with the asymmetry of cause and effect. This article critiques the causal reading of time reversal. First, I argue that the (...) causal reading requires time-reversal-related models to be understood as representing distinct possible worlds and, on such a reading, causal relations are compatible with time-reversal symmetry. Second, I argue that the former approach does, however, raise serious sceptical problems regarding the causal relations of paradigm causal processes and as a consequence there are overwhelming reasons to prefer a non-causal reading of time reversal, whereby time reversal leaves causal relations invariant. On the non-causal reading, time-reversal symmetry poses no significant conceptual nor epistemological problems for causation. _1_ Introduction _1.1_ The directionality argument _1.2_ Time reversal _2_ What Does Time Reversal Reverse? _2.1_ The B- and C-theory of time _2.2_ Time reversal on the C-theory _2.3_ Answers _3_ Does Time Reversal Reverse Causal Relations? _3.1_ Causation, billiards, and snooker _3.2_ The epistemology of causal direction _3.3_ Answers _4_ Is Time-Reversal Symmetry Compatible with Causation? _4.1_ Incompatibilism _4.2_ Compatibilism _4.3_ Answers _5_ Outlook. (shrink)

“The universe is expanding, not contracting.” Many statements of this form appear unambiguously true; after all, the discovery of the universe’s expansion is one of the great triumphs of empirical science. However, the statement is time-directed: the universe expands towards what we call the future; it contracts towards the past. If we deny that time has a direction, should we also deny that the universe is really expanding? This article draws together and discusses what I call ‘C-theories’ of time — (...) in short, philosophical positions that hold time lacks a direction — from different areas of the literature. I set out the various motivations, aims, and problems for C-theories, and outline different versions of antirealism about the direction of time. (shrink)

The notions of conservation and relativity lie at the heart of classical mechanics, and were critical to its early development. However, in Newton’s theory of mechanics, these symmetry principles were eclipsed by domain-specific laws. In view of the importance of symmetry principles in elucidating the structure of physical theories, it is natural to ask to what extent conservation and relativity determine the structure of mechanics. In this paper, we address this question by deriving classical mechanics—both nonrelativistic and relativistic—using relativity and (...) conservation as the primary guiding principles. The derivation proceeds in three distinct steps. First, conservation and relativity are used to derive the asymptotically conserved quantities of motion. Second, in order that energy and momentum be continuously conserved, the mechanical system is embedded in a larger energetic framework containing a massless component that is capable of bearing energy. Imposition of conservation and relativity then results, in the nonrelativistic case, in the conservation of mass and in the frame-invariance of massless energy; and, in the relativistic case, in the rules for transforming massless energy and momentum between frames. Third, a force framework for handling continuously interacting particles is established, wherein Newton’s second law is derived on the basis of relativity and a staccato model of motion-change. Finally, in light of the derivation, we elucidate the structure of mechanics by classifying the principles and assumptions that have been employed according to their explanatory role, distinguishing between symmetry principles and other types of principles that are needed to build up the theoretical edifice. (shrink)

This paper formulates generalized versions of the general principle of relativity and of the principle of equivalence that can be applied to general abstract spaces. It is shown that when the principles are applied to the Hilbert space of a quantum particle, its law of coupling to electromagnetic fields is obtained. It is suggested to understand the Aharonov-Bohm effect in light of these principles, and the implications for some related foundational controversies are discussed.

The chief motivation for epiphenomenalist dualism is its promise to solve dualism’s causal exclusion problem without inducing causal overdetermination or violations of the causal closure of the physical. This paper argues that epiphenomenalist dualism is itself susceptible to an exclusion problem. The problem exploits symmetries of determination and influence generated by a wide class of physical theories. Further, I argue that there is an interference effect between solving epiphenomenalist dualism's exclusion problem and using epiphenomenalist dualism as a solution to the (...) causal exclusion problem. What emerges is an overlooked, empirically-motivated challenge to epiphenomenalist dualism. (shrink)

To this day, a hundred and fifty years after Mendeleev's discovery, the overal structure of the periodic system remains unaccounted for in quantum-mechanical terms. Given this dire situation, a handful of scientists in the 1970s embarked on a quest for the symmetries that lie hidden in the periodic table. Their goal was to explain the table's structure in group-theoretical terms. We argue that this symmetry program required an important paradigm shift in the understanding of the nature of chemical elements. The (...) idea, in essence, consisted of treating the chemical elements, not as particles, but as states of a superparticle. We show that the inspiration for this came from elementary particle physics, and in particular from Heisenberg's suggestion to treat the proton and neutron as different states of the nucleon. We provide a careful study of Heisenberg's last paper on the nature of elementary particles, and explain why the Democritean picture of matter no longer applied in modern physics and a Platonic symmetry-based picture was called for instead. We show how Heisenberg's Platonic philosophy came to dominate the field of elementary particle physics, and how it found its culmination point in Gell-Mann's classification of the hadrons in the eightfold way. We argue that it was the success of Heisenberg's approach in elementary particle physics that sparked the group-theoretical approach to the periodic table. We explain how it was applied to the set of chemical elements via a critical examination of the work of the Russian mathematician Abram Ilyich Fet the Turkish-American physicist Asim Orhan Barut, before giving some final reflections. (shrink)

Against what is commonly accepted in many contexts, it has been recently suggested that both deterministic and indeterministic quantum theories are not time‐reversal invariant, and thus time is handed in a quantum world. In this paper, I analyze these arguments and evaluate possible reactions to them. In the context of deterministic theories, first I show that this conclusion depends on the controversial assumption that the wave‐function is a physically real scalar field in configuration space. Then I argue that answers which (...) restore invariance by assuming the wave‐function is a ray in Hilbert space fall short. Instead, I propose that one should deny that the wave‐function represents physical systems, along the lines proposed by the so‐called primitive ontology approach. Moreover, in the context of indeterministic theories, I argue that time‐reversal invariance can be restored suitably redefining its meaning. (shrink)

The principle of energy conservation is widely taken to be a se- rious difficulty for interactionist dualism (whether property or sub- stance). Interactionists often have therefore tried to make it satisfy energy conservation. This paper examines several such attempts, especially including E. J. Lowe’s varying constants proposal, show- ing how they all miss their goal due to lack of engagement with the physico-mathematical roots of energy conservation physics: the first Noether theorem (that symmetries imply conservation laws), its converse (that conservation (...) laws imply symmetries), and the locality of continuum/field physics. Thus the “conditionality re- sponse”, which sees conservation as (bi)conditional upon symme- tries and simply accepts energy non-conservation as an aspect of interactionist dualism, is seen to be, perhaps surprisingly, the one most in accord with contemporary physics (apart from quantum mechanics) by not conflicting with mathematical theorems basic to physics. A decent objection to interactionism should be a posteri- ori, based on empirically studying the brain. (shrink)

Suppose that one thinks that certain symmetries of a theory reveal “surplus structure”. What would a formalism without that surplus structure look like? The conventional answer is that it would be a reduced theory: a theory which traffics only in structures invariant under the relevant symmetry. In this paper, I argue that there is a neglected alternative: one can work with a sophisticated version of the theory, in which the symmetries act as isomorphisms.

Attempts to find perennial elements in Aristotle’s cosmology are doomed to failure because his distinction of sub- and supra-lunary realms no longer holds. More fruitful approaches to the contemporary importance of Aristotelian cosmology must focus on parities of reasoning rather than content. This paper highlights the striking parallels between Aristotle’s use of symmetry arguments in cosmology and instances of Noether’s First Theorem in contemporary physics. Both observe simple motion, find symmetries in that motion, argue from those symmetries to notions of (...) conservation, and then conclude to cosmological structure. These parallels reveal an enduring relevance for Aristotelian cosmology that does not depend on positing an enduring content to his cosmological claims. (shrink)

The CPT theorem states that any causal, Lorentz-invariant, thermodynamically well-behaved quantum field theory must also be invariant under a reflection symmetry that reverses the direction of time, flips spatial parity, and conjugates charge. Although its physical basis remains obscure, CPT symmetry appears to be necessary in order to unify quantum mechanics with relativity. This paper attempts to decipher the physical reasoning behind proofs of the CPT theorem in algebraic quantum field theory. Ultimately, CPT symmetry is linked to a systematic reversal (...) of the C*-algebraic Lie product that encodes the generating relationship between observables and symmetries. In any physically reasonable relativistic quantum field theory it is always possible to systematically reverse this generating relationship while preserving the dynamics, spectra, and localization properties of physical systems. Rather than the product of three separate reflections, CPT symmetry is revealed to be a single global reflection of the theory’s state space. (shrink)