Physically locating the present: A case of reading physics as a contribution to philosophy

By means of an example, special relativity and presentism, I argue for the importance of reading history of physics as a contribution to philosophy, and for the fruitfulness of this approach to doing integrated history and philosophy of science. Within philosophy of physics, presentism is widely regarded as untenable in the light of special relativity. I argue that reading Newton's Principia as a contribution to philosophy reveals a law-constitutive approach to the unity of what there is, from which an alternative approach to presentism within physics emerges. This view respects the methodological and epistemological commitments of philosophy of physics in “taking special relativity seriously”, but proposes an alternative approach to the status of spacetime (as epistemic) and to the ground of what is real (law-constitution). While this approach to presentism does not preserve all of the contemporary presentist desiderata, it offers the possibility that the spatiotemporal extent of an existing thing is less than its entire history as represented in the block universe. I argue that the approach warrants further philosophical investigation.     

Theory (In-)Equivalence and conventionalism in f(R) gravity

f(R) Gravity is the most natural extension of General Relativity within Riemannian Geometry. Due to (inter alia) its potential capacity for a unified treatment of early and late-time cosmic expansion, it has enjoyed recent attention in astrophysics and cosmology. I critically examine three inter-related claims found in the pertinent physics literature, of general interest to the philosopher of science. 1. f(R) Gravity is equivalent to a particular Brans-Dicke Theory. 2. The spacetime geometry underpinning f(R) Gravity has substantial conventional elements. 3. f(R) Gravity is an instance of a theory in which the distinction between matter and spacetime is conventional. Whilst the first claim can be vindicated in precise terms, the remaining two claims, I submit, are unwarranted – at least for the reasons usually adduced. On different grounds, though, the case for conventionalism about spacetime geometry in f(R) Gravity (as well as General Relativity) turns out to be considerably stronger.     

Minkowski spacetime and Lorentz invariance: The cart and the horse or two sides of a single coin?

Michel Janssen and Harvey Brown have driven a prominent recent debate concerning the direction of an alleged arrow of explanation between Minkowski spacetime and Lorentz invariance of dynamical laws in special relativity. In this article, I critically assess this controversy with the aim of clarifying the explanatory foundations of the theory. First, I show that two assumptions shared by the parties—that the dispute is independent of issues concerning spacetime ontology, and that there is an urgent need for a constructive interpretation of special relativity—are problematic and negatively affect the debate. Second, I argue that the whole discussion relies on a misleading conception of the link between Minkowski spacetime structure and Lorentz invariance, a misconception that in turn sheds more shadows than light on our understanding of the explanatory nature and power of Einstein׳s theory. I state that the arrow connecting Lorentz invariance and Minkowski spacetime is not explanatory and unidirectional, but analytic and bidirectional, and that this analytic arrow grounds the chronogeometric explanations of physical phenomena that special relativity offers.     

Newton–Cartan theory and teleparallel gravity: The force of a formulation

It is well-known that Newtonian gravity, commonly held to describe a gravitational force, can be recast in a form that incorporates gravity into the geometry of the theory: Newton–Cartan theory. It is less well-known that general relativity, a geometrical theory of gravity, can be reformulated in such a way that it resembles a force theory of gravity; teleparallel gravity does just this. This raises questions. One of these concerns theoretical underdetermination. I argue that these theories do not, in fact, represent cases of worrying underdetermination. On close examination, the alternative formulations are best interpreted as postulating the same spacetime ontology. In accepting this, we see that the ontological commitments of these theories cannot be directly deduced from their mathematical form. The spacetime geometry involved in a gravitational theory is not a straightforward consequence of anything internal to that theory as a theory of gravity. Rather, it essentially relies on the rest of nature (the non-gravitational interactions) conspiring to choose the appropriate set of inertial frames.     

Taking times out: Tense logic as a theory of time

Ulrich Meyer’s book The Nature of Time uses tense logic to argue for a ‘modal’ view of time, which replaces substantial times (as in Newton’s Absolute Time) with ‘ersatz times’ constructed using conceptually basic tense operators. He also argues against Bertrand Russell’s relationist theory, in which times are classes of events, and against the idea that relativity compels the integration of time and space (called by Meyer the Inseparability Argument). I find fault with each of these negative arguments, as well as with Meyer’s purported reconstruction of empty spacetime from tense operators and substantial spatial points. I suggest that Meyer’s positive project is best conceived as an elimination of time in the mode of Julian Barbour's The End of Time.     

On the time reversal invariance of classical electromagnetic theory

David Albert claims that classical electromagnetic theory is not time reversal invariant. He acknowledges that all physics books say that it is, but claims they are “simply wrong” because they rely on an incorrect account of how the time reversal operator acts on magnetic fields. On that account, electric fields are left intact by the operator, but magnetic fields are inverted. Albert sees no reason for the asymmetric treatment, and insists that neither field should be inverted. I argue, to the contrary, that the inversion of magnetic fields makes good sense and is, in fact, forced by elementary geometric considerations. I also suggest a way of thinking about the time reversal invariance of classical electromagnetic theory—one that makes use of the invariant four-dimensional formulation of the theory—that makes no reference to magnetic fields at all. It is my hope that it will be of interest in its own right, Albert aside. It has the advantage that it allows for arbitrary curvature in the background spacetime structure, and is therefore suitable for the framework of general relativity. The only assumption one needs is temporal orientability.     

Principle or constructive relativity

Appealing to Albert Einstein's distinction between principle and constructive theories, Harvey Brown has argued for an interpretation of the theory of relativity as a dynamic and constructive theory. Brown's view has been challenged by Michel Janssen and in this paper I investigate their dispute. I argue that their disagreement appears larger than it actually is due to the two frameworks used by Brown and Janssen to express their respective views: Brown's appeal to Einstein's principle–constructive distinction and Janssen's framing of the disagreement as one over the question whether relativity provides a kinematic or a dynamic constraint. I appeal to a distinction between types of theories drawn by H. A. Lorentz two decades before Einstein's distinction to argue that Einstein's distinction represents a false dichotomy. I argue further that the disagreement concerning the kinematics–dynamics distinction is a disagreement about labels but not about substance. There remains a genuine disagreement over the explanatory role of spacetime geometry and here I agree with Brown arguing that Janssen sees a pressing need for an explanation of Lorentz invariance where no further explanation is needed.     

The Principle of Equivalence

We start from John Norton's analysis (1985) of the reach of Einstein's version of the principle of equivalence which is not a local principle but an extension of the relativity principle to reference frames in constant acceleration on the background of Minkowski spacetime. We examine how such a point of view implies a profound, and not generally recognised, reconsideration of the concepts of inertial system and field in physics. We then reevaluate the role that the infinitesimal principle, if adequately formulated, can legitimately be claimed to play in general relativity. We show that what we call the ‘punctual equivalence principle’ has significant physical content and that it permits the derivation of the geodesic law.     

On geometric objects,the non-existence of a gravitational stress-energy tensor,and the uniqueness of the Einstein field equation

The question of the existence of gravitational stress-energy in general relativity has exercised investigators in the field since the inception of the theory. Folklore has it that no adequate definition of a localized gravitational stress-energetic quantity can be given. Most arguments to that effect invoke one version or another of the Principle of Equivalence. I argue that not only are such arguments of necessity vague and hand-waving but, worse, are beside the point and do not address the heart of the issue. Based on a novel analysis of what it may mean for one tensor to depend in the proper way on another, which, en passant, provides a precise characterization of the idea of a “geometric object”, I prove that, under certain natural conditions, there can be no tensor whose interpretation could be that it represents gravitational stress-energy in general relativity. It follows that gravitational energy, such as it is in general relativity, is necessarily non-local. Along the way, I prove a result of some interest in own right about the structure of the associated jet bundles of the bundle of Lorentz metrics over spacetime. I conclude by showing that my results also imply that, under a few natural conditions, the Einstein field equation is the unique equation relating gravitational phenomena to spatiotemporal structure, and discuss how this relates to the non-localizability of gravitational stress-energy. The main theorem proven underlying all the arguments is considerably stronger than the standard result in the literature used for the same purposes (Lovelock's theorem of 1972): it holds in all dimensions (not only in four); it does not require an assumption about the differential order of the desired concomitant of the metric; and it has a more natural physical interpretation.     

Have we lost spacetime on the way? Narrowing the gap between general relativity and quantum gravity

Important features of space and time are taken to be missing in quantum gravity, allegedly requiring an explanation of the emergence of spacetime from non-spatio-temporal theories. In this paper, we argue that the explanatory gap between general relativity and non-spatio-temporal quantum gravity theories might significantly be reduced with two moves. First, we point out that spacetime is already partially missing in the context of general relativity when understood from a dynamical perspective. Second, we argue that most approaches to quantum gravity already start with an in-built distinction between structures to which the asymmetry between space and time can be traced back.     

The priority of internal symmetries in particle physics

In this paper, I try to decipher the role of internal symmetries in the ontological maze of particle physics. The relationship between internal symmetries and laws of nature is discussed within the framework of “Platonic realism.” The notion of physical “structure” is introduced as representing a deeper ontological layer behind the observable world. I argue that an internal symmetry is a structure encompassing laws of nature. The application of internal symmetry groups to particle physics came about in two revolutionary steps. The first was the introduction of the internal symmetries of hadrons in the early 1960s. These global and approximate symmetries served as means of bypassing the dynamics. I argue that the realist could interpret these symmetries as ontologically prior to the hadrons. The second step was the gauge revolution in the 1970s, where symmetries became local and exact and were integrated with the dynamics. I argue that the symmetries of the second generation are fundamental in the following two respects: (1) According to the so-called “gauge argument,” gauge symmetry dictates the existence of gauge bosons, which determine the nature of the forces. This view, which has been recently criticized by some philosophers, is widely accepted in particle physics at least as a heuristic principle. (2) In view of grand unified theories, the new symmetries can be interpreted as ontologically prior to baryon matter.     

Theories of Newtonian gravity and empirical indistinguishability

In this essay, I examine the curved spacetime formulation of Newtonian gravity known as Newton–Cartan gravity and compare it with flat spacetime formulations. Two versions of Newton–Cartan gravity can be identified in the physics literature—a “weak” version and a “strong” version. The strong version has a constrained Hamiltonian formulation and consequently a well-defined gauge structure, whereas the weak version does not (with some qualifications). Moreover, the strong version is best compared with the structure of what Earman (World enough and spacetime. Cambridge: MIT Press) has dubbed Maxwellian spacetime. This suggests that there are also two versions of Newtonian gravity in flat spacetime—a “weak” version in Maxwellian spacetime, and a “strong” version in Neo-Newtonian spacetime. I conclude by indicating how these alternative formulations of Newtonian gravity impact the notion of empirical indistinguishability and the debate over scientific realism.     

On miracles and spacetime

What have recently been dubbed two ‘miracles’ of general relativity—(1) that all non-gravitational interactions are locally governed by Poincaré invariant dynamical laws; and (2) that, in the regime of experimental practice in which curvature effects may be ignored, the local Poincaré symmetries of the dynamical laws governing matter fields coincide with the local Poincaré symmetries of the dynamical metric field—remain unaccounted for in that theory. In this paper, I demonstrate that these two ‘miracles’ admit of a natural explanation in one particular successor theory to general relativity—namely, perturbative string theory. I argue that this point has important implications when considering both the ‘chronogeometricity’ (that is, the object in question being surveyed by rods and clocks built from matter fields) and spatiotemporal status of the dynamical metric field in both general relativity and perturbative string theory.     

Local reduction in physics

A conventional wisdom about the progress of physics holds that successive theories wholly encompass the domains of their predecessors through a process that is often called “reduction.” While certain influential accounts of inter-theory reduction in physics take reduction to require a single “global” derivation of one theory׳s laws from those of another, I show that global reductions are not available in all cases where the conventional wisdom requires reduction to hold. However, I argue that a weaker “local” form of reduction, which defines reduction between theories in terms of a more fundamental notion of reduction between models of a single fixed system, is available in such cases and moreover suffices to uphold the conventional wisdom. To illustrate the sort of fixed-system, inter-model reduction that grounds inter-theoretic reduction on this picture, I specialize to a particular class of cases in which both models are dynamical systems. I show that reduction in these cases is underwritten by a mathematical relationship that follows a certain liberalized construal of Nagel/Schaffner reduction, and support this claim with several examples. Moreover, I show that this broadly Nagelian analysis of inter-model reduction encompasses several cases that are sometimes cited as instances of the “physicist׳s” limit-based notion of reduction.     

Poincaré's Contributions to Relativistic Dynamics

In this paper I concentrate on the dynamic aspects of the special theory of relativity (in the non-Minkowski formalism), and not on the kinematic part of the story as is usually done. Following up the dynamic story leads to a new point of view as to Poincaré's important role in the development of special relativity. Much of Poincaré's dynamic work did not enter into Einstein's 1905 theory, since Einstein was mainly occupied with kinematics. However, the dynamic part is most fundamental in the development of the special theory of relativity after 1905. In this paper I consider the main developments of relativistic dynamics in which I demonstrate that much response to Poincaré's dynamic research can be found. I argue that Poincaré's dynamic work assisted in departing from Einstein's electrodynamic theory towards relativistic dynamics (independent of electrodynamics).     

The twins and the bucket: How Einstein made gravity rather than motion relative in general relativity

In publications in 1914 and 1918, Einstein claimed that his new theory of gravity in some sense relativizes the rotation of a body with respect to the distant stars (a stripped-down version of Newton's rotating bucket experiment) and the acceleration of the traveler with respect to the stay-at-home in the twin paradox. What he showed was that phenomena seen as inertial effects in a space-time coordinate system in which the non-accelerating body is at rest can be seen as a combination of inertial and gravitational effects in a (suitably chosen) space-time coordinate system in which the accelerating body is at rest. Two different relativity principles play a role in these accounts: (a) the relativity of non-uniform motion, in the weak sense that the laws of physics are the same in the two space-time coordinate systems involved; (b) what Einstein in 1920 called the relativity of the gravitational field, the notion that there is a unified inertio-gravitational field that splits differently into inertial and gravitational components in different coordinate systems. I provide a detailed reconstruction of Einstein's rather sketchy accounts of the twins and the bucket and examine the role of these two relativity principles. I argue that we can hold on to (b) but that (a) is either false or trivial.     

Would two dimensions be world enough for spacetime?

We consider various curious features of general relativity, and relativistic field theory, in two spacetime dimensions. In particular, we discuss: the vanishing of the Einstein tensor; the failure of an initial-value formulation for vacuum spacetimes; the status of singularity theorems; the non-existence of a Newtonian limit; the status of the cosmological constant; and the character of matter fields, including perfect fluids and electromagnetic fields. We conclude with a discussion of what constrains our understanding of physics in different dimensions.     

The constitutive a priori and the distinction between mathematical and physical possibility

This paper is concerned with Friedman׳s recent revival of the notion of the relativized a priori. It is particularly concerned with addressing the question as to how Friedman׳s understanding of the constitutive function of the a priori has changed since his defence of the idea in his Dynamics of Reason. Friedman׳s understanding of the a priori remains influenced by Reichenbach׳s initial defence of the idea; I argue that this notion of the a priori does not naturally lend itself to describing the historical development of space-time physics. Friedman׳s analysis of the role of the rotating frame thought experiment in the development of general relativity – which he suggests made the mathematical possibility of four-dimensional space-time a genuine physical possibility – has a central role in his argument. I analyse this thought experiment and argue that it is better understood by following Cassirer and placing emphasis on regulative principles. Furthermore, I argue that Cassirer׳s Kantian framework enables us to capture Friedman׳s key insights into the nature of the constitutive a priori.     

Looking forward,not back: Supporting structuralism in the present

The view that the fundamental kind properties are intrinsic properties enjoys reflexive endorsement by most metaphysicians of science. But ontic structural realists deny that there are any fundamental intrinsic properties at all. Given that structuralists distrust intuition as a guide to truth, and given that we currently lack a fundamental physical theory that we could consult instead to order settle the issue, it might seem as if there is simply nowhere for this debate to go at present. However, I will argue that there exists an as-yet untapped resource for arguing for ontic structuralism – namely, the way that fundamentality is conceptualized in our most fundamental physical frameworks. By arguing that physical objects must be subject to the ‘Goldilock's principle’ if they are to count as fundamental at all, I argue that we can no longer view the majority of properties defining them as intrinsic. As such, ontic structural realism can be regarded as the most promising metaphysics for fundamental physics, and that this is so even though we do not yet claim to know precisely what that fundamental physics is.     

Holographic space and time: Emergent in what sense?

This paper proposes a metaphysics for holographic duality. In addition to the AdS/CFT correspondence I also consider the dS/CFT conjecture of duality. Both involve non-perturbative string theory and both are exact dualities. But while the AdS/CFT keeps time at the margins of the story, the dS/CFT conjecture gives to time the “space” it deserves by presenting an interesting holographic model of it. My goals in this paper can be summarized in the following way. First, I argue that the formal structure and physical content of the duality do not support the standard philosophical reading of the relation in terms of grounding. Second, I put forward a philosophical scheme mainly extrapolated from the double aspect monism theory. I read holographic duality in this framework as it seems to fit the mathematical and physical structure of the duality smoothly. Inside this framework I propose a notion of spacetime emergence alternative to those ones commonly debated in the AdS/CFT physics and philosophy circles.