COSMO-MASTER

Spelling out the story above, providing context, tying the chapters together, comparing the upshots and drawbacks of a strict spacetime-matter dichotomy.

Mathematics makes such abundant use of the word ‘space’, it’s dubious that armchair necessary and sufficient conditions can be distilled to guide its application in physical theory as contrasted with ‘matter’. I suggest instead that the distinction is best grasped as a contingent historical development, and then often with difficulty, particularly when projecting the terms from paradigmatic cases to later developments involving new concepts. Upon survey, it would appear that invariably space and matter should stand in the right relationship, metaphorically that of container to contents. Secondly, there must be available a notion of place (topos, locus) capable of supporting a distinction between natural and enforced motion. Originally, this amounted to the need for unmoved places. This essay illustrates these requirements over a broad span of theory, beginning with the pre-Socratics and extending into the twentieth century. Eventually, we will see the distinction between space and matter disappear in various theories.

Classical field theories, like electromagnetism and Newtonian gravity, might appear to treat matter and field as very different kinds of things.  In fact, even before one considers quantum physics or general relativity, there are good reasons to collapse the divide and classify fields, like the electromagnetic field, as matter.  The electromagnetic field possesses energy, momentum, mass, velocity, and acceleration.  The electromagnetic field exerts and experiences forces.  The electromagnetic field is not merely a way of encoding interactions between charged bodies and does not owe its existence to charged sources.  The electromagnetic field does not closely resemble point particles, but there are better models of matter than point particles.  The case for classifying the gravitational field as matter looks a bit different than the case for the electromagnetic field because Newtonian gravity is not a relativistic theory.  Understanding fields as matter paves a smoother road to general relativity and quantum field theory, theories that do not draw a sharp distinction between fields and matter.

The standard physicist’s story goes that general relativity contains a principled distinction between spacetime and matter. However, in practice, there are many models of matter at play, with varying assumptions and constructions. This chapter examines how these matter models function within general relativity and how they blur the line between matter and spacetime. 

We begin with the basic concept of a stress-energy tensor at points of spacetime, the paradigm of matter in GR. However, a closer look at how stress–energy tensors are defined in practice shows that their very construction already presupposes aspects of the spacetime geometry. We then turn to compact objects—white dwarfs, neutron stars, and black holes—whose modeling requires understanding both local thermodynamic properties (pressure, viscosity etc.) and global gravitational properties (mass, multipole moments etc.). Strikingly, very different physical systems—ordinary stars and black holes—can share similar global descriptions (e.g., the Schwarzschild solution). Operationally, we infer their presence through their gravitational effects, as if they were all matter. Finally, we consider various non-local notions of mass-energy to ask whether they measure the energy of spacetime or of matter, focusing on the question of whether (and how) different mass-energy concepts depend crucially on different aspects of spacetime structure for their definition. 

Because these various concepts involve spacetime to differing degrees, we argue that there is no unique spacetime-matter distinction to be drawn. Rather, cataloguing these concepts in general relativity reveals that “matter” and “spacetime” are not binary categories but points along a modeling continuum. Which side of the spectrum we place them on depends on the context, purpose, and explanatory aims of the model in question. Nonetheless, the persistence of the spacetime-matter distinction reflects its pragmatic and explanatory value.

Abstract tbc

In classical relativistic field theory, fields like the electromagnetic potential A_a(x) or a perfect fluid are usually taken to be matter fields. This is because, besides having dynamics and being able to interact, they have associated energy–or a stress-energy tensor.  In this work we discuss whether and how a generalisation of these criteria to quantum fields is possible. We first discuss the notion of quantum matter in Minkowski space-time, specially analysing the importance of perturbative/non perturbative QFT. We then consider the extension to general metrics g_ab and focus on two properties that in principle one should ascribe to matter: vacuum energy and particle production. We show how the criterion for matter needs to be carefully adjusted to include these phenomena, and we show that some criteria posed in the literature are not able to do so. The main reason is the presence of curvature terms in the stress-energy tensor.  Finally, we conclude that although a matter criterion is still possible, the metric g_ab cannot be seen as purely geometry and has to also include field properties, i.e., an egalitarian posture in the sense of Lehmkuhl (2009).

The “observables” view of general relativity takes it to be similar to gauge theories, and, as it happens in this sort of theory, that the physical content of the model has to be encoded in its observables, understood as invariant phase space functions in the canonical formulation of the theory. When applying these ideas, some authors have found that only correlations would be observable in diffeomorphism invariant theories. This position is especially popular in the quantum gravity community, as it supports the possibility of having theories in which spacetime is not fundamental. In this chapter, I oppose this view by arguing that spatiotemporal relations, such as whether two events are timelike or the proper time between them, can also be represented as invariant phase space functions. In this sense, I conclude that analyzing general relativity as a gauge theory does not force one to adopt a position in which the spacetime-matter distinction becomes thinner or in which spacetime does not play a fundamental role in the theory.

There are two current and arguably controversial projects in the philosophy of physics that go hand in hand. First, inspired by contemporary physics, Niels Martens and collaborators challenge what they dub the "Democritean-Newtonian tradition of assuming a strict conceptual dichotomy between spacetime and matter". Second, tipped off by what has become jargon, Rasmus Jaksland and Kian Salimkhani urge philosophers of quantum gravity to specify their claims on the 'emergence of spacetime' in terms of concrete spatiotemporal aspects. This chapter will reflect on these developments and explore to what extent traditional concepts and categorizations have to give. First, the Martens et al. approach is criticized as basically engineering its result. Then, it is argued that their central claims are nevertheless correct for three reasons: (1) certain case studies, (2) more general conceptual and interpretational issues in the philosophy of physics, and (3) a criterion of fruitfulness assessing which concepts should be used. Finally, connecting back to the initial critique, it is demonstrated how the dichotomy may be defended by a few plausible tweaks that, however, render the dichotomy merely conventional – unless one adopts an essentialist view.

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I consider the significance of the spin-2 approach for understanding the spacetime/matter distinction for General Relativity (GR). To this end, I examine the four central ways in which a spin-2 approach—prima facie conceived as a theory in its own right—has been said to relate to GR—or, more precisely, its globally hyperbolic and thereby (arguably) physically relevant subsector (call it GR-HYP): (1) the spin-2 approach subsumes GR-HP; (2) GR-HYP subsumes the spin-2 approach; (3) the spin-2 approach and GR-HYP are empirically equivalent (though not theoretically so); and (4) the spin-2 approach and GR-HYP are fully theoretically equivalent, i.e., merely different formulations of a single underlying theory. I show that positions (1)-(3) are untenable, and make a positive case for (4), drawing on a theorem by Boulanger et al.'s 2001 ``Inconsistency of interacting, multi-graviton theories". I then expand on and critically discuss the various ways how (4) breaks the spacetime/matter distinction.

In general relativity, gravitational waves influence spacetime geometry. Two Cauchy surfaces both with vanishing stress–energy tensors may nonetheless evolve differently if distinct gravitational waves pass between them. Hence, if matter is identified solely with the stress–energy tensor, one prominent version of Mach’s principle—the one Einstein initially endorsed, according to which matter fully determines geometry—fails. A relationist might respond by expanding the ontology of matter to include gravitational waves, which exhibit many matter-like features, as in Wheeler’s notion of “geons.” But this move trivializes the debate between relationists and substantivalists: the disagreement collapses into a question of whether gravitational waves should be called matter or not. Worse still, treating gravitational waves as matter brings relationists closer to the substantivalists, who often regard the metric field as a matter-like entity. For relationists, nothing really matters, since gravitational waves are matter in vacuum spacetime; for substantivalists, nothing really matters, since vacuum spacetime itself is substance. This chapter argues that the breakdown of the spacetime–matter dichotomy in the case of gravitational waves exposes a corresponding breakdown in the substantivalism–relationalism debate. I then propose a non-trivial reconstruction of the debate by appealing to the gravitational arrow of time.

This chapter investigates the question whether black holes should be categorized as a form of spacetime or matter. Drawing on relationships between many available definitions of black holes, formation mechanisms of black holes, and Wheeler’s geon program, we will argue that both spacetime and matter camps are committed to a form of conceptual rigidity. One either (1) ends up with an incomplete picture that focuses on a too narrow class of models and definitions, or (2) becomes committed to risky reduction programs. Both positions become an argumentative burden; the distinction between spacetime and matter breaks down when faced with physical practice, because there is little to be gained by insisting on it, and plenty to lose.

One of the enduring insights of philosophy of quantum gravity is the convergence across competing approaches that spacetime and/or matter seem not to be fundamental – they appear to emerge from underlying structure which is, in important respects, non-spatiotemporal and/or non-material (c.f., Wüthrich and Huggett 2025). Emergence points to yet another argument questioning substance-kind dualism between spacetime and matter, not least because of the aspiration for a unified ‘theory of everything’ merging general relativity and quantum field theory. The last 20 years or so, however, have seen a backlash against the gridlock in quantum gravity, with scholars contemplating whether the so-called guiding principle of unification has hampered progress. In the face of this backlash, I contend that black hole evaporation offers a fresh argument for unification than what is standardly presented. Because reconciling our current best theories of spacetime and matter depends crucially on transitioning seamlessly between semi-classical and quantum gravity, the domains of black hole thermodynamics and black hole statistical mechanics respectively, I argue that the reductionist project in black hole physics reinvigorates and elevates challenges to the fundamentality of the spacetime-matter distinction.

We investigate the issue whether the accelerated expansion of space should be regarded as an effect of matter or geometry. Early-time accelerated expansion is posited by the theory of cosmic inflation, which generally assumes a scalar field, the “inflaton,” is responsible for it; late-time accelerated expansion is explained by a posited dark energy, which is often represented as the cosmological constant. Whereas the inflaton field is naturally regarded as a kind of “matter” or “energy,” the cosmological constant is often regarded as geometrical. One phenomenon – accelerated expansion, two ontological characters – material and geometrical. We resolve the apparent inconsistency by explicating the matter-geometry distinction in general relativity, concluding that the cosmological constant is in fact better regarded as material.

Abstract tbc

This chapter cautions against drawing conventionalist conclusions about the spacetime–matter distinction from equivalences of “spacetime” Lagrangians and “matter” Lagrangians. The case examined is from cosmological inflation: the formal equivalence between single-scalar-field inflation (“matter”) and Starobinsky’s curvature-squared inflation (“spacetime”), seemingly undermining the distinction. However, following Norton’s account of idealisation, it is argued that features of idealised models are mistaken for features of nature. The equivalence is shown to dissolve once known physics such as the Higgs field is included. Perhaps the spacetime-matter distinction is undermined for other reasons given in this volume, but not for pragmatic decisions of modelling practices.

The supersubstantivalist thesis has traditionally been discussed in “universal” terms: either spacetime is the only fundamental substance and that matter is, in some sense, an aspect or derivative of spacetime, or matter is the only fundamental substance and spacetime is, in some sense, an aspect or derivative of spacetime. We argue that recent “Janus-faced” models such as Superfluid Dark Matter (SFDM) invite a novel contextual reinterpretation of the thesis. In SFDM, the dark matter field Φ behaves both as matter and as spacetime, while baryonic matter does not. This suggests a contextual or sectoral form of supersubstantivalism: the unity of spacetime and matter is realized only within a specific physical domain, namely the dark sector. This chapter reconstructs how such a position simultaneously betrays and preserves the spirit of classical supersubstantivalism. It betrays it, because the thesis no longer applies to all that exists; yet it preserves it, because a part of the material domain still manifests spacetime-like substance. We claim that this restricted realization requires us to rethink the very scope of the spacetime–matter distinction and the main thesis of supersubstantivalism more generally.

The chapter examines whether a primitive ontological approach—according to which physical theories are defined by primitive variables representing matter on a spatio-temporal background, together with non-primitive dynamical ones corresponding to the laws—can be extended to cosmology. While the ΛCDM model and modified gravity theories initially appear to fit this framework, recent analyses of superfluid dark matter (SFDM) suggest that the boundary between matter and spacetime may become obscure, thereby calling into question one of the key assumptions of the primitive ontology. By considering the case of analogue gravity, where the dynamics of the perturbations of a quantum condensate is specified by an effective metric, we consider whether a coherent distinction between matter and space-time can still be upheld, and hence whether the primitive ontological program remains a viable strategy for the foundations of cosmology.

This chapter uses analogue gravity as a tool to explore and to problematize the conceptual distinction between spacetime and matter as fundamental constituents of the universe. One particular system class, Bose-Einstein condensates is used to show how spacetime and matter on it can be simulated using processes having no qualitative connection to the system being simulated. Here a static collection of particles in a single quantum state supporting classical sound waves uses a change in how the collection is tuned as a support for those waves to simulate particle production due to the expansion of the universe. It is argued that we have reason to think that the fundamental constituents of the universe are plausibly, radically unlike how they appear in our current theories.

This proposed chapter offers a historical perspective on the question how supersymmetry has confronted the traditional spacetime-matter dichotomy, focusing on the related development of supergravity and superstring theory in the 1970s and early 1980s. Chronologically considering (1) the initial formulation of supergravity, (2) the exploration of extended supergravity theories in higher dimensions, and (3) the rise of superstring theory, we highlight how notions of spacetime and matter were reflected (and sometimes transcended) in supersymmetric theory construction. Importantly, while the basic concept of supersymmetry itself blurs the conceptual distinction between spacetime and matter, as put to use by theorists it mostly functioned in linking perspectives that either underscored a matter or spacetime point of view. The account put forward in this chapter provides much-needed historical footing for the further foundational analysis of supergravity and superstring theory.

The distinction between spacetime and matter constitutes one of the oldest and most common assumptions of philosophy of physics, dating back at least to Newton. At the same time, recent advances in theoretical physics suggest that this distinction might be on shakier ground than we thought. In this paper, we investigate the status of the distinction between spacetime and matter in the context of theories of supergravity, i.e. the supersymmetric extension of Einstein's general relativity, and of their quantum extension in string theory. We find that in supergravity the status of the spacetime/matter distinction depends on subtle features of the geometry of supergravity, i.e. supergeometry. In string theory, the situation becomes even more complex, since the status of the spacetime/matter distinction turns out to depend not only on the underlying supergeometry, but also on the strength of interactions and quantum effects in a given model of string theory. Overall, our analysis provides the first attempt at evaluating the spacetime/matter distinction in supergravity and supersymmetric theories; it also gives a natural starting point for the philosophical analysis of supergravity, a field currently highly underdeveloped and ripe for philosophical analysis.

Metaphysicians tend to have very little patience with talk about concepts. They want to talk about the world, not about how we talk about the world. There’s no trouble, so the argument goes, with talking about tables; we can talk about them without worrying too much about the concept `table’, whatever that is. Similarly, if we want to talk about matter and spacetime, we do not need to fiddle around too much with the concepts `matter’ and `spacetime’.  But the table example is misleading: our ability to talk about tables is still mediated by concepts, it is just that we are so familiar with the workings of those concepts that we rarely stop to examine them. The same is not true of `spacetime’ and `matter’. In this chapter, I argue that, in order to even get our metaphysical theorizing off the ground, we need to engage in the analysis of the concepts of `spacetime’ and `matter’.  I argue that the standard representationalist approach to concepts—according to which conceptual content is understood in terms of what part of the world a concept represents—is not fit for purpose when it comes to theories of physics, astrophysics and cosmology. It leaves little room, for example, for a nuanced assessment of the `spacetime is a container’ metaphor: either it is (substantivalism) or it is not (relationalism). In its place, I argue for a Brandomian inferentialist-pragmatist approach, according to which (scientific) conceptual content is understood in terms of the norms of deployment of that concept within a (scientific) linguistic community. This account equips us with a more appropriate toolbox with which to better understand the myriad ways in which our physical theories come to be about the world. It highlights what is useful about `spacetime is a container’ metaphor, and what is a hindrance. By doing so, it opens the door to a number of previously unavailable hybrid views regarding spacetime, matter, and their relationship. 

This chapter investigates the origins of the spacetime–matter distinction through Euler’s conception of absolute space and time as the framework that grounds inertial motion. Drawing on the Réflexions sur l’espace et le tems (1750) and the Theoria motus (1765), I show how Euler’s distinction between internal and external causes of motion grounds an early form of the divide between spacetime and matter, while simultaneously rendering this division unstable. If we reject the doctrine that inertia is due to internal causes then spacetime assumes a quasi-material role as its external cause. I trace this tension forward to general relativity, where the geodesic principle and general covariance reconfigure inertia as (arguably) gravitational in origin, challenging the basis for the classical metaphysical distinction between spacetime and matter. The chapter thus situates Euler’s mechanics as a pivotal case in the historical constitution—and ongoing reinterpretation—of the spacetime–matter dichotomy.

The spacetime-matter distinction is centered around a dualism between some kind of container and stuff contained in that container. The former is identified with a pair (M, g) of a smooth manifold with a Lorentzian metric, and the latter then encompasses all fields in the Standard Model, i.e. fermionic fields, the Higgs field and gauge fields. Within the Standard Model, however, gauge fields play an entirely distinct role from fermionic fields and the Higgs field. In fact, gauge fields are in many respects similar to the gravitational field, which exhibits two types of gauge symmetry: local Lorentz invariance and diffeomorphism invariance. This additional diffeomorphism invariance is unique to gravity because it describes the container itself, rather than a field in that container. Based on these observations we propose a spacetime-force-matter trichotomy.

This chapter considers what the significance of giving up the spacetime-matter distinction could be by considering a particular manner in which it has already been given up. Insofar as the spacetime-matter distinction is necessary to ground the modal status and explanatory power of laws of nature (Wigner), the distinction has been replaced by a more general and more abstract distinction between the kinematics and dynamics of a theory (Curiel). I characterize this transition as a Hegelian “sublation”—the original spacetime-matter distinction is both cancelled by (in some respects) and conserved by (in other respects) the new kinematics-dynamics distinction. The consequences of this sublation for important metaphysical issues, like the substantivalism-relationalism debate and the ontological status of “abstract” spaces like the Hilbert space in quantum mechanics are considered.

The question that concerns us is how to draw the distinction between spacetime and matter. But there are two other well-known distinctions that are relevant to this question. The first is Quine’s distinction between ontology – what there is – and ideology – what one can say about what there is. The second is the distinction between the external and internal degrees of freedom of a theory. This chapter first discusses an intuitive picture of field theories, on which spacetime is part of a theory’s ontology and matter part of its ideology. It then rejects this picture in favour of one in which both spacetime and matter are ontology. The paper proposes that one can better explain the difference between spacetime and matter in terms of the external-internal distinction: matter-properties are had by spacetime. This provides a systematic way to (re-draw) the spacetime-matter distinction in terms of another distinction already relevant to physical practice.