Niels Linnemann

Recently, Baron and Le Bihan (2023) have suggested revisiting the causal theory of spacetime, noting that advancements in physics, particularly causal set theory, and metaphysics offer new counters to the criticisms of Smart (1969) and Earman (1972)—criticisms that, they say, defeated the original causal theory of spacetime. Baron and Le Bihan propose that, while the traditional identity causal theory, which seeks to equate spacetime relations with causal relations, is still inadequate, a revised approach could succeed if identity is replaced by grounding and if the grounding base is that of causal set theory. This non-identity causal theory of spacetime posits, in other words, that spatiotemporal relations are grounded in the fundamental causal relations associated with causal sets—in alleged line with the original aim of understanding spacetime through causality. In this paper, we argue that the new arguments put forward by Baron and Le Bihan do little to meet the challenges of Smart and Earman with the result that their non-identity theory does not fare better in addressing these original criticisms than the identity theory. To this end, we will demonstrate that their new arguments make assumptions that (1) are not shared in these historical criticisms of causal theories of spacetime, and, at the same time, (2) are either indecisive or false. Furthermore, we argue that, even with these assumptions, the identity theory can still do just as well as the non-identity theory.

Two approaches to elevating certain laws of nature over others have come to prominence recently. On the one hand, according to the meta-laws approach, there are meta-laws, laws which relate to laws as those laws relate to particular facts. On the other hand, according to the modal, or non-absolutist, approach, some laws are necessary in a stricter sense than others. Both approaches play an important role in current research, questioning the ‘orthodoxy’ represented by the leading philosophical theories of natural laws—Humeanism, the DTA view, dispositional essentialism and primitivism. This paper clarifies the relations between these two emerging approaches, as well as their applicability to physical laws and the status of the challenges they pose for standard theories of laws of nature. We first argue that, despite some significant similarities between the two approaches (especially in the context of Lange’s counterfactual account of laws), they are in general distinct and largely independent of each other. Then, we argue that the support for meta-laws from physical theory and practice is more questionable than usually presented.

The programme of ‘constructive axiomatics’, promulgated by Hans Reichenbach in 1924, seeks to build up the architecture of our best theories of physics from basic axioms supposedly imbued with immediate and indubitable empirical content. Taking inspiration from Reichenbach, Hermann Weyl proposed his own ‘causal-inertial’ approach to the constructive axiomatisation of Einstein’s general relativity, according to which a relativistic spacetime can be constructed solely from the trajectories of light rays and freely-falling particles; this project, however, came to fruition only in 1972, with the constructive axiomatisation of general relativity due to Ehlers, Pirani, and Schild (‘EPS’).One century since Reichenbach, and fifty years since EPS, this book is a celebration of the constructive axiomatic methodology. It achieves four main tasks. First, it provides a thoroughgoing presentation of the EPS axiomatisation, closing missing loopholes, identifying problematic axioms, and so forth—in this way, one gains a much-improved appreciation of the extent to which a causal-inertial approach to general relativity might succeed, and of what such an approach might offer. Second, it synthesises and assesses the vast but disparate literature on constructive axiomatics which has arisen over the past century and sets the methodology in its proper philosophical context. Third, it generalises the approach to apply to quantum spacetimes. And fourth, it applies the approach to the context of non-relativistic spacetime physics. All in all, the book demonstrates that constructive axiomatics is live-and-kicking; the book will become the go-to resource for this way of philosophising about the nature of space and time.

According to the standard Humean account of laws of nature, laws are selected partly as a result of an optimal trade-off between the scientific virtues of simplicity and strength. Roberts and Woodward have recently objected that such trade-offs play no role in how laws are chosen in science. In this paper, we first discuss an example from the field of automated scientific discovery which provides concrete support for Roberts and Woodward’s point that scientific theories are chosen based on a single-virtue threshold. However, we then use this very same example as a starting point to argue that i) by insisting on a single best theory, Humeans rely on an overly simplistic conception of trade-offs, that ii) this conception should give way to one which allows for a Pareto front of equally optimal theories, and iii) that given this new conception, threshold behaviour for a virtue like strength is a) compatible with the existence of a genuine trade-off and b) can even play the positive role of a selection criterion.

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.

It has recently become popular to analyze scenarios in which we guess, in terms of a trade‐off between the accuracy of our guess (namely, its credence) and its specificity (namely, how many answers it rules out). Dorst and Mandelkern describe an account of guessing, based on epistemic utility theory (EUT), in which permissible guesses vary depending on how one weighs accuracy against specificity. We provide a minimal formal account of guessing that: (i) does not employ EUT, but rests on how such trade‐offs are treated in the sciences; (ii) is relatively parsimonious; and (iii) is consistent with a variety of more specific models that describe what an agent is doing when they (rationally) guess. Our account also recovers patterns of guessing and predictions about typical outcomes of guessing, as identified by Dorst and Mandelkern. Furthermore, we focus on how permissible guesses can be improved upon, via changes in an agent's credence distribution. Such better permissible guesses can be generated in solving Fermi problems—guessing problems of a type that has received almost no attention in the philosophical literature—which we also analyze. Our account strengthens the case for understanding guessing (now, very broadly considered) in terms of accuracy‐specificity trade‐offs.

The self-interaction spin-2 approach to GR has been extremely influential in the particle physics community. Leaving no doubt regarding its heuristic value, we argue that any view of the metric field of GR as nothing but a stand-in for a self-coupling field in at spacetime runs into a dilemma: either the view is physically incomplete in so far as it requires recourse to GR after all, or it leads to an absurd multiplication of alternative viewpoints on GR rendering any understanding of the metric field as nothing but a spin-2 field in at spacetime unjustified.

The aim to provide a causal theory of spacetime is not new. The overall program, however, was largely deemed unsuccessful, chiefly due to criticism voiced by Smart (Monist 53:385–395, 1969), Nerlich (Br J Philos Sci 33(4):361–388, 1982) and Earman (Synthese 24:74–86, 1972). Recently, Baron and Le Bihan (Noûs 58:202–224, 2023) have argued that developments in contemporary physics should make us reconsider this verdict. More precisely, they argue the emergence of spacetime from causal set theory (CST), where “the metric structure of spacetime can be recovered from its causal structure” (Baron and Le Bihan 2023, 2), “suggests a very natural way to reformulate the causal theory of spacetime” (ibid., 9)—an account which they end up dubbing the non-identity causal theory. This paper questions the success of Baron and Le Bihan’s non-identity theory. It is shown that (1) the specific grounding Baron and Le Bihan propose for timelike and spacelike relations is not plausible even when charitably reconstructed; and (2) that a causal theory of spacetime based on general relativity is just as successful for establishing a non-identity theory as a theory based on CST. In short then, we argue that the causal theory of spacetime proposed by Baron and Le Bihan is supported just as well (or badly) by the physics that already took centre stage in the original discussions of the causal theory of spacetime.

Recent work in the physics literature demonstrates that, in particular classes of rotating spacetimes, physical light rays in general do not traverse null geodesics. Having presented this result, we discuss its philosophical significance, both for the clock hypothesis (and, in particular, a recent purported proof thereof for light clocks), and for the operational meaning of the metric field. 1Introduction 2Fletcher's Theorem 2.1Maudlin on the clock hypothesis in special relativity 2.2Fletcher’s result in special relativity 2.3Fletcher’s theorem in general relativity 3Electromagnetism and the Geometrical-Optical Limit 3.1Maxwell’s equations in curved spacetime 3.2The geometrical-optical limit 3.3Rotating spacetimes 3.4Aren’t Gödel spacetimes unphysical? 4The Clock Hypothesis and Chronogeometry 4.1Natural and mathematical observations 4.2Clock registry discord 4.3Chronogeometry 5Conclusion.

A common feature of all standard theories of the laws of nature is that they are "absolutist": They take laws to be either all metaphysically necessary or all contingent. Science, however, gives us reason to think that there are laws of both kinds, suggesting that standard theories should make way for "non-absolutist" alternatives: theories which accommodate laws of both modal statuses. In this paper, we set out three explanatory challenges for any candidate non-absolutist theory and discuss the prospects of the two extant candidates in light of these challenges. We then develop our own non-absolutist theory, the essentialist DTA account, which combines the nomic-necessitation or DTA account with an essentialist approach to metaphysical modality in order to meet the three explanatory challenges. Finally, we argue that the distinction between kinematical and dynamical laws found in physical theories supports both non-absolutism in general and our proposed essentialist DTA view in particular.

We show by means of the AdS/CFT correspondence in the context of quantum gravity how inter-representational relations—loosely speaking relations among different equivalent representations of one and the same physics—can play out as a tool for intra-theoretical developments and thus boost theory development in the context of discovery. More precisely, we first show that, as a duality, the AdS/CFT correspondence cannot in itself testify to the quantum origin of gravity (though it may be utilized for this purpose). We then establish through two case studies from emergent gravity (Jacobson (2016); Verlinde (2017)) that the holographic AdS/CFT correspondence can, however, still excel as a guiding principle towards the quantum origin of gravity (similar in nature to quantisation).

It has long been thought that observing distinctive traces of quantum gravity in a laboratory setting is effectively impossible, since gravity is so much weaker than all the other familiar forces in particle physics. But the quantum gravity phenomenology community today seeks to do the (effectively) impossible, using a challenging novel class of `tabletop' Gravitationally Induced Entanglement (GIE) experiments, surveyed here. The hypothesized outcomes of the GIE experiments are claimed by some (but disputed by others) to provide a `witness' of the underlying quantum nature of gravity in the non-relativistic limit, using superpositions of Planck-mass bodies. We inspect what sort of achievement it would possibly be to perform GIE experiments, as proposed, ultimately arguing that the positive claim of witness is equivocal. Despite various sweeping arguments to the contrary in the vicinity of quantum information theory or given low-energy quantum gravity, whether or not one can claim to witness the quantum nature of the gravitational field in these experiments decisively depends on which out of two legitimate modelling paradigms one finds oneself in. However, by situating GIE experiments in a tradition of existing experiments aimed at making gravity interestingly quantum in the laboratory, we argue that, independently of witnessing or paradigms, there are powerful reasons to perform the experiments, and that their successful undertaking would indeed be a major advance in physics.

How does metaphysical necessity relate to the modal force often associated with natural laws? Fine argues that natural necessity can neither be obtained from metaphysical necessity via forms of restriction nor of relativization — and therefore pleads for modal pluralism concerning natural and metaphysical necessity. Wolff, 898–906, 2013) aims at providing illustrative examples in support of applying Fine’s view to the laws of nature with specific recourse to the laws of physics: On the one hand, Wolff takes it that equations of motion can count as examples of physical laws that are only naturally but not metaphysically necessary. On the other hand, Wolff argues that a certain conservation law obtainable via Noether’s second theorem is an instance of a metaphysically necessary physical law. I show how Wolff’s example for a putatively metaphysically necessary conservation law fails but argue that so-called topological currents can nevertheless count as metaphysically necessary conservation laws carrying physical content. I conclude with a remark on employing physics to answer questions in metaphysics.

Prominently, Norton argues against constructivism about spacetime theories, the doctrine that spatiotemporal structure in the dynamics only has derivative status. Among other things, he accuses Brown and Pooley's dynamical approach to special relativity of being merely half-way constructivist: setting up relativistic fields as presupposed in the dynamical approach to special relativity already requires spatiotemporal background structure. We first assess a recent solution proposal by Menon and then provide our very own defense of constructivism along two independent lines.

The empirical coherence problem of quantum gravity is the worry that a theory which does not fundamentally contain local beables located in space and time—such as is arguably the case for certain approaches to quantum gravity—cannot be connected to measurements and thus has its prospects of being empirically adequate undermined. Spacetime functionalism à la Lam and Wüthrich is said to solve this empirical coherence problem as well as bridging a severe conceptual gap between spatiotemporal structures of classical spacetime theories on the one hand, and the non-spatiotemporal structures in quantum gravity approaches on the other hand. The aim of this essay is to offer a deflationary account of both the empirical coherence problem and the spatiotemporal gap problem as they are claimed to arise at least prima facie for current theories of quantum gravity by Huggett and Wüthrich :276–285, 2013), Lam and Wüthrich and Le Bihan. I defend the view that spacetime functionalism is set up to address a problem which can usually be solved without it; and that it is wrongly claimed to solve another problem which for any actual account of quantum gravity is in fact currently non-existent anyway.

In a recent article in this journal, Sus purports to account for what have been identified as the ‘two miracles’ of general relativity—that (1) the local symmetries of all dynamical equations for matter fields coincide, and (2) the symmetries of the dynamical equations governing matter fields coincide locally with the symmetries of the metric field—by application of the familiar result that every symmetry of the action is also a symmetry of the resulting equations of motion. In this reply, we argue that, while otherwise exemplary in its clarity, Sus’ paper fails in this regard, for it rests upon a illegitimate application of the aforementioned result. Thus, we conclude, pace Sus, that these two miracles persist in general relativity.

Principles are central to physical reasoning, particularly in the search for a theory of quantum gravity, where novel empirical data are lacking. One principle widely adopted in the search for QG is ultraviolet completion: the idea that a theory should hold up to all possible high energies. We argue— contra standard scientific practice—that UV-completion is poorly motivated as a guiding principle in theory-construction, and cannot be used as a criterion of theory-justification in the search for QG. For this, we explore the reasons for expecting, or desiring, a UV-complete theory, as well as analyse how UV-completion is used, and how it should be used, in various specific approaches to QG. 1Introduction 1.1Principles in theory development and evaluation 2Primer on UV-Completion, Renormalizability, and All That 2.1Renormalizability and UV-completion 2.2Other forms of UV-completion 3Why Should QG Be UV-Complete? 3.1UV-completion and fundamentality 3.2UV-completion and minimal length 4UV-Completion in Different Approaches to QG 4.1String theory 4.2Asymptotic safety 4.3Causal dynamical triangulation 4.4Higher derivative approaches 4.5Supergravity 4.6Causal set theory 4.7Canonical QG 4.8Loop quantum gravity 4.9Approaches based on alternative gravitational theories 4.10Emergent gravity approaches 5UV-Completion as a Guiding Principle in QG 6Conclusion.

General relativity cannot be formulated as a perturbatively renormalizable quantum field theory. An argument relying on the validity of the Bekenstein–Hawking entropy formula aims at dismissing gravity as non-renormalizable per se, against hopes that d-dimensional GR could turn out to have a non-perturbatively renormalizable d–dimensional quantum field theoretic formulation. In this note we discuss various forms of highly problematic semi-classical extrapolations assumed by both sides of the debate concerning what we call The Entropy Argument, and show that a large class of dimensional reduction scenarios leads to the blow-up of Bekenstein–Hawking entropy.