A Philosophy of Physics Workshop

We adapt to the context of quantum theory the treatment, familiar in relativity theory, of a reference frame as a tetrad. Since a tetrad is a set of four orthonormal vectors at a spacetime point, it encodes a timelike direction, three orthogonal spatial directions, and units; and so it gives a configuration in spacetime (a spatial orientation and state of motion) of an idealized infinitesimal apparatus (“rulers and a clock”). So a natural “first guess” is that the state of a quantum reference frame should be an assignment of complex amplitudes to a set of tetrads. We develop this idea, in terms of bundles over spacetime of bases of the tangent spaces.

This paper is a companion to two other papers. It emphasises the main conceptual aspects of our proposal, while the other two papers give physical details. It also explains the main contrast between those two papers. Namely: (i) the first considers a single spacetime geometry, so that a quantum reference frame, on our proposal, gives a superposition of perspectives on that geometry; while (ii) the second considers different spacetime geometries, which will imply that a quantum reference frame, on our proposal, can describe a superposition of perspectives on a superposition of geometries—not “just” a superposition of perspectives on a single geometry. The main mathematical idea for representing this contrast will be choosing between (i) the orthonormal frame bundle, for a given spacetime geometry; (ii) the frame bundle in the usual sense of containing all bases of all spacetime points’ tangent spaces.

There is not much discussion of the metaphysics of path integrals in the literature. That is surprising, since path integrals have played a crucial role in physical theorizing for nearly a century. So in this paper, I formulate and develop several realist accounts of the metaphysics of path integrals, focusing in particular on path integrals in non-relativistic quantum mechanics and in quantum field theories which admit of fully rigorous mathematical formulations. As I argue, these accounts are quite attractive: they can be used to defend realism, address worries about explanation and reduction which path integrals raise, and more generally, bring metaphysics into closer contact with contemporary physical theorizing.  

We investigate the spacetime-matter distinction in general relativity by focusing on what it means for something to be matter. First, we ask: does the stress-energy tensor provide a unique standard for the matter-spacetime distinction? We highlight a form of shiftiness: whether the same system contributes stress-energy or not can depend on modelling contexts and choices. Second, we study other concepts which play various matter roles: quasi-local and global mass concepts. If these, too, are matter concepts, they undermine a unique spacetime-matter distinction -- the shiftiness compounds. As we'll argue, across these various matter concepts, there is no one ontological line between spacetime and matter, no one intrinsic conceptual line demarcating the boundaries of the matter concept, and no one extrinsic conceptual line between spacetime and matter. 

 At some level, every mathematician is a pluralist (i.e. they hold that there are multiple legitimate ways to go about doing mathematics). This said, mathematics is often seen to be a paradigm case of certainty with mathematicians able to share each other's results. Two responses to this problem have emerged. The dominant view is that such apparent difference is (mostly) illusory, and just a matter of the way our minds work. Mathematical reality is uniform, and all that changes is how we refer to that reality. A different (and more radical) answer is that it is the uniformity that is illusory; really mathematical reality is fractured, and it is only by dint of similarity of proofs that we can transfer results from one area to another. In this paper I try to find a middle ground. Drawing on work in the literature on perspectivism in the philosophy of science, combined with a particular moderate perspective on metasemantics, I argue that we can view mathematics as perspectival in nature.

 The physical significance of black hole thermodynamics depends in part on how its systems are identified. Traditional arguments focus on stationary black holes with event horizons, whose global and teleological definition raises conceptual difficulties for identifying thermodynamic systems. The framework of isolated and dynamical horizons offers a broader and more general conceptualization: horizon equilibrium does not require global stationarity of the spacetime, and dynamical horizons permit the study of evolving black holes through exact mechanical balance laws. Quasi-local horizons, however, may not be uniquely fixed by the spacetime: dynamical horizons, in particular, depend on the choice of foliation. In this talk, I argue that this dependence by itself does not establish their thermodynamic inadequacy. Assessing the physical-and-thermodynamic significance of quasi-local horizons requires distinguishing their invariance under changes of representation, their capacity to identify physical systems, and their thermodynamic behavior. The quasi-local framework is already geometrically covariant; its uniqueness and stability results constrain the identification of a black hole horizon; and its balance laws supply physical (albeit not full) resources for a thermodynamic interpretation. I therefore propose a criterion of physical adequacy that permits objective, reference-dependent descriptions while retaining substantive requirements on boundary selection (with associated state comparison) and thermal exchange. This supports a realist attitude towards black hole thermodynamics and provides a clearer basis for investigating its statistical-mechanical foundations.

Ongoing debates on scientific realism have seen a resurgence of perspectivism, the view that physical descriptions are often intelligible only in relation to a perspective or frame, without this relativity implying subjectivism or antirealism (Giere 2006; Massimi 2022). In the philosophy of physics, the notion of perspectivism has been invoked mainly in discussions of the metaphysics of reference frames in general relativity and in the relational interpretation of quantum mechanics (Rovelli 1996; Adlam 2024; Chua and Ramirez-Murguieitio-Ramirez, manuscript).

Concurrently, there has been steady development in the field of effective realism (ER), the view that we should commit to the reality of entities, structures, and laws only within the domain in which a theory is empirically successful (Williams 2019). ER has been applied to precisify the ontology of quantum field theory (Fraser 2020; Williams 2019), to interpret quantum mechanics (Egg 2021; Fraser and Vickers 2025), and to explain the persistence of so-called theoretical relics (Robertson and Wilson 2023).

In a recent contribution, Ladyman & Lorenzetti (forthcoming) have defended ER against the objections raised by Saatsi (2022) by connecting ER with ontic structural realism, framing it in terms of Dennett’s notion of real patterns (Dennett 1991) and indexing those patterns to specific scales. This contribution aims to draw on these latter developments in ER literature to develop a perspectival notion of scale relativity, as opposed to frame relativity. To this end, I propose a taxonomy of the fundamental types of scale (spatial and temporal) and their derivatives, together with an analysis of the features that distinguish scales from frames, notably their asymmetry and lack of intertranslatability. I relate these features to the concept of mathematical approximation, and I illustrate the relevance of the notion of scale through a series of case studies from the philosophical debate on thermodynamics. The result is a notion of scientific truth necessarily indexed to a scale, as truth-at-a-scale.

Are Humean and non-Humean accounts of laws of nature on a par in the face of the problem of induction? There are two battlefields. The first concerns whether subscribing to non-Humeanism can cure inductive vertigo: the worry that observed regularities may be a matter of cosmic luck and could fall apart at any moment. The second concerns whether subscribing to Humeanism makes this vertigo inevitable. Non-Humeans appeal to necessary connections to claim an advantage on one or both battlefields, with Armstrong (1983) as a prominent example. Beebee (2011) forcefully defends Humeanism on the first battlefield: non-Humeanism does not fare better in convincing the inductive sceptic.

More recently, however, Bhogal (2021) has pressed the second question, arguing that Humeanism has an “internal problem”: scepticism about induction “naturally flows from” Humean commitments. I defend Humeanism against this “internal problem”. Bhogal’s main reason is that the Humean lacks explanations of the most general fundamental patterns that are projected. I argue that this claim is either false, because the Humean does have resources to explain these patterns, or irrelevant, because the kind of explanation the Humean does lacks is irrelevant to inductive vertigo. I also rebut a related and potentially stronger objection to Humeanism on this second battlefield: that denying “metaphysical glue” removes our grounds for expecting observed regularities to continue.

For 40-plus years, physicists, especially high-energy physicists have extolled the ``effective field theory” view of quantum field theory.  A key idea has been about renormalisation. Whatever non-renormalizable interactions may occur at higher energies beyond our reach, their contributions to (the probabilities for) physical processes decline with decreasing energy, rapidly enough that they are negligible at the energies we can reach. Philosophers have picked up on this. Recently, they suggested that this sheds light on the philosophical topic of scientific realism: both how to formulate it, and whether it is right.

 In this talk, I will begin by celebrating the current conception of EFTs, especially for QFT. 

Then I will argue that it is compatible with scientific realism (following the lead of e.g. Wayne Myrvold). Then I will give a bit more detail about the reduction of one theory to another, in application to quantum field theories. Of course, my irenic stance will leave many questions unanswered. In particular, I will end by looking into the abyss of minuscule length scales.