# Projects in Progress

Physical Coherence and Time's Emergence (under review)

It is often said that time vanishes in quantum gravity. One general approach to quantum gravity accepts this fundamental timelessness but seeks to derive time's emergence at a non-fundamental level. To better assess such approaches, I develop the criterion of physical coherence and situate it in context by applying it to two programs for time's emergence, drawing from recent works by Chua and Callender (2021) and Chua (forthcoming): semiclassical time and thermal time. Unlike some recent arguments for the metaphysical incoherence of time's emergence, which rule out all claims of time’s emergence `from on high' once we’ve fixed a definition of metaphysical emergence, my criterion of physical coherence leaves open the possibility that some programs in quantum gravity may succeed on their own terms in providing a physically coherent derivation of time from no-time. This sets a challenge for proponents of time's emergence to clarify the conceptual foundations of their program, while at the same time acting as a litmus test for a program's success.

The Toll of the Tolman Effect: On the Status of the Classical Temperature in General Relativity (Joint work with Craig Callender)

The Tolman effect seems to suggest that a system in thermodynamic equilibrium, extended over a region of varying gravitational potential, exhibits a temperature gradient. This seems to run contrary to classical thermodynamics, and raises questions about how to interpret it, questions that we think philosophers of physics have not considered seriously to date. We make four claims. Firstly, we argue that, contrary to much of the contemporary literature on the Tolman effect, it was Einstein -- not Tolman -- who first argued for the Tolman effect. Secondly, we argue that the standard interpretation of the Tolman effect, in terms of `local temperature', leads to the breakdown of much of classical thermodynamics. Thirdly, we argue that Einstein's preferred interpretation in terms of the `wahre Temperatur' -- what we'll call global temperature -- rescues thermodynamics at the cost of local inaccessibility and a lack of contact with phase transitions. Finally, the Tolman effect is often interpreted in terms of redshift, which is itself interpreted in terms of energy and how it gravitates. While many, including Einstein's derivations, have adopted such an interpretation, we provide an alternative interpretation in terms of the general inability, in general relativity, to find local clocks which extend indefinitely far away without distortion -- they slow down because of metric variations. This leads us to propose a third, novel, option with connections to a proposal of Einstein's elsewhere, which we'll call the `wahre-local temperature'. On this view, temperature -- and thermodynamics -- is defined only in relation to local clocks and only to the extent that metric variations can be ignored.

## Putting Pressure Under Pressure: On the Status of the Classical Pressure in Relativity (draft available upon request!)

Much of the century-old debate surrounding the status of thermodynamics in relativity has centered on the search for a suitably relativistic temperature; recent work by Chua (2023) has suggested that the classical temperature concept – consilient as it is in classical settings – ‘falls apart’ in relativity. However, these discussions have still tended to assume an unproblematic Lorentz transformation for – specifically, the Lorentz invariance of – the pressure concept. Here I argue that, just like the classical temperature, the classical concept of pressure breaks down in relativistic settings. This situation suggests a new thermodynamic limit – a ‘rest frame limit’ – without which an unambiguous thermodynamic description of systems does not emerge. I end by briefly discussing how thermodynamics, in requiring preferred frames, bears on the idea of so-called symmetry-to-reality inferences.

Relativistic Locality from Electromagnetism to Quantum Field Theory (Joint work with Chip Sebens, invited contribution to an OUP collected volume on Many-Worlds Interpretations and Locality, edited by Alyssa Ney)

Electromagnetism is the paradigm case of a theory that satisfies relativistic locality. This can be proven by demonstrating that, once the theory’s laws are imposed, the state of a region fixes what happens in a certain portion of the future: the converging light-cone with that region as its base. The Klein-Gordon and Dirac equations meet the same standard. We show that this standard can also be applied to quantum field theory (without collapse) by examining two different ways of assigning states (reduced density matrices) to regions of space. One method begins from field wave functionals and the other from particle wave functions (states in Fock space). We take this kind of analysis of the fundamental dynamics of Everettian (no collapse) quantum field theory to demonstrate that the many-worlds interpretation of quantum physics is local. We argue that this fundamental locality is compatible with either local or global (non-local) accounts of the non-fundamental branching of worlds, countering an objection that has been raised to the Sebens-Carroll derivation of the Born Rule from self-locating uncertainty.

Decoherence, Branching, and the Born Rule for a Mixed-State Everettian Multiverse (joint work with Eddy Keming Chen, under review, preprint available here)

In Everettian quantum mechanics, justifications for the Born rule appeal to self-locating uncertainty or decision theory. Such justifications have focused exclusively on a pure-state Everettian multiverse, represented by a wave function. Recent works in quantum foundations suggest that it is viable to consider a mixed-state Everettian multiverse, represented by a (mixed-state) density matrix. Here, we develop the conceptual foundations for decoherence and branching in a mixed-state multiverse, and extend the standard Everettian justifications for the Born rule to this setting. This extended framework provides a unification of 'classical' and 'quantum' probabilities, and additional theoretical benefits, for the Everettian picture.

## Do Black Holes Evaporate? (under review)

Since Hawking first predicted that black holes lose mass and `evaporate' via Hawking radiation, the phenomenon has become a linchpin of black hole research. However, the derivation of black hole evaporation requires some global notion of mass-energy conservation, which in turn rests on assuming that the spacetime in question has certain idealized properties; the ubiquitous ones are stationarity and asymptotic flatness. By examining these two idealizations and how they cannot be appropriately `de-idealized' in describing actual physical systems, I argue that we lack justification at present for concluding that actual black holes evaporate.

## The Diaulos of Asymptotic Reasoning and De-Idealization (Joint work with Yichen Luo)

It is doubtless that scientific inquiry inextricably involves the use of idealizations: for ease of calculation and representation, we assume the absence of friction, the perfect sphericity of cows, or the impeccable rationality of human beings. Idealizations are, strictly speaking, false. Yet they play a crucial role in many of our best sciences in representing all sorts of phenomena, from coffee cups to black holes. Much ink has thus been spilled over how to justify them. A predominant view focuses on justifying these idealizations via de-idealization procedures. A more recent cluster of views, due to Potochnik (2017) and Knuttila & Morgan (2019), pushes back by arguing that these idealizations stand on their own and need no explicit de-idealization, and that de-idealization is too demanding, respectively. I’ll argue that this disagreement hinges on a strong philosopher’s construct of de-idealization, an idea that itself needs to be de-idealized. I explicate two weaker senses in which idealizations can be de-idealized.