A Q&A with Helleman Fellow Ruward Mulder

A year ago, AIP awarded a Helleman postdoctoral fellowship to philosopher of physics Ruward Mulder. Mulder completed his PhD in the Department of History and Philosophy of Science at Cambridge University and last fall began working with James Weatherall in the Logic and Philosophy of Science (LPS) Department at the University of California, Irvine. We checked in with him to see how his work is progressing.

Can you tell us a little about the goals of your fellowship work?

On both formal and philosophical levels, I explore the space of spacetime theories. This “space” is populated by a surprising variety of formulations—some well-known, others only partly conceived—that all purport to describe relativistic gravity. I’m a philosopher of physics particularly interested in this kind of underdetermination, when different theories can make the same predictions, sometimes even exactly so. To this end, I analyze three cases.

First, the so-called “geometric trinity of gravity”—comprising general relativity (which employs curvature as the explanation of gravitational effect), teleparallel gravity (which uses a flat but torsionful spacetime), and symmetric teleparallel gravity (which breaks the compatibility between metric and connection)—is a trio of quantitatively equivalent theories. Yet, in recent years several responses to this underdetermination have been emerging in very precise ways, such as Occamism, spacetime functionalism, or reinterpretational approaches. I clarify what kind of differences these make: are they mere reformulations of the same physics, or do they offer fundamentally distinct pictures of reality?

Second, I revisit the idea, going back to Reichenbach, that different spacetime models can be made empirically equivalent by postulating “universal forces.” I build on recent work by James Weatherall and J.B. Manchak, who show that for a reasonable assumption of how such “forces” should behave (namely, that they’re represented by a rank-2 tensor in the geodesics equation) this cannot always be done for general relativistic models. I then exploit this proof to systematically discover equivalent models and to evaluate their physical feasibility under this force concept.

A third project explores another result by Weatherall and Manchak: that general relativity is significantly less susceptible to such underdetermination than its Newtonian predecessor, when formulated geometrically (as in Newton-Cartan theory). The difference, I show, arises from the degeneracy of the metric tensor in the non-relativistic theory—a technical feature that dissolves the glue between space and time.

Taken together, I’m mapping out a concrete spacetime footing for Kyle Stanford’s “Problem of Unconceived Alternatives,” which says that we cannot trust our current best scientific theories to be true, because, as a historical fact, scientists in the past have repeatedly failed to exhaust the space of plausible alternative theories. Rather than such abstraction, I believe that at least the nearby neighborhood of the space of alternative spacetime theories can be systematically mapped. This also blurs the lines between “conceived” and “unconceived”. For example, a theory that breaks the Hausdorff condition, modeling gravity via Einstein algebras, is not entirely conceived of, but can hardly be said to be unconceived. In this systematic way, we don’t just learn about gravity—we learn what it means to theorize about spacetime in the first place.

What makes UC Irvine a good place to continue this work, and how have things been going?

The LPS department at UC Irvine is a unique environment with many students working on a wide range of foundational issues in physics, formal epistemology, behavioral science, logic and mathematics, and much more. It is therefore a hugely inspiring and educational place to be, for not only is the department so broadly engaged, the individual researchers also move seamlessly between these topics—a sign of confident, high-quality research.

For my own work, I’m grateful for the Helleman Fellowship’s support in enabling me to pursue these questions in this environment, for I am lucky to have James Weatherall, J.B. Manchak, and Kyle Stanford nearby at this department. This has also meant stepping up my game in formal methods, having spent part of the year studying meta-mathematics, category theory, the fiber-bundle formulation of gauge theories, and even a return to set theory (one is never too late to admit not getting the basics!). Also, we have regular meetings where we discuss our work or read some articles on topics like determinism in relativity theory. Earlier this year, several students organized a high-level reading group on the foundations of algebraic quantum field theory, which was spectacular given the time and care we took to walk through the issues in a precise way. At LPS, I often had the experience of doing serious philosophy in the middle of a physics conference, without wanting it any other way.

Since arriving at UCI, I’ve had the chance to present my research within the department, and at conferences in New Orleans, Toronto, Caltech, and San Diego, with many more to come. Two new papers are written and under review, and two more drafts nearing completion. It’s been a productive and exciting year, and I look forward to continuing this work in such a dynamic academic home.