Concepts
A conceptual map of the questions motivating the research.
Geometry as a Starting Point
Most physical theories treat geometry as a background — a stage on which dynamics play out. A recurring question in the foundations of physics is whether this is the right description. The research takes this question seriously as a starting point, not a conclusion.
The Problem of Local Structure
Standard formulations of physical law are remarkably good at describing what happens, but they leave open a prior question: why does local structure take the form it does? Existing frameworks typically introduce auxiliary assumptions. Whether those assumptions have a deeper geometric justification, or whether they are genuinely independent inputs, remains an open structural problem.
Persistence and Physical Identity
What makes a physically distinguishable object the same object across time? This is not merely a philosophical puzzle — it bears directly on how physical theories individuate the entities they describe. Current frameworks handle this in ways that are often implicit, and the assumptions involved are rarely examined at the level of the geometry. The research treats this as an open question worth taking seriously on its own terms.
Wave-Particle Duality as a Structural Question
The interpretive literature on wave-particle duality is extensive, but interpretation and explanation are not the same thing. Most accounts accept the descriptive formalism and ask what to make of it; fewer ask whether the formalism itself is pointing at something the geometry should account for directly. The latter question is harder, less settled, and more interesting.
For the papers and results that develop these ideas, see Research.
K.L. Spalding 