Burgess and the bucket: the emergence of spacetime in classical theories of gravitation

Abstract The paper studies in detail a precise formal construction of spacetime from matter suggested by the logician John Burgess. We presuppose a continuous and perdurantistic matter ontology. The result is a systematic method to translate claims about the geometry of a flat relativistic, or classical, spacetime into claims about geometrical relations between matter points. The approach is extended to electric and magnetic fields by treating them as multifields defined on matter, rather than as fields in the vacuum. A few tentative suggestions are made to adapt the method to general relativity and to quantum theories.