The Ontology of the Curvature of Empty Space in the Geometrodynamics of Clifford and Wheeler

Abstract

For nearly two decades before 1972, Professor John Wheeler pursued a research program in physics that was predicated on a monistic ontology which W. K. Clifford had envisioned in 1870 and which Wheeler (1962b, p. 225) epitomized in the following words: “There is nothing in the world except empty curved space. Matter, charge, electromagnetism, and other fields are only manifestations of the bending of space. Physics is geometry.” In an address to a 1960 Philosophy Congress (Wheeler, 1962a), he began with a qualitative synopsis of the protean role of curvature in endowing the one presumed ultimate substance, empty curved space, with a sufficient plurality of attributes to account for the observed diversity of the world. Said he:

... Is space-time only an arena within which fields and particles move about as “physical” and “foreign” entities? Or is the four-dimensional continuum all there is? Is curved empty geometry a kind of magic building material out of which everything in the physical world is made: (1) slow curvature in one region of space describes a gravitational field; (2) a rippled geometry with a different type of curvature somewhere else describes an electromagnetic field; (3) a knotted-up region of high curvature describes a concentration of charge and mass-energy that moves like a particle? Are fields and particles foreign entities immersed in geometry, or are they nothing but geometry?

It would be difficult to name any issue more central to the plan of physics than this: whether space-time is only an arena, or whether it is everything [p. 361].

I owe warm thanks to Allen Janis, Morris Kline, Gerald Massey, John Porter, and John Stachel for the substantial benefit which this paper had from conversations or correspondence with them. Clark Glymour kindly sent me preprints cited here.