Making space for fundamentals

Abstract

Frank Arntzenius says this book is not primarily concerned with overarching themes and that his main goal is to examine some loosely related topics. These all have to do with what theories of modern physics imply (or at least suggest) about the structure and contents of space and time. Each of the eight chapters focuses on a different potential implication and may be read independently. But the author does acknowledge that two overarching themes emerge. The first theme is that much of modern physics is best understood as positing novel spaces—physical objects distinct from ordinary 3-dimensional space (or the 4-dimensional space–time of relativity) while sharing some elements of geometric structure. The second is that ‘‘our knowledge of the structure of the world derives from one basic idea: the idea that the laws of the world are simple in terms of the fundamental objects and predicates’’. I will return to these themes after discussing the contents of each chapter. After a gentle introduction to the structure postulated for time by Newtonian and then relativistic physics, Arntzenius devotes the rest of Chapter 1 to explaining and then assessing the prospects of the view that time has no structure. Basically Julian Barbour’s view, the idea is that its metric, topological and order structure are not fundamental features of time, but rather derive from non-temporal relations among what happens at each moment. Using minimal mathematics, Arntzenius explains how to formulate Barbourian versions of Newtonian, special relativistic and general relativistic space–time theories. After showing why none of these is clearly empirically inferior to a standard version formulated within a relatively rich temporal structure, he presents and assesses objections to each. Barbourian general relativity faces the strongest such objections. Barbour himself expresses confidence that further development of his programme to encompass a combination of general relativity with quantum theory will overcome them. But Arntzenius declines to pursue his