Foundations of Space-Time Theories: Relativistic Physics and Philosophy of Science

Michael Friedman
Pages: 402
https://www.jstor.org/stable/j.ctt7ztj02

1. Front Matter
(pp. i-vi)
(pp. vii-x)
3. Preface
(pp. xi-2)
4. I Introduction: Relativity Theory and Logical Positivism
(pp. 3-31)

The relationship between the development of relativity theory and twentieth-century philosophy of science is both fascinating and complex. On the one hand, relativity theory, perhaps more so than any other scientific theory, developed against a background of explicitly philosophical motivations. As is well known, both Leibnizean relationalism and Machian empiricism figured prominently in Einstein’s thought. On the other hand, twentieth-century philosophy of science, and logical positivism in particular, is almost inconceivable without relativity, for relativity theory was second only toPrincipia Mathematicaas an intellectual model for the positivists.¹ It appeared to realize all their most characteristic ideals, from a...

5. II Space-Time Theories
(pp. 32-70)

All the physical theories considered in this book will be treated as theories about space-time: the set of all places-at-a-time or all actual and possible events. Our theories postulate various types of geometrical structure on this set and picture the material universe—the set of allactualevents—as embedded within in it. According to the present point of view, then, the basic or primitive elements of our theories are of two kinds: space-time and its geometrical structure; and matter fields—distributions of mass, charge, and so on—which represent the physical processes and events occurring within space-time. Our theories...

6. III Newtonian Physics
(pp. 71-124)

In this chapter I intend to formulate Newtonian physics from the space-time point of view. The basic object of Newtonian physics will be the space-time manifold M; various geometrical structures will be defined on M; and these geometrical structures will be related to the processes and events that occur within space-time by field equations and laws of motion. Looking at our Newtonian theories in this way leads to several surprising results. First, in an important sense Newtonian physics is as four-dimensional as special relativity and general relativity. Second, it is as generally covariant as general relativity. Third, Newtonian gravitation theory,...

7. IV Special Relativity
(pp. 125-176)

The space-time of special relativity—hereafter referred to asMinkowskispace-time—is, like the space-time of Newtonian kinematics, a flat, four-dimensional affine manifold. Minkowski space-time is often required to satisfy global conditions (namely, to be globally Euclidean or homeomorphic to R⁴), but, as in my treatment of Newtonian kinematics, I prefer to use only local field equations. Since Minkowski space-time is a flat manifold, our first local condition is the existence of an affine connectionDwith the field equation K = 0. Our equation of motion is the geodesic law for this connection:

${D_{T\sigma }}{T_\sigma } = 0$

and there are always coordinate...

8. V General Relativity
(pp. 177-215)

General relativity, unlike the theories we have discussed so far, is standardly presented from the space-time point of view. The theory describes a four-dimensional differentiable manifold; its field equations and laws of motion are written in generally covariant tensor form; the field equations and laws of motion together determine the geometrical structure of space-time and how that structure constrains physical events and processes; and so on. Traditionally, of course, these were thought to be distinctive features that separated general relativity from previous theories. From our present point of view, however, these aspects of the general theory simply represent a new...

9. VI Relationalism
(pp. 216-263)

In the preceding chapters I have presented a markedly (some would say naively) literal picture of our space-time theories. Their subject matter is taken to be a highly theoretical entity, the space-time manifold; they attribute various types of geometrical structure to this entity; and they relate such geometrical structure to the physical processes and events occurring within space-time. I think there can be little doubt that this picture has a number of attractive features. It gives a relatively simple and precise account of the content of our different space-time theories, thereby making their comparison especially perspicuous, and it provides a...

10. VII Conventionalism
(pp. 264-339)

Conventionalism, like relationalism, raises skeptical doubts about the structures postulated by our space-time theories. Whereas ontological relationalism raises doubts about the domain of individuals of our theories—whether it is permissible to quantify over the entire manifold of space-time points—conventionalism raises doubts about the geometrical properties and relations, especially the metrical properties and relations, that are defined on this domain—whether or not it includes unoccupied points. Thus, conventionalism, as I understand it, is closely connected withideologicalrelationalism. We shall explore their interconnections in more detail as we proceed.

The basic conventionalist strategy is to argue that certain...

11. Appendix: Differential Geometry
(pp. 340-367)
12. Bibliography
(pp. 368-376)
13. Index
(pp. 377-385)
14. Back Matter
(pp. 386-386)