Abstract

Spacetime theories are typically associated with one of three relativity principles--the Principle of Galilean Relativity, Special Relativity, or General Relativity. While it is generally agreed that a relativity principle functions as some type of symmetry requirement on a theory, there is much disagreement concerning the precise nature of these symmetry requirements. Relativity principles are formulated alternatively as symmetry requirements on the spacetime geometry, as symmetry requirements on a class of equivalent frames, as symmetry requirements on a class of physical systems, and finally, as covariance requirements on the form of the laws of a theory. The first concern of this dissertation is to provide an analysis of these various types of symmetry requirements and then to investigate their logical relations. ;The Principle of General Relativity is the most problematic of all the relativity principles. It is a controversial matter whether this principle is a symmetry requirement of the same type as the other relativity principles and whether this principle has any nontrivial theoretical content. One position on these issues is represented by Vladimir Fock who claims that there is no theoretically significant Principle of General Relativity. A second position is represented by Eugene Wigner who maintains that the Principle of General Relativity is nontrivial, but that it is a principle of a different type than the geometrical relativity principles. A third position is represented James Anderson who argues that all three relativity principles may be construed as symmetry requirements on the "absolute objects" of a theory. The second concern of the dissertation is to critically examine each of these three positions and then, if necessary, to develop a more adequate fourth position. ;The essay begins with an intuitive development of the concept of symmetry. The ideas developed here are then reflected in a more formal analysis of symmetry properties in terms of a symme-group. The essay continues with an analysis of relativity principles as covariance requirements. This mode of interpretation is seen to be inadequate for a variety of reasons, the primary reasons being the fact that a covariance group need not bear any specific relation to a theory and the fact that the relativity group of a theory need not coincide with any special covariance group. ;It is then argued that the Principles of Special Relativity and Galilean Relativity are to be construed primarily as symmetry requirements on the spacetime geometry. Given certain standard assumptions about the relation between spacetime geometry and the class of systems in a spacetime, these principles are consequently also symmetry requirements on the class of systems in a spacetime and on a class of physically equivalent frames of a spacetime. The Principle of General Relativity cannot be interpreted in any of these ways. ;Anderson's concept of the absolute objects of a theory is now employed to define the class of physical systems of a theory. From this perspective, it is seen that the three relativity principles are all mutually incompatible and nontrivial symmetry requirements on the class of physical systems of a theory. It is then concluded that the geometrical relativity principles are associated first with each individual system of a theory, and consequently with the class of systems of a theory, while the Principle of General Relativity is associated only with a class of systems and not with any individual system. Thus both Wigner and Anderson are vindicated