Absolute Space and Conventionalism

Abstract

experiment in the context of a four-dimensional formulation of Newtonian theory. I will proceed by outlining a number of alternative global structures for Newtonian space-time. Corresponding to each structure is an appropriate Newtonian theory; namely, a theory whose postulates are appropriate mathematical variants of the postulates of Newtonian mechanics and gravitation, and which posits the given structure as the structure for space-time. I will argue that if we adopt a conventionalist attitude towards these theories, then we can consistently maintain that the basic principles of Newtonian theory are true, and yet deny the Newtonian's claim that certain observable phenomena must be interpreted in terms of acceleration relative to some non-material spatial entity. While I will focus on Newton's experiment of the rotating globes, I believe that my arguments also apply to his bucket experiment. I will begin my discussion, in section 2, by presenting three different ways of formulating the structure of Newtonian space-time. In section 3, I will contrast the ways in which the realist and the conventionalist view the relative ontological status of these different structures. In section 4, I will examine Newton's 'rotating globe' experiment, with particular emphasis on the difficulties which this experiment raises for the conventionalist. Finally, in section 5, I will try to show how the conventionalist can deal with these difficulties by using the results developed in sections 2 and 3. 2 Newton's remarks in the Scholium to his definitions in the Principia suggest that space-time consists of 'absolute space persisting through absolute time'. A space-time described in this way can be thought of as having a direct product structure Space x Time, where Space is R3, Euclidean three-space, and Time is represented by R, the real numbers. For any pair of points in this space-time, there is a uniquely defined spatial separation and a uniquely defined temporal separation. I will refer to a space-time with the structure R3 x R as 'Newton's space-time', N. According to a second formulation, the structure of 'flat Newtonian