Machian dynamics

We have seen how Newton attacked spatio-temporal relationism not through a typical philosophical argument that might be argued by a substantivalist, but by claiming that “absolute” space and time were necessary for dynamics. Inertially moving systems are radically distinguished from those which, under the influence of external forces, are not moving inertially. But, to make sense of motion in a constant direction and at a constant speed, we need an absolute frame relative to which constant direction is constant and relative to which our changing positions are to be measured, and we need an absolute lapse of time (up to a linear transformation) relative to which constant speed is constant. The discovery that absolute place and velocity play no role and can be eliminated even in the framework of Newtonian dynamics in favor of Galilean or neo-Newtonian spacetime with its class of inertial frames should give the relationist no comfort.

In Chapter 16 we briefly sketched the version of relationism proposed by Mach. The core of this program sought a “cosmic” solution to the problem of the reference frame relative to which accelerations were absolute, with the source of the inertial forces sought in acceleration-dependent relations of test systems to the distant “fixed stars.” We noted that Mach's proposal remained shrouded in vagueness and that subsequent proposals in his vein were generally deemed unsatisfactory. In the twentieth century a new kind of Machianism has been proposed by J. Barbour and B. Bertotti. It is to their theory that we must now turn our attention.