Part 4

In Part 4, Barbour begins to discuss quantum mechanics and its interpretations, a quite polular business in recent philosophy of science. And you will begin to understand how elusive "mist" with three colors play their roles. The crucial point is that Shroedinger introduced configuration space as the arena for quantum mechanics. Unlike most other works on quantum mechanics, Barbour's exposition is readable and intelligible in that the role of ψ is visualized in terms of the figures of probability density.

The crucial part of Barbour's idea comes around pp. 241-2. Schroedinger's configuration space has external factors of space and time, in addition to relative configuration. Thus, as was the case in the Newtonian mechanics, energy and angular momentum of any subsystem become crucial for its time-development. This can be expressed, schematically, in terms of the state function ψ of that subsystem.

(1) ψ(relative configuration, center of mass, orientation, time)

However, from the Machian point of view, the frame (space and time) can be reconstructed from the dynamics of the whole system; thus when we consider the state function Ψ(large psi, remember) for the whole system, the wave function becomes:

(2) Ψ(relative configuration).

Barbour argues that this is the essence of the Wheeler-DeWitt equation for quantum gravity. What is crucial here is that the wave function (for the whole universe) was rewritten only in terms of relative configuration, without external space and time, and this boils down to the time-independent version of Schroedinger equation.