BARBOUR: My conjecture is that some Platonia is the true arena of the universe and that its structure has a deep influence on whatever physics, classical or quantum, is played out in it. In particular, I believe the phenomenon that we call the Big Bang is not some violent explosion that took place in the distant past. It is simply the highly special place in Platonia that I call Alpha.
JB: I never heard or read other physicists talk like that. What do they make of Platonia?
BARBOUR: Platonia is a special case of a very basic concept in physics called a configuration space. It has been around for a long time, long before relativity. The technical name for any Platonia is a stratified manifold the strata are what I call frontiers. Stratified manifolds are what remain if you take the potentially redundant absolute structure out of configuration spaces. Stratified manifolds have been recognized as significant for at least sixty years. But somehow configuration spaces, or the leaner stratified manifolds, have never acquired the glamor of Einstein's space time or the Hilbert space of quantum mechanics. They are the Cinderellas of theoretical physics. I see quantum cosmology as the Prince Charming that cannot live without them. It's a hunch I have come to from thinking so much about those basic questions: What is time? What is motion?
JB: So what do you do in Platonia?
BARBOUR: There are two tasks: first of all, can you describe classical physics using that picture? That's really where my main work has been done, showing that everything Newton could do with absolute space and time can be done more economically in Platonia. That's the first thing Bertotti and I showed. Then we found that Einstein's general relativity, which was created as a theory of space time, can be recast as a timeless theory in the appropriate Platonia. This is closely related to the discovery that Dirac made and leads on to the second task: what are the implications of the 'Platonic structure' of general relativity in the quantum universe? This is relevant because quantum theories are generally arrived at by starting from a classical picture and performing something which is called quantization.
For non physicists it's a rather difficult thing to grasp. But you can see where the idea of a timeless universe will come from if you consider the way quantum wave mechanics was discovered by Schrodinger in 1926. In classical Newtonian physics, if you have three particles they will always be at definite positions at definite times. They will form some triangle, and the center of mass of the triangle will be somewhere and it will have some orientation. Now what quantum mechanics says is that, until observations are made, for all these quantities, there are no definite values, but only probabilities, all of which change in time.