BARBOUR: That has always proved to be difficult to attack, because if you try to get your hands on time, it's always slipping through your fingers. People are sure that it's there but they can't get hold of it. Now my feeling is that they can't get hold of it is because it isn't there at all. That what we think is the flow of time and even seeing motion is actually an illusion. But I come to that after seeing what the quantum mechanics of the complete universe might be like.
JB: Sounds tough. Have you got a simple picture?
BARBOUR: Let's take a simple model; suppose there were just three particles in the universe and nothing else. In some instant they would be in certain positions relative to each other and would form some triangle. Newton claimed that this triangle has in addition some position in absolute space and that it's changing in time. What I'm saying is that there isn't any of that external framework of space and time, there's just the possible triangles that the particles form. The triangles do not occur somewhere in absolute space at some instant of time, some Now. The triangles are the Nows. You are forced to some view like this if the invisible framework is denied. If we had a universe with a million particles in it there would be some relative configuration of those million particles and nothing else. That would form one Now, and all the different ways you could arrange all the million particles would make all the different possible Nows. I think the actual Nows of this universe are more sophisticated constructs involving fields, but Nows formed by arrangements of particles can get the idea across.
JB: Didn't Einstein abolish Nows?
BARBOUR: In fact no. He only showed that they do not follow one another in a unique sequence. There is no absolute simultaneity in the universe, or at least not in the classical universe. But relative simultaneity remains, and Nows as I define them form an integral part of Einstein's theory. Actually the discovery of Dirac that started all my interest in time was that Nows appeared to be far more significant in the quantum world than one might have expected coming from the normal interpretation of Einstein's relativity.
What really intrigues me is that the totality of all possible Nows of any definite kind has a very special structure. You can think of it as a landscape, or country. Each point in the country is a Now. I call it Platonia, because it is timeless and created by perfect mathematical rules. Most strikingly, it is lopsided with a most definite end and frontiers that are there by sheer logical necessity. For example, if you consider triangles as Nows, the land of these Nows comes to an absolute end in the degenerate triangle in which all three particles coincide. This point is so special I call it Alpha. Other frontiers, like ribs, are formed by the special triangles in which two particles coincide and the third is at some distance from them. Finally, another kind of frontier is formed by collinear configurations all the three particles are on one line. The Platonia for triangles is like a pyramid with three faces. Its apex is Alpha. All the points on its faces correspond to collinear configurations, and the faces meet in the ribs formed by the triangles with two coincident vertices.
JB: I like the sound of Platonia, but what is it good for?