The reason that Schrodinger could create a picture of quantum mechanics like that is because he was using the Newtonian concepts of absolute space and time. The framework that they create makes it possible to give probabilities for the triangles formed by three particles to be in different positions and for the probabilities to change in time. There's an independent time which is nothing to do with the contents of the universe. But if you are trying to construct a universe where you say there's no external framework of space and time in which the contents exist, then you can't give probabilities for the particles to be in certain overall positions in the universe and have some overall orientation, because there's no meaning to that. And nor can the probabilities change in time, because there isn't any time in which they can change. The most simple minded attempt to reconcile quantum physics with the idea that there's no invisible framework holding up the universe and that idea is made very plausible by the 'Platonic structure' of general relativity leads you to a picture in which there are just probabilities given once and for all for the relative configurations of the universe. So if we had a three particle universe the probabilities would just be for where the three particles are relative to each other, say, two close together and one further apart. That's the complete story static probabilities for static configurations, which are what I identify with Nows.
Thus, quite a simple argument leads to a picture where you just have possible Nows, and the Nows are defined by how the things in the universe are arranged. That's all you get out of the theory. In fact this picture, which Dirac helped to create, crystallized something over 30 years ago. It is described by an equation called the Wheeler DeWitt equation. (John Wheeler prodded Bryce DeWitt into its derivation. If it really turns out to be the equation of the universe, the episode will be a rerun of the way Hooke badgered Newton into his solution of Kepler's problem.) People found it very difficult to make sense of the static universe that seemed to emerge. However, I find the arguments that lead to it are strong. There is support for it in the structure of Einstein's theory and in the structure of quantum mechanics. The equation would never have been found if that were not the case. So I take the picture seriously and try and make sense of it, and ask how can we nevertheless recover from it a picture of our world; how can it be that I can sit here and see my own hands moving, yours too, if the world is completely static?
JB: Does this have anything to do with your idea of time capsules?
BARBOUR: Yes. Suppose we accept the quantum universe is static and timeless. How can we reconcile that with actually seeing motion and remembering the past? In fact, besides the direct sensing of change of one kind or another, the only direct evidence we have for time and the past comes from records, which include memories. Now records, either natural like fossils or man made, are so ubiquitous we can easily forget how remarkable their existence is according to the current understanding of classical mechanics. This is the problem of the extraordinarily low entropy of the universe. It was emphasized a century ago by Boltzmann. In the modern context of general relativity, Roger Penrose keeps on pointing out what a huge problem it is. All statistical arguments based on classical mechanics suggest the universe ought to have a vastly higher entropy and exist in a state in which records simply cannot form. Penrose wants to explain the low entropy and the arrow of time by a new physics which is explicitly time asymmetric and comes with a built in arrow of time and forces the universe to begin in a highly uniform state. My own view is that, paradoxically, the arrow of time may be easier to explain in a theory in which there is no time at all.