Julian Barbour - The End of Time - The Next Revolution in Physics

The picture that emerges is very simple. The quantum counterpart of Machian classical dynamics is a static wave function ψ on Platonia. The rules that govern its variation from point to point in Platonia involve only the potential and the best-matching ‘distance’. Both are ‘topographic features’ of the timeless arena. Surveyors sent to map it would find them. They would see that the mists of Platonia respect its topography. It determines where the mist collects.

The year 1980 was another turning point in my life. It was when Bruno Bertotti and I thought we might have found a new theory of gravitation, only to learn that the two ideas on which we had based it were already an integral part of Einstein’s theory. Karel Kuchař’s intervention rounded off our work but also brought it to an end. It was something of an anticlimax. Bruno became increasingly involved in experiments using spacecraft, aimed at detecting the gravitational waves predicted by Einstein’s theory. For a year or two I actually stopped doing physics and became politically active in the newly founded Social Democratic Party (the SDP). However, the old interests soon revived. Margaret Thatcher’s decisive general election victory in 1983 hastened the process.

Two things occupied me through the 1980s. First, I wrote the book from which I quoted the comments about Kepler. It had always been my ambition to write about absolute and relative motion, and in 1984 I signed a contract with Cambridge University Press for a book of four hundred pages covering the period from Newton to Einstein and including an account of my work with Bruno. When I embarked upon it, it occurred to me that I ought to find out why Newton had said what he had. What had given him the idea of absolute space? Might it not be an idea to look at what Galileo had said? I made a wonderful mistake by asking those questions. Before I knew what was happening, my research into Galileo dragged me ever further into past history, through the Copernican revolution to the work of Ptolemy and all the way back to the pre-Socratic philosophers. By reading the actual works of scientists such as Ptolemy, Kepler and Galileo, I found that the early history of mechanics and astronomy was far more interesting than any account of it I could find by the professional historians of science. They had missed all sorts of fascinating things, and their histories were quite inadequate. Inspired by Kepler’s comment that the ways by which men discover things in the heavens are almost as interesting as the things themselves, I started to write about all the early work. I spent from 1985 to 1988 writing a completely unplanned book: The Discovery of Dynamics . My sympathetic and understanding editor at Cambridge, Simon Capelin, agreed to publish it as the first of a two-volume work. The second volume was to be the book originally proposed and should have been completed a year or two later. However, that got badly delayed by a parallel development that turned my interest to physics that does not yet exist at the same time as I was working backward to the early history.

As I mentioned earlier, Bruno and I had been completely concerned with classical physics. We had wanted to show that Mach had been right and that his ideas could lead to new classical physics; we had given not a moment’s thought to any quantum implications they might have. Quantum cosmology was a world beyond our ken. It is strange what sparks a desire to work on something. My lack of interest in quantum gravity was particularly odd, since it was the early work done in that field which, through the remark by Dirac, quoted in the Preface, had set me on my long trek. It was the same work that had led to the work of Baierlein, Sharp and Wheeler that Bruno and I had come to see as the implementation of Mach’s ideas within general relativity. Not even working with Karel Kuchař, one of the world’s leading experts in quantum gravity, provided the stimulus I needed. Perhaps it all seemed too daunting. I needed the example and encouragement that came from a new friend, Lee Smolin.

I first met Lee a few weeks before I travelled to Salt Lake City in the autumn of 1980. It was quite a dramatic time for me since I had just narrowly escaped death through an insidious appendix that had burst without giving me any pain. My only symptoms were tiredness, slight sickness and the merest hint of stomach pain. Luckily my vigilant doctor sent me to hospital as a precaution. An X-ray proved difficult to interpret, and after quite lengthy deliberation the doctors decided to open me up. They found that any further delay could have been fatal. Seeing my state, the surgeon apparently commented that ‘this must be a very brave man’, believing I must have been in agony. In fact, I had been cheerfully reading The Times without any discomfort only half an hour before the operation. The day after I came back from hospital still convalescing, two American physicists visiting Oxford phoned to say that they had heard from Roger Penrose about my interest in Mach’s principle. Could they come and see me? They came the next day, and I greeted them in my dressing gown.

One was Lee, then a young postdoc. The meeting changed both of our lives significantly. He proved very receptive to the ideas of Leibniz and Mach to which I introduced him, while he encouraged me to see what application they might have to the problem to which he had decided to devote himself – quantum gravity. We met several times in the next few years, and collaborated on an attempt to formulate Leibniz’s philosophical system, his ‘monadology’, in mathematical form. I think we made some real progress. Lee has written about his view of things in his The Life of the Cosmos . Certain aspects of our work together were decisive in my own elaboration of the notion of time capsules and my conviction that the ultimate and only truly real things are the instants of time. As far as I am aware, Leibnizian ideas offer the only genuine alternative to Cartesian-Newtonian materialism which is capable of expression in mathematical form. What especially attracts me to them is the importance, indeed primary status, given to structure and distinguishing attributes, and the insistence that the world does not consist of infinitely many essentially identical things – atoms moving in space – but is in reality a collection of infinitely many things, each constructed according to a common principle yet all different from one another. Space and time emerge from the way in which these ultimate entities mirror each other. I feel sure that this idea has the potential to turn physics inside out – to make the interestingly structured appear probable rather than improbable. Before he became a poet, T. S. Eliot studied philosophy. He remarked, ‘In Leibniz there are possibilities.’

In 1988, when I had finished my book on the discovery of dynamics, I spent three weeks with Lee at Yale, and began to think seriously how one might make sense of the embryonic form of quantum gravity that had been developed from about the time of Einstein’s death in 1955, leading to the publication of the Wheeler-DeWitt equation in 1967. During the next four years, Lee and I had many discussions. Although we eventually followed different paths – Lee is reluctant to give up time as a primary element in physics – the ideas I want to describe in the final part of the book crystallized during those discussions. For me, their attraction stems from the inherent plausibility of Platonia as the arena of the universe and the implication of Schrödinger’s breathtaking step into a rather similar configuration space. As I see it now, the issue is simple.

You can play different games in one and the same arena. You can also adjust the rules of a game as played in one arena so that it can be played in a different arena. Both general relativity and quantum mechanics are complex and highly developed theories. In the forms in which they were originally put forward, they seem to be incompatible. What I found to my surprise was that it does seem to be possible to marry the two in Platonia. The structures of both theories, stripped of their inessentials, mesh. What if Schrödinger, immediately after he had created wave mechanics, had returned to his Machian paper of only a year earlier and asked himself how Machian wave mechanics should be formulated? His Machian paper implicitly required Platonia to be the arena of the universe, while any wave mechanics simply had to be formulated on a configuration space. Such is Platonia, though it is not quite the hybrid Newtonian Q he had used. But the structure of Machian wave mechanics would surely have been immediately obvious to him, especially if he had taken to heart Mach’s comments on time. As a summary of the previous chapter, here are the steps to Machian wave mechanics in their inevitable simplicity.