The End of Time: The Next Revolution in Physics

(1) (p. 61) I have written at considerable length about the early history of astronomy and mechanics and the absolute versus relative debate in my Absolute or Relative Motion? This has recently been reprinted as a paperback with the new title The Discovery of Dynamics (OUP, 2001). I still hope to complete a further volume bringing the story up to the present, and much has already been written, but my plans are in flux because of the developments mentioned at the end of the Preface and at various places in these notes. Readers wanting a full academic (and mathematical) treatment of the topics presented in Parts 2 and 3 of this book are asked to consult the above and the papers (Barbour 1994a, 1999, 2000, 2001), which cite earlier papers. For references to recent developments see p. 358 and my website (www.julianbarbour.com).

(2) (p. 64) In the main body of the text, I mention the importance of the fortunate circumstances of the world in enabling physicists to avoid worrying about foundations. Another very important factor is the clarity of the notion of empty space, developed so early by the Greek mathematicians, which deeply impressed Newton. He felt that he really could see space in his mind’s eye, and regarded it as being rather like some infinite translucent block of glass. He and many other mathematicians pictured its points as being like tiny identical grains of sand that, close-packed, make up the block. But this is all rather ghostly and mysterious. Unlike glass and tiny grains of sand, which are just visible, space and its points are utterly invisible. This is a suspect, unreal world.

We are not bound to hang onto old notions. We can open our eyes to something new. Let me try to persuade you that points of space are not what mathematicians would sometimes have us believe. Imagine yourself in a magnificent mountain range, and that someone asked, ‘Where are you?’ Would you kneel down with a magnifying glass and look for that invisible ‘point’ at which you happen to be in the ‘space’ that the mountain range occupies? You would look in vain. Indeed, you would never do such a silly thing. You would just look around you at the mountains. They tell you where you are. The point you occupy in the world is defined by what the world looks like as seen by you: it is a snapshot of the world as seen by you. Real points of space are not tiny grains of sand, they are actual pictures. To see the point where you are in the world, you must look not inward but outward.

The plaque near the grave of Christopher Wren in St. Paul’s Cathedral says simply: ‘If you seek a monument, look around you.’ The point where you are is a monument too, and you see it by looking around you. It is this sort of change of mindset that I think we need if we are to understand the universe and time.

To conclude this note, a word about what is perhaps the most serious problem in my approach. It is how to deal with infinity. As so far defined, each place in Platonia corresponds to a configuration of a finite number of objects. Such a universe is like an island of finite extent. One could allow the configurations to have infinite extent and contain infinitely many objects. That is not an insuperable problem. The difficulty arises with the operations that one needs to perform. As presented in this book, the operations work only if the points in Platonia, the instants of time, are in some sense finite. There may be ways around this problem—Einstein’s theory can deal beautifully with either finite or infinite universes—but infinity is always rather difficult. There is something ‘beyond the horizon’, and we can never close the circle of cause and effect. In short, we cannot build a model of a completely rational world. Precisely for this reason Einstein’s first and most famous cosmological model was spatially finite, closed up on itself. The constructions of this book are to be seen as a similar attempt to create a rational model of the universe in which the elusive circle does close.

In fact, if the work with Niall O Murchadha mentioned at the end of the Preface, which suggests that absolute distance can be eliminated as a basic concept (see Box 3), can be transformed into a complete theory, the problem of infinity may well be solved in the process. If size has no meaning, the distinction between a spatially finite or infinite universe becomes meaningless.

CHAPTER 5: NEWTON’S EVIDENCE