So how can we let the kingfisher fly? As few things delight me more than a kingfisher in flight, this is a matter of some interest to me. The answer that suddenly came to me in the summer of 1991 (which, of course, is a place in Platonia, not a time) was that the flight of the kingfisher is ultimately an illusion, though it rests on something that is very special and just as real as we take flight to be. It is flight without flight. Let me return to the imagery of the blue mist that shimmers over Platonia. It is easy to locate the instant of my death – I see the point in that great configuration space in which I stand on the bank of the stream. Now let me make an assumption in the hallowed tradition of Boltzmann: only the probable is experienced. The blue mist measures probability. Therefore, in accordance with the tradition, the blue mist must shine brightly at the point in Platonia in which I see the kingfisher frozen in flight above the water. I experienced the scene, so it must have a high probability. But there is still no motion.
I do not think there can be any. But there can be something else. As I mentioned in Part 1, nobody really knows what it is in our brains that corresponds to conscious experience. I make no pretence to any expertise here, but it is well known that much processing goes on in the brain and, employing normal temporal language, we can confidently assert that what we seem to experience in one instant is the product of the processing of data coming from a finite span of time.
This is all I need. It enables me to make the working conjecture that I outline in Part 1 – that when we think we see motion at some instant, the underlying reality is that our brain at that instant contains data corresponding to several different positions of the object perceived to be in motion. My brain contains, at any one instant, several ‘snapshots’ at once. The brain, through the way in which it presents data to consciousness, somehow ‘plays the movie’ for me.
Down in Plato’s cave, thanks to the perfect representation of everything that is, I can look more closely at the point in the model of Platonia that contains me at the point of death. I can look into my brain and see the state of all its neurones. And what do I see? I see, coded in the neuronal patterns, six or seven snapshots of the kingfisher just as they occurred in the flight I thought I saw. This brain configuration, with its simultaneous coding of several snapshots, nevertheless belongs to just one point of Platonia. Near it are other points representing configurations in which the correct sequence of snapshots that give a kingfisher in flight is not present. Either some of the snapshots are not there, or they are jumbled up in the wrong order. There are infinitely many possiblilities, and they are all there. They must be, since there is a place in Platonia for everything that is logically possible.
Now, at all the corresponding points the blue mist will have a certain intensity, for in principle the laws of quantum mechanics allow the mist to seep into all the nooks and crannies of Platonia. Indeed, the first quantum commandment is that all possibilities must be explored. But the laws that mandate exploration also say that the blue mist will be very unevenly distributed. In some places it will be so faint as to be almost invisible, even with the acuity of vision we acquire in Plato’s cave for things mathematical. There will also be points where it shines with the steely blue brilliance of Sirius – or the kingfisher’s wings. And again my conjecture is this: the blue mist is concentrated and particularly intense at the precise point in Platonia in which my brain does contain those perfectly coordinated ‘snapshots’ of the kingfisher and I am conscious of seeing the bird in flight.
As I explained in Chapter 2, a time capsule, as I define it, is in itself perfectly static – it is, after all, one of Plato’s forms. However, it is so highly structured that it creates the impression of motion. In the chapters that follow, we shall see if there is any hope that static quantum cosmology will concentrate the wave function of the universe on time capsules. As logical possibilities, they are certainly out there in Platonia. But will ψ find them?
Dynamics Without Dynamics (p. 258) In this section I refer to investigations by various authors. Their studies will be found in the bibliography. Physicists really interested in the semiclassical approach may also like to consult the review article by Vilenkin (1989), the paper by Brout (1987), the final part of Zeh (1992, 1999) and the introductory article by Kiefer (1997). The fullest account of my own ideas is Barbour (1994a).
CHAPTER 19
Latent Histories and Wave Packets
All interpretations of quantum mechanics face two main issues. First, the theory implies the existence of far more ‘furniture’ in the world than we see. I have suggested that the ‘missing furniture’ is simply other instants of time that we cannot see because we experience only one at a time. The other issue is why our experiences suggest so strongly a macroscopic universe with a unique, almost classical history. In the very process of creating wave mechanics, Schrödinger found a most interesting connection between quantum and classical physics that cast a great deal of light on this problem. The interpretation he based on it was soon seen to be untenable, but it is full of possibilities and continues to play an important role. It is the starting point of other interpretations, including the one I advocate, so I should like to say something about it.
In the 1820s and 1830s, William Rowan Hamilton, whom we have already met, established a fascinating and beautiful connection between the two great paradigms of physical thought of his time – the wave theory of light and the Newtonian dynamics of particles. Cornelius Lanczos, a friend of Einstein and author of the fine book The Variational Principles of Mechanics, opens his chapter on these things with a quotation from Exodus: ‘Put off thy shoes from off thy feet, for the place whereon thou standest is holy ground.’ Let me quote Lanczos – he is not exaggerating:
We have done considerable mountain climbing. Now we are in the rarefied atmosphere of theories of excessive beauty and we are nearing a high plateau on which geometry, optics, mechanics, and wave mechanics meet on common ground. Only concentrated thinking, and a considerable amount of re-creation, will reveal the full beauty of our subject in which the last word has not yet been spoken. We start with … Hamilton’s own investigations in the realm of geometrical optics and mechanics. The combination of these two approaches leads to de Broglie’s and Schrödinger’s great discoveries, and we come to the end of our journey.
The italics are mine. Lanczos’s account does end with Schrödinger’s discoveries, but I think it can be taken one step further. By the way, do not worry about the call for ‘concentrated thinking’. If you have got this far, you will not fail now.
Hamilton made several separate discoveries, but the most fundamental result is simple and easy to visualize. Two characteristic situations are encountered in wave theory – ‘choppy’ waves, as on a squally sea, and regular wave patterns. Hamilton was studying the connection between Kepler’s early theory of light rays and the more modern wave theory introduced by Young and Fresnel. Hamilton assumed that light passing through lenses took the form of very regular, almost plane waves of one frequency (Figure 45).