the theory of computation Chapters 5, 6, 9, 10, 13, 14
the theory of evolution Chapters 8, 13, 14.
The next chapter is about the first and most important of the four strands, quantum physics.
2
Shadows
There is no better, there is no more open door by which you can enter into the study of natural philosophy, than by considering the physical phenomena of a candle.
In his popular Royal Institution lectures on science, Michael Faraday used to urge his audiences to learn about the world by considering what happens when a candle burns. I am going to consider an electric torch (or flashlight) instead. This is quite fitting, for much of the technology of an electric torch is based on Faraday’s discoveries.
I am going to describe some experiments which demonstrate phenomena that are at the core of quantum physics. Experiments of this sort, with many variations and refinements, have been the bread and butter of quantum optics for many years. There is no controversy about the results, yet even now some of them are hard to believe. The basic experiments are remarkably austere. They require neither specialized scientific instruments nor any great knowledge of mathematics or physics — essentially, they involve nothing but casting shadows. But the patterns of light and shadow that an ordinary electric torch can cast are very strange. When considered carefully they have extraordinary ramifications. Explaining them requires not just new physical laws but a new level of description and explanation that goes beyond what was previously regarded as being the scope of science. But first, it reveals the existence of parallel universes. How can it? What conceivable pattern of shadows could have implications like that?
Imagine an electric torch switched on in an otherwise dark room. Light emanates from the filament of the torch’s bulb and fills out part of a cone. In order not to complicate the experiment with reflected light, the walls of the room should be totally absorbent, matt black. Alternatively, since we are only imagining these experiments, we could imagine a room of astronomical size, so that there is no time for any light to reach the walls and return before the experiment is completed. Figure 2.1 illustrates the situation. But it is somewhat misleading: if we were observing the torch from the side we should be able to see neither it nor, of course, its light. Invisibility is one of the more straightforward properties of light. We see light only if it enters our eyes (though we usually speak of seeing the object in our line of sight that last affected that light).
FIGURE 2.1 Light from an electric torch (flashlight).
We cannot see light that is just passing by. If there were a reflective object in the beam, or even some dust or water droplets to scatter the light, we could see where it was. But there is nothing in the beam, and we are observing from outside it, so none of its light reaches us. An accurate representation of what we should see would be a completely black picture. If there were a second source of light we might be able to see the torch, but still not its light. Beams of light, even the most intense light that we can generate (from lasers), pass through each other as if nothing were there at all.
Figure 2.1 does show that the light is brightest near the torch, and gets dimmer farther away as the beam spreads out to illuminate an ever larger area. To an observer within the beam, backing steadily away from the torch, the reflector would appear ever smaller and then, when it could only be seen as a single point, ever fainter. Or would it? Can light really be spread more and more thinly without limit? The answer is no. At a distance of approximately ten thousand kilometres from the torch, its light would be too faint for the human eye to detect and the observer would see nothing. That is, a human observer would see nothing; but what about an animal with more sensitive vision? Frogs’ eyes are several times more sensitive than human eyes — just enough to make a significant difference in this experiment. If the observer were a frog, and it kept moving ever farther away from the torch, the moment at which it entirely lost sight of the torch would never come. Instead, the frog would see the torch begin to flicker. The flickers would come at irregular intervals that would become longer as the frog moved farther away. But the brightness of the individual flickers would not diminish. At a distance of one hundred million kilometres from the torch, the frog would see on average only one flicker of light per day, but that flicker would be as bright as any that it observed at any other distance.
Frogs cannot tell us what they see. So in real experiments we use photomultipliers (light detectors which are even more sensitive than frogs’ eyes), and we thin out the light by passing it through dark filters, rather than by observing it from a hundred million kilometres away. But the principle is the same, and so is the result: neither apparent darkness nor uniform dimness, but flickering, with the individual flickers equally bright no matter how dark a filter we use. This flickering indicates that there is a limit to how thinly light can be evenly spread. Borrowing the terminology of goldsmiths, one might say that light is not infinitely ‘malleable’. Like gold, a small amount of light can be evenly spread over a very large area, but eventually if one tries to spread it out further it gets lumpy. Even if gold atoms could somehow be prevented from clumping together, there is a point beyond which they cannot be subdivided without ceasing to be gold. So the only way in which one can make a one-atom-thick gold sheet even thinner is to space the atoms farther apart, with empty space between them. When they are sufficiently far apart it becomes misleading to think of them as forming a continuous sheet. For example, if each gold atom were on average several centimetres from its nearest neighbour, one might pass one’s hand through the ‘sheet’ without touching any gold at all. Similarly, there is an ultimate lump or ‘atom’ of light, a photon. Each flicker seen by the frog is caused by a photon striking the retina of its eye. What happens when a beam of light gets fainter is not that the photons themselves get fainter, but that they get farther apart, with empty space between them (Figure 2.2). When the beam is very faint it can be misleading to call it a ‘beam’, for it is not continuous. During periods when the frog sees nothing it is not because the light entering its eye is too weak to affect the retina, but because no light has entered its eye at all.
This property of appearing only in lumps of discrete sizes is called quantization. An individual lump, such as a photon, is called a quantum (plural quanta). Quantum theory gets its name from this property, which it attributes to all measurable physical quantities — not just to things like the amount of light, or the mass of gold, which are quantized because the entities concerned, though apparently continuous, are really made of particles. Even for quantities like distance (between two atoms, say), the notion of a continuous range of possible values turns out to be an idealization. There are no measurable continuous quantities in physics. There are many new effects in quantum physics, and on the face of it quantization is one of the tamest, as we shall see. Yet in a sense it remains the key to all the others, for if everything is quantized, how does any quantity change from one value to another? How does any object get from one place to another if there is not a continuous range of intermediate places for it to be on the way? I shall explain how in Chapter 9, but let me set that question aside for the moment and return to the vicinity of the torch, where the beam looks continuous because every second it pours about 1014 (a hundred trillion) photons into an eye that looks into it.