David Sumpter

and others developed quantitative ways of coping, well before the photon had been conceived. Photon scattering can now accommodate all scattering phenomena, but as Johnsen points out, it is computationally messy. Chapter six is a tough one for those of us who belong to the rays and waves tradition. It includes transparency, reflection and refraction but is titled simply ‘Scattering with interference’. We are in quantal territory here. The first paragraph is wonderfully uncompromising, and I can’t resist quoting it in full: “Light does not bend in a lens, it doesn’t bounce off the surface of glass, and it doesn’t spread out after passing through a small hole. It doesn’t even travel in a straight line. The happiest day of my scientific life came when I read Feynman’s QED and learned that refraction, reflection, and diffraction — things I had known since the fifth grade — were all lies. More accurately they are illusions. It appears that light bends, bounces and spreads out. The illusions are so good that you can base solid mathematical predictions on them, but careful thought and further experiments show that more is going on.” In classical optics, electromagnetic waves travel through space at the speed of light and interfere with each other when they meet to add their amplitudes or cancel each other, depending on their phase relationships. In quantum optics, all that can be observed is the emission or absorption of a photon. Between these events the wave in transit has phase and is capable of interference, but cannot be located. It can only be described in terms of the probability that it will encounter an atomic electron, and then release all its unitary energy. For someone with a basically Newtonian mindset, the bizarreness of this formulation comes from the idea that the energy of the photon somehow dissipates into a probability cloud, and then gets itself together again for an interaction with matter. It seems I am not alone in this failure of imagination. But, having admitted this failing, it has to be said that quantum optics provides an accurate and apparently complete account of all the well-known optical phenomena — reflection, refraction, diffraction and so on. The reader should consult Feynman [1] to be convinced of this. In his classic textbook [4], Rodney Loudon tells us: “It is never the photons themselves that interfere, one with another, but rather the probability amplitudes that describe their propagation from the input to the output.” Fortunately, most of the formalisms that describe the interference phenomena that form the basis of classical optics also hold for the probability waves of quantum optics. I will give a single example of the jolt I received from the new photon thinking. I have worked on multilayer reflectors (butterfly wings, fish scales) on and off since about 1970. In a thin film some light is reflected from the upper surface and some from the lower surface, and these two wavefronts interfere, constructively or destructively, to produce a high reflectance for some wavelengths and low for others. This, I now learn, is wrong. What really happens is that photons are scattered from molecules throughout the film, some continue forwards, delaying the phase of the continuing beam (refraction), and some backwards (reflection). The surfaces themselves are unimportant, as is explained by Feynman [1] on pages 103–109. It turns out that the many probability amplitude vectors from the backscattered photons add up to give a resultant that can be resolved into two vectors that look as though they have come from the upper and lower surfaces. And the mathematics is magically the same. In his last chapter, Johnsen gets into what he describes earlier as the truly weird parts of quantum mechanics that are not relevant to biology. Quantum entanglement is a phenomenon in which two photons emitted simultaneously from the same crystal appear to communicate with each other over vast distances. As Johnsen says: “If nothing else about light bothers you, quantum entanglement really should”. Enough. I am grateful to this book for forcing me to come to terms with a number of aspects of light that I had been delinquent enough to ignore, and in a way that was a pleasure — like a long walk in hilly country.