includes a term that is non-zero even for zero momentum (and zero potential), namely the mass times the speed of light squared. It is only the combination of this "mass energy" and the energy associated with momentum that is conserved in relativistic processes, which means it is possible to convert mass energy to kinetic energy and vice versa. With this observation, we can understand why the mass of a hydrogen atom is less than the mass of an electron plus the mass of a proton, and why nuclear reactions can be used to produce enormous amounts of energy. Finally, we'll see that with the new definitions, energy and momentum can be non-zero and finite even in a limit where the mass is taken to zero, assuming that the velocity is that of light. Furthermore, the relationship between energy and momentum for massless particles is exactly the same as for classical electromagnetic waves. We will soon see that these similarities between massless particles travelling at the speed of light and electromagnetic waves are not a coincidence. PART II: QUANTUM MECHANICS Light as a particle To introduce quantum mechanics, we'll begin by pointing out a few simple phenomena that classical mechanics and classical electromagnetism cannot seem to explain. One of these, the "photoelectric effect" (in which electromagnetic radiation liberates electrons from a metal), suggests strongly that light comes in discrete bundles or quanta of energy, with the energy in each quantum proportional to the frequency. We can think of these quanta as particles of light, called "photons", which together make up the electromagnetic wave. Properties of quanta If the photon description of light is correct, we should be able to explain wave-like phenomena via the behaviour of individual photons. We will quickly realise that this is only possible with some drastic departures from the rules of classical physics. To begin, we'll discuss the photon interpretation of familiar experiments involving polarizers. For photons of light polarized in the same direction as a polarizer, or perpendicular to the polarizer, it must be that all the photons pass through, or none of the photons pass through, respectively. However, in order to explain the partial attenuation observed for any other polarization, we will be forced to conclude that for a stream of these identically polarized photons, some pass through the polarizer and some do not. Even with complete knowledge about the initial polarization, we cannot predict the fate of any individual photon, only the probability that it will pass through the polarizer. This indeterminacy is a central difference between quantum mechanics and classical mechanics: whereas in classical mechanics, we could hope to predict the precise future evolution of a system, in quantum mechanics we can only predict the probabilities for the various possible outcomes of an experiment.