simplify the world on the basis of sound intuition, but most often they do it because they have no other choice. There is a well-known allegory that physicists like to tell: If you are walking at night on a poorly lit street and you notice that your car keys are not in your pocket, where is the first place you look? Under the nearest streetlight, of course. Why? Not because you expect that you would necessarily lose your keys there, but rather because that is the only place you are likely to find them! So, too, much of physics is guided by looking where the light is.
Nature has so often been kind to us that we have come to take it sort of for granted. New problems are usually first approached using established tools, whether or not it is clear that they are appropriate, because it is all we can do at the time. If we are lucky, we can hope that even in gross approximation, some element of the essential physics has been captured. Physics is full of examples where looking where the light is has revealed far more than we had any right to expect. One of them took place shortly after the end of World War II, in a chain of events that carried with it elements of high drama and at the same time heralded the dawn of a new era in physics. The final result was the picture we now have of how physical theory evolves as we explore the universe on ever smaller or larger scales. This idea, which I never see discussed in popular literature, is fundamental to the way modern physics is done.
The war was over, physicists were once again trying to explore fundamental questions after years of war-related work, and the
great revolutions of the twentieth century—relativity and quantum mechanics—had been completed. A new problem had arisen when physicists attempted to reconcile these two developments, both of which I shall describe in more detail later in the book. Quantum mechanics is based on the fact that at small scales, and for small times, not all quantities associated with the interactions of matter can be simultaneously measured. Thus, for example, the velocity of a particle and its position cannot be exactly determined at the same instant, no matter how good the measuring apparatus. Similarly, one cannot determine the energy of a particle exactly if one measures it over only a limited time interval. Relativity, on the other hand, stipulates that measurements of position, velocity, time, and energy are fundamentally tied together by new relationships that become more evident as the speed of light is approached. Deep inside of atoms, the motion of particles is sufficiently fast that the effects of relativity begin to show themselves, yet at the same time the scales are small enough so that the laws of quantum mechanics govern. The most remarkable consequence of the marriage of these two ideas is the prediction that for times that are sufficiently small so that it is impossible to measure accurately the energy contained in a certain volume, it is impossible to specify how many particles are moving around inside it. For example, consider the motion of an electron from the back of your TV tube to the front. (Electrons are microscopic charged particles, which, along with protons and neutrons, make up all atoms of ordinary matter. In metals, electrons can move about under the action of electric forces to produce currents. Such electrons are emitted by the metal tip of a heating element in the back of the TV and strike the screen at the front and cause it to shine, producing the picture you see.) The laws of quantum mechanics tell us that for any very short interval it is impossible
to specify exactly which trajectory the electron takes, while at the same time attempting to measure its velocity. In this case, when relativity is incorporated into the picture, it suggests that if this is the case, during this short interval one cannot claim with certainty that there is only one electron traveling along. It is possible that spontaneously both