Or consider an isolated molecule composed of two atoms shaped something like a dumbbell-a molecule of salt, it might be. Such a molecule rotates about an axis through the line connecting the two atoms. But in the world of quantum mechanics, the realm of the very small, not all orientations of our dumbbell molecule are possible. It might be that the molecule could be oriented in a horizontal position, say, or in a vertical position, but not at many angles in between. Some rotational positions are forbidden. Forbidden by what? By the laws of nature. The universe is built in such a way as to limit, or quantize, rotation. We do not experience this directly in everyday life; we would find it startling as well as awkward in sitting-up exercises, to find arms outstretched from the sides or pointed up to the skies permitted but many intermediate positions forbidden. We do not live in the world of the small, on the scale of 10−13 centimeters, in the realm where there are twelve zeros between the decimal place and the one. Our common-sense intuitions do not count. What does count is experiment-in this case observations from the far infrared spectra of molecules. They show molecular rotation to be quantized.
The idea that the world places restrictions on what humans might do is frustrating. Why shouldn’t we be able to have intermediate rotational positions? Why can’t we travel faster than the speed of light? But so far as we can tell, this is the way the universe is constructed. Such prohibitions not only press us toward a little humility; they also make the world more knowable. Every restriction corresponds to a law of nature, a regularization of the universe. The more restrictions there are on what matter and energy can do, the more knowledge human beings can attain. Whether in some sense the universe is ultimately knowable depends not only on how many natural laws there are that encompass widely divergent phenomena, but also on whether we have the openness and the intellectual capacity to understand such laws. Our formulations of the regularities of nature are surely dependent on how the brain is built, but also, and to a significant degree, on how the universe is built.
For myself, I like a universe that includes much that is unknown and, at the same time, much that is knowable. A universe in which everything is known would be static and dull, as boring as the heaven of some weakminded theologians. A universe that is unknowable is no fit place for a thinking being. The ideal universe for us is one very much like the universe we inhabit. And I would guess that this is not really much of a coincidence.
CHAPTER 3
To punish me for my contempt for authority,
Fate made me an authority myself.
EINSTEIN
ALBERT EINSTEIN was born in Ulm, Germany, in 1879, just a century ago. He is one of the small group of people in any epoch who remake the world through a special gift, a talent for perceiving old things in new ways, for posing deep challenges to conventional wisdom. For many decades he was a saintly and honored figure, the only scientist the average person could readily name. In part because of his scientific accomplishments, at least dimly grasped by the public; in part because of his courageous positions on social issues; and in part because of his benign personality, Einstein was admired and revered throughout the world. For scientifically inclined children of immigrant parents, or those growing up in the Depression, like me, the reverence accorded Einstein demonstrated that there were such people as scientists, that a scientific career might not be totally beyond hope. One major function he involuntarily served was as a scientific role model. Without Einstein, many of the young people who became scientists after 1920 might never have heard of the existence of the scientific enterprise. The logic behind Einstein’s Special Theory of Relativity could have been developed a century earlier, but, although there were some premonitory insights by others, relativity had to wait for Einstein. Yet fundamentally the physics of special relativity is very simple, and many of the essential results can be derived from high school algebra and pondering a boat paddling upstream and downstream. Einstein’s life was rich in genius and irony, a passion for the issues of his time, insights into education, the connection between science and politics, and was a demonstration that individuals can, after all, change the world.
As a child Einstein gave little indication of what was to come. “My parents,” he recalled later, “were worried because I started to talk comparatively late, and they consulted the doctor because of it… I was at that time… certainly not younger than three.” He was an indifferent student in elementary school, where he said the teachers reminded him of drill sergeants. In Einstein’s youth, a bombastic nationalism and intellectual rigidity were the hallmarks of European education. He rebelled against the dull, mechanized methods of teaching. “I preferred to endure all sorts of punishment rather than learn to gabble by rote.” Einstein was always to detest rigid disciplinarians, in education, in science and in politics.
At five he was stirred by the mystery of a compass. And, he later wrote, “at the age of 12 I experienced a second wonder of a totally different nature in a little book dealing with Euclidean plane geometry… Here were assertions, as for example the intersection of the three altitudes of a triangle in one point, which-though by no means evident-could nevertheless be proved with such certainty that any doubt appeared to be out of the question. This lucidity and certainty made an indescribable impression upon me.” Formal schooling provided only a tedious interruption to such contemplations. Einstein wrote of his self-education: “At the age of 12 to 16 I familiarized myself with the elements of mathematics together with the principles of differential and integral calculus. In doing so I had the good fortune of finding books which were not too particular in their logical rigor, but which made up for this by permitting the main thoughts to stand out clearly and synoptically… I also had the good fortune of getting to know the essential results and methods of the entire field of the natural sciences in an excellent popular exposition, which limited itself almost throughout to qualitative aspects… a work which I read with breathless attention.” Modern popularizers of science may take some comfort from these words.
Not one of his teachers seems to have recognized his talents. At the Munich Gymnasium, the city’s leading secondary school, one of the teachers told him, “You’ll never amount to anything, Einstein.” At age fifteen it was strongly suggested that he leave school. The teacher observed, “Your very presence spoils the respect of the class for me.” He accepted this suggestion with gusto and spent many months wandering through northern Italy, a high school dropout in the 1890s. Throughout his life he preferred informal dress and manner. Had he been a teen-ager in the 1960s or 1970s rather than the 1890s, conventional people would almost certainly have called him a hippie.
Yet his curiosity about physics and his wonder about the natural universe soon overcame his distaste for formal education, and he found himself applying, with no high school diploma, to the Federal Institute of Technology in Zurich, Switzerland. He failed the entrance examination, enrolled himself in a Swiss high school to satisfy his deficiencies, and was admitted to the Federal Institute the following year. But he was still a mediocre student. He resented the prescribed curriculum, avoided the lecture room and tried to pursue his true interests. He later wrote: “The hitch in this was, of course, the fact that you had to cram all this stuff into your mind for the examination, whether you liked it or not.”