by Carl Sagan
If the universe had natural laws that governed its behavior to the same degree of regularity that determines a crystal of salt, then, of course, the universe would be knowable. Even if there were many such laws, each of considerable complexity, human beings might have the capability to understand them all. Even if such knowledge exceeded the information-carrying capacity of the brain, we might store the additional information outside our bodies-in books, for example, or in computer memories-and still, in some sense, know the universe.
Human beings are, understandably, highly motivated to find regularities, natural laws. The search for rules, the only possible way to understand such a vast and complex universe, is called science. The universe forces those who live in it to understand it. Those creatures who find everyday experience a muddled jumble of events with no predictability, no regularity, are in grave peril. The universe belongs to those who, at least to some degree, have figured it out.
It is an astonishing fact that there are laws of nature, rules that summarize conveniently-not just qualitatively but quantitatively-how the world works. We might imagine a universe in which there are no such laws, in which the 1080 elementary particles that make up a universe like our own behave with utter and uncompromising abandon. To understand such a universe we would need a brain at least as massive as the universe. It seems unlikely that such a universe could have life and intelligence, because beings and brains require some degree of internal stability and order. But even if in a much more random universe there were such beings with an intelligence much greater than our own, there could not be much knowledge, passion or joy.
Fortunately for us, we live in a universe that has at least important parts that are knowable. Our common-sense experience and our evolutionary history have prepared us to understand something of the workaday world. When we go into other realms, however, common sense and ordinary intuition turn out to be highly unreliable guides. It is stunning that as we go close to the speed of light our mass increases indefinitely, we shrink toward zero thickness in the direction of motion, and time for us comes as near to stopping as we would like. Many people think that this is silly, and every week or two I get a letter from someone who complains to me about it. But it is a virtually certain consequence not just of experiment but also of Albert Einstein’s brilliant analysis of space and time called the Special Theory of Relativity. It does not matter that these effects seem unreasonable to us. We are not in the habit of traveling close to the speed of light. The testimony of our common sense is suspect at high velocities.
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
THAT WORLD WHICH BECKONS LIKE A LIBERATION
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.”
He managed to graduate only because his close friend Marcel Grossmann assiduously attended classes and shared his notes with Einstein. On Grossmann’s death many years later, Einstein wrote: “I remember our student days. He the irreproachable student, I myself disorderly and a dreamer. He, on good terms with the teachers and understanding everything; I a pariah, discontented and little loved… Then the end of our studies-I was suddenly abandoned by everyone, standing at a loss on the threshold of life.” By immersing himself in Grossmann’s notes, he managed to graduate from college. But, he recalled, studying for the final examinations “had such a deterring effect on me that… I found the consideration of any scientific problem distasteful to me for an entire year… It is little short of a miracle that modern methods of instruction have not already completely strangled the holy curiosity of inquiry, because what this delicate little plant needs most, apart from initial stimulation, is freedom; without that it is surely destroyed… I believe that one could even deprive a healthy beast of prey of its voraciousness, if one could force it with a whip to eat continuously whether it were hungry or not…” His remarks should be sobering to those of us engaged in higher education in science. I wonder how many potential Einsteins have been permanently discouraged through competitive examinations and the forced feeding of curricula.
After supporting himself with odd jobs, and being passed over for positions he considered desirable, Einstein accepted an offer as an examiner of applications at the Swiss Patent Office in Berne, an opportunity made available through the intervention of Marcel Grossmann’s father. About the same time he rejected his German nationality and became a Swiss citizen. Three years later, in 1903, he married his college sweetheart. Almost nothing is known about which patent applications Einstein approved and which he rejected. It would be interesting to know whether any of the proposed patents stimulated his thinking in physics.
One of his biographers, Banesh Hoffman, writes that at the Patent Office, Einstein “soon learned to do his chores efficiently and this let him snatch precious morsels of time for his own surreptitious calculations, which he guiltily hid in a drawer when footsteps approached.” Such were the circumstances attending the birth of the great relativity theory. But Einstein later nostalgically recalled the Patent Office as “that secular cloister where I hatched my most beautiful ideas.”
On several occasions he was to suggest to colleagues that the occupation of lighthouse keeper would be a suitable position for a scientist-because the work would be comparatively easy and would allow the contemplation necessary to do scientific research. “For Einstein,” said his collaborator Leopold Infeld, “loneliness, life in a lighthouse, would be most stimulating, would free him from so many of the duties which he hates. In fact it would be for him the ideal life. But nearly every scientist thinks just the opposite. It was the curse of my life that for a long time I was not in a scientific atmosphere, that I had no one with whom to talk physics.”
Einstein also believed that there was something dishonest about making money by teaching physics. He argued that it was far better for a physicist to support himself by some other simple and honest labor, and do physics in his spare time. When making a similar remark many years later in America, Einstein mused that he would have liked to be a plumber, and was promptly awarded honorary membership in the plumbers’ union.
In 1905 Einstein published four research papers, the product of his spare time at the Swiss Patent Office, in the leading physics journal of the time, the Annalen der Physik. The first demonstrated that light has particle as well as wave properties, and explained the previously baffling photoelectric effect in which electrons are emitted by solids when irradiated by light. The second explored the nature of molecules by explaining the statistical “Brownian motion” of suspended small particles. And the third and fourth introduced the Special Theory of Relativity and for the first time expressed the famous equation, E = mc2, which is so widely quoted and so rarely understood.
The equation expresses the convertibility of matter into energy, and vice versa. It extends the law of the conservation of energy into a law of conservation of energy and mass, stating that energy and mass can be neither created nor destroyed-although one form of energy or matter can be converted into another form. In the equation, E stands for the energy equivalent of the mass m. The amount of energy that could, under ideal circumstances, be extracted from a mass m is mc2, where c is the velocity of light = 30 billion centimeters per second. (The velocity of light is always written as lower-case c, never as upper-case.) If we measure m in grams and c in centimeters per second, E is measured in a unit of energy called ergs. The complete conversion of one gram of mass into energy thus releases 1 × (3 × 1010)2 = 9 × 1020 ergs, which is the equivalent of the explosion of roughly a thousand tons of TNT. Thus enormous energy resources are contained in tiny amounts of matter, if only we knew how to extract the energy. Nuclear weapons and nuclear power plants are common terrestrial examples of our halting and ethically ambiguous efforts to extract the energy that Einstein showed was present in all of matter. A thermonuclear weapon, a hydrogen bomb, is a device of terrifying power-but even it is capable of extracting less than one percent of mc2 from a mass m of hydrogen.
Einstein’s four papers published in 1905 would have been an impressive output for the full-time research work of a physicist over a lifetime; for the spare-time work of a twenty-six-year-old Swiss patent clerk in a single year it is nothing short of astonishing. Many historians of science have called 1905 the Annus Mirabilis, the miracle year. There had been, with uncanny resemblances, only one previous such year in the history of physics-1666, when Isaac Newton, aged twenty-four, in enforced rural isolation (because of an epidemic of bubonic plague) produced an explanation for the spectral nature of sunlight, invented differential and integral calculus, and devised the universal theory of gravitation. Together with the General Theory of Relativity, first formulated in 1915, the 1905 papers represent the principal output of Einstein’s scientific life.
Before Einstein, it was widely held by physicists that there were privileged frames of ref
erence, such things as absolute space and absolute time. Einstein’s starting point was that all frames of reference-all observers, no matter what their locale, velocity or acceleration-would see the fundamental laws of nature in the same way. It seems likely that Einstein’s view on frames of reference was influenced by his social and political attitudes and his resistance to the strident jingoism he found in late-nineteenth-century Germany. Indeed, in this sense the idea of relativity has become an anthropological commonplace, and social scientists have adopted the idea of cultural relativism: there are many different social contexts and world views, ethical and religious precepts, expressed by various human societies, and most of comparable validity.
Special relativity was at first by no means widely accepted. Attempting once again to break into an academic career, Einstein submitted his already published relativity paper to Berne University as an example of his work. He evidently considered it a significant piece of research. It was rejected as incomprehensible, and he was to remain at the Patent Office until 1909. But his published work did not go unnoticed, and it slowly began to dawn on a few of the leading European physicists that Einstein might well be one of the greatest scientists of all time. Still, his work on relativity remained highly controversial. In a letter of recommendation for Einstein for a position at the University of Berlin, a leading German scientist suggested that relativity was a hypothetical excursion, a momentary aberration, and that, despite it, Einstein really was a first-rate thinker. (His Nobel Prize, which he learned about during a visit to the Orient in 1921, was awarded for his paper on the photoelectric effect and “other contributions” to theoretical physics. Relativity was still considered too controversial to be mentioned explicitly.)