Einstein

DURING the summer of 1905, while fulfilling his duties in the patent office in Bern, Switzerland, Albert Einstein was fiddling with a tantalizing outcome of the special theory of relativity he'd published in June. His new insight, at once simple and startling, led him to wonder whether "the Lord might be laughing ... and leading me around by the nose."

But by September, confident in the result, Einstein wrote a three-page supplement to the June paper, publishing perhaps the most profound afterthought in the history of science. A hundred years ago this month, the final equation of his short article gave the world E = mc².

In the century since, E = mc² has become the most recognized icon of the modern scientific era. Yet for all its symbolic worth, the equation's intimate presence in everyday life goes largely unnoticed. There is nothing you can do, not a move you can make, not a thought you can have, that doesn't tap directly into E = mc². Einstein's equation is constantly at work, providing an unseen hand that shapes the world into its familiar form. It's an equation that tells of matter, energy and a remarkable bridge between them.

Before E = mc², scientists described matter using two distinct attributes: how much the matter weighed (its mass) and how much change the matter could exert on its environment (its energy). A 19th century physicist would say that a baseball resting on the ground has the same mass as a baseball speeding along at 100 miles per hour. The key difference between the two balls, the physicist would emphasize, is that the fast-moving baseball has more energy: if sent ricocheting through a china shop, for example, it would surely break more dishes than the ball at rest. And once the moving ball has done its damage and stopped, the 19th-century physicist would say that it has exhausted its capacity for exerting change and hence contains no energy.

After E = mc², scientists realized that this reasoning, however sensible it once seemed, was deeply flawed. Mass and energy are not distinct. They are the same basic stuff packaged in forms that make them appear different. Just as solid ice can melt into liquid water, Einstein showed, mass is a frozen form of energy that can be converted into the more familiar energy of motion. The amount of energy (E) produced by the conversion is given by his formula: multiply the amount of mass converted (m) by the speed of light squared (c²). Since the speed of light is a few hundred million meters per second (fast enough to travel around the earth seven times in a single second), c² , in these familiar units, is a huge number, about 100,000,000,000,000,000.

A little bit of mass can thus yield enormous energy. The destruction of Hiroshima and Nagasaki was fueled by converting less than an ounce of matter into energy; the energy consumed by New York City in a month is less than that contained in the newspaper you're holding. Far from having no energy, the baseball that has come to rest on the china shop's floor contains enough energy to keep an average car running continuously at 65 m.p.h. for about 5,000 years.

Before 1905, the common view of energy and matter thus resembled a man carrying around his money in a box of solid gold. After the man spends his last dollar, he thinks he's broke. But then someone alerts him to his miscalculation; a substantial part of his wealth is not what's in the box, but the box itself. Similarly, until Einstein's insight, everyone was aware that matter, by virtue of its motion or position, could possess energy. What everyone missed is the enormous energetic wealth contained in mass itself.

The standard illustrations of Einstein's equation - bombs and power stations - have perpetuated a belief that E = mc² has a special association with nuclear reactions and is thus removed from ordinary activity.

This isn't true. When you drive your car, E = mc² is at work. As the engine burns gasoline to produce energy in the form of motion, it does so by converting some of the gasoline's mass into energy, in accord with Einstein's formula. When you use your MP3 player, E = mc² is at work. As the player drains the battery to produce energy in the form of sound waves, it does so by converting some of the battery's mass into energy, as dictated by Einstein's formula. As you read this text, E = mc² is at work. The processes in the eye and brain, underlying perception and thought, rely on chemical reactions that interchange mass and energy, once again in accord with Einstein's formula.

The point is that although E=mc² expresses the interchangeability of mass and energy, it doesn't single out any particular reaction for executing the conversion. The distinguishing feature of nuclear reactions, compared with the chemical reactions involved in burning gasoline or running a battery, is that they generate less waste and thus produce more energy - by a factor of roughly a million. And when it comes to energy, a factor of a million justifiably commands attention. But don't let the spectacle of E=mc² in nuclear reactions inure you to its calmer but thoroughly pervasive incarnations in everyday life.

That's the content of Einstein's discovery. Why is it true?

Einstein's derivation of E = mc² was wholly mathematical. I know his derivation, as does just about anyone who has taken a course in modern physics. Nevertheless, I consider my understanding of a result incomplete if I rely solely on the math. Instead, I've found that thorough understanding requires a mental image - an analogy or a story - that may sacrifice some precision but captures the essence of the result.

Here's a story for E = mc². Two equally strong and skilled jousters, riding identical horses and gripping identical (blunt) lances, head toward each other at an identical speed. As they pass, each thrusts his lance across his breastplate toward his opponent, slamming blunt end into blunt end. Because they're equally matched, neither lance pushes farther than the other, and so the referee calls it a draw.

This story contains the essence of Einstein's discovery. Let me explain.

Einstein's first relativity paper, the one in June 1905, shattered the idea that time elapses identically for everyone. Instead, Einstein showed that if from your perspective someone is moving, you will see time elapsing slower for him than it does for you. Everything he does - sipping his coffee, turning his head, blinking his eyes - will appear in slow motion.

This is hard to grasp because at everyday speeds the slowing is less than one part in a trillion and is thus imperceptibly small. Even so, using extraordinarily precise atomic clocks, scientists have repeatedly confirmed that it happens just as Einstein predicted. If we lived in a world where things routinely traveled near the speed of light, the slowing of time would be obvious.

Let's see what the slowing of time means for the joust. To do so, think about the story not from the perspective of the referee, but instead imagine you are one of the jousters. From your perspective, it is your opponent - getting ever closer - who is moving. Imagine that he is approaching at nearly the speed of light so the slowing of all his movements - readying his joust, tightening his face - is obvious. When he shoves his lance toward you in slow motion, you naturally think he's no match for your swifter thrust; you expect to win. Yet we already know the outcome. The referee calls it a draw and no matter how strange relativity is, it can't change a draw into a win.

After the match, you naturally wonder how your opponent's slowly thrusted lance hit with the same force as your own. There's only one answer. The force with which something hits depends not only on its speed but also on its mass. That's why you don't fear getting hit by a fast-moving Ping-Pong ball (tiny mass) but you do fear getting hit by a fast-moving Mack truck (big mass). Thus, the only explanation for how the slowly thrust lance hit with the same force as your own is that it's more massive.

This is astonishing. The lances are identically constructed. Yet you conclude that one of them - the one that from your point of view is in motion, being carried toward you by your opponent on his galloping horse - is more massive than the other. That's the essence of Einstein's discovery. Energy of motion contributes to an object's mass.

AS with the slowing of time, this is unfamiliar because at everyday speeds the effect is imperceptibly tiny. But if, from your viewpoint, your opponent were to approach at 99.99999999 percent of the speed of light, his lance would be about 70,000 times more massive than yours. Luckily, his thrusting speed would be 70,000 times slower than yours, and so the resulting force would equal your own.

Once Einstein realized that mass and energy were convertible, getting the exact formula relating them - E = mc² - was a fairly basic exercise, requiring nothing more than high school algebra. His genius was not in the math; it was in his ability to see beyond centuries of misunderstanding and recognize that there was a connection between mass and energy at all.

A little known fact about Einstein's September 1905 paper is that he didn't actually write E = mc²; he wrote the mathematically equivalent (though less euphonious) m = E/c², placing greater emphasis on creating mass from energy (as in the joust) than on creating energy from mass (as in nuclear weapons and power stations).

Over the last couple of decades, this less familiar reading of Einstein's equation has helped physicists explain why everything ever encountered has the mass that it does. Experiments have shown that the subatomic particles making up matter have almost no mass of their own. But because of their motions and interactions inside of atoms, these particles contain substantial energy - and it's this energy that gives matter its heft. Take away Einstein's equation, and matter loses its mass. You can't get much more pervasive than that.

Its singular fame notwithstanding, E = mc² fits into the pattern of work and discovery that Einstein pursued with relentless passion throughout his entire life. Einstein believed that deep truths about the workings of the universe would always be "as simple as possible, but no simpler." And in his view, simplicity was epitomized by unifying concepts - like matter and energy - previously deemed separate. In 1916, Einstein simplified our understanding even further by combining gravity with space, time, matter and energy in his General Theory of Relativity. For my money, this is the most beautiful scientific synthesis ever achieved.

With these successes, Einstein's belief in unification grew ever stronger. But the sword of his success was double-edged. It allowed him to dream of a single theory encompassing all of nature's laws, but led him to expect that the methods that had worked so well for him in the past would continue to work for him in the future.

It wasn't to be. For the better part of his last 30 years, Einstein pursued the "unified theory," but it stubbornly remained beyond his grasp. As the years passed, he became increasingly isolated; mainstream physics was concerned with prying apart the atom and paid little attention to Einstein's grandiose quest. In a 1942 letter, Einstein described himself as having become a "a lonely old man who is displayed now and then as a curiosity because he doesn't wear socks."

Today, Einstein's quest for unification is no curiosity - it is the driving force for many physicists of my generation. No one knows how close we've gotten. Maybe the unified theory will elude us just as it dodged Einstein last century. Or maybe the new approaches being developed by contemporary physics will finally prevail, giving us the ultimate explanation of the cosmos. Without a unified theory it's hard to imagine we will ever resolve the deepest of all mysteries - how the universe began- so the stakes are high and the motivation strong.

But even if our science proves unable to determine the origin of the universe, recent progress has already established beyond any doubt that a fraction of a second after creation (however that happened), the universe was filled with tremendous energy in the form of wildly moving exotic particles and radiation. Within a few minutes, this energy employed E = mc² to transform itself into more familiar matter - the simplest atoms - which, in the course of about a billion years, clumped into planets and stars.

During the 13 billion years that have followed, stars have used E = mc² to transform their mass back into energy in the form of heat and light; about five billion years ago, our closest star - the sun - began to shine, and the heat and light generated was essential to the formation of life on our planet. If prevailing theory and observations are correct, the conversion of matter to energy throughout the cosmos, mediated by stars, black holes and various forms of radioactive decay, will continue unabated.

In the far, far future, essentially all matter will have returned to energy. But because of the enormous expansion of space, this energy will be spread so thinly that it will hardly ever convert back to even the lightest particles of matter. Instead, a faint mist of light will fall for eternity through an ever colder and quieter cosmos.

The guiding hand of Einstein's E = mc² will have finally come to rest.

Brian Greene, a professor of physics and mathematics at Columbia, is the author of "The Elegant Universe" and "The Fabric of the Cosmos."

Is it advisable for one who is not an expert on economic and social issues to express views on the subject of socialism? I believe for a number of reasons that it is.

Let us first consider the question from the point of view of scientific knowledge. It might appear that there are no essential methodological differences between astronomy and economics: scientists in both fields attempt to discover laws of general acceptability for a circumscribed group of phenomena in order to make the interconnection of these phenomena as clearly understandable as possible. But in reality such methodological differences do exist. The discovery of general laws in the field of economics is made difficult by the circumstance that observed economic phenomena are often affected by many factors which are very hard to evaluate separately. In addition, the experience which has accumulated since the beginning of the so-called civilized period of human history has -- as is well known -- been largely influenced and limited by causes which are by no means exclusively economic in nature. For example, most of the major states of history owed their existence to conquest. The conquering peoples established themselves, legally and economically, as the privileged class of the conquered country. They seized for themselves a monopoly of the land ownership and appointed a priesthood from among their own ranks. The priests, in control of education, made the class division of society into a permanent institution and created a system of values by which the people were thenceforth, to a large extent unconsciously, guided in their social behavior.

But historic tradition is, so to speak, of yesterday; nowhere have we really overcome what Thorstein Veblen called "the predatory phase" of human development. The observable economic facts belong to that phase and even such laws as we can derive from them are not applicable to other phases. Since the real purpose of socialism is precisely to overcome and advance beyond the predatory phase of human development, economic science in its present state can throw little light on the socialist society of the future.

Second, socialism is directed toward a social-ethical end. Science, however, cannot create ends and, even less, instill them in human beings; science, at most, can supply the means by which to attain certain ends. But the ends themselves are conceived by personalities with lofty ethical ideals and -- if these ends are not stillborn, but vital and vigorous -- are adopted and carried forward by those many human beings who, half-unconsciously, determine the slow evolution of society.

For these reasons, we should be on our guard not to overestimate science and scientific methods when it is a question of human problems; and we should not assume that experts are the only ones who have a right to express themselves on questions affecting the organization of society. Innumerable voices have been asserting for some time now that human society is passing through a crisis, that its stability has been gravely shattered. It is characteristic of such a situation that individuals feel indifferent or even hostile toward the group, small or large, to which they belong. In order to illustrate my meaning, let me record here a personal experience. I recently discussed with an intelligent and well-disposed man the threat of another war, which in my opinion would seriously endanger the existence of mankind, and I remarked that only a supranational organization would offer protection from that danger. Thereupon my visitor, very calmly and coolly, said to me: "Why are you so deeply opposed to the disappearance of the human race?"

I am sure that as little as a century ago no one would have so lightly made a statement of this kind. It is the statement of a man who has striven in vain to attain an equilibrium within himself and has more or less lost hope of succeeding. It is the expression of a painful solitude and isolation from which so many people are suffering in these days. What is the cause? Is there a way out?

It is easy to raise such questions, but difficult to answer them with any degree of assurance. I must try, however, as best I can, although I am very conscious of the fact that our feelings and strivings are often contradictory and obscure and that they cannot be expressed in easy and simple formulas.

Man is, at one and the same time, a solitary being and a social being. As a solitary being, he attempts to protect his own existence and that of those who are closest to him, to satisfy his personal desires, and to develop his innate abilities. As a social being, he seeks to gain the recognition and affection of his fellow human beings, to share in their pleasures, to comfort them in their sorrows, and to improve their conditions of life. Only the existence of these varied, frequently conflicting strivings accounts for the special character of a man, and their specific combination determines the extent to which an individual can achieve an inner equilibrium and can contribute to the well-being of society. It is quite possible that the relative strength of these two drives is, in the main, fixed by inheritance. But the personality that finally emerges is largely formed by the environment in which a man happens to find himself during his development, by the structure of the society in which he grows up, by the tradition of that society, and by its appraisal of particular types of behavior. The abstract concept "society" means to the individual human being the sum total of his direct and indirect relations to his contemporaries and to all the people of earlier generations. The individual is able to think, feel, strive, and work by himself; but he depends so much upon society--in his physical, intellectual, and emotional existence--that it is impossible to think of him, or to understand him, outside the framework of society. It is "society" which provides man with food, home, the tools of work, language, the forms of thought, and most of the content of thought; his life is made possible through the labor and the accomplishments of many millions past and present who are all hidden behind small word "society."

It is evident, therefore, that the dependence of the individual upon society is a fact of nature which cannot be abolished -- just as in the case of ants and bees. However, while the whole life process of ants and bees is fixed down to the smallest detail by rigid, hereditary instincts, the social pattern and interrelationships of human beings are very variable susceptible to change. Memory, the capacity to make combinations, the gift of oral communication have made possible developments among human beings which are dictated by biological necessities. Such developments manifest themselves in traditions, institutions, and organizations; in literature; in scientific and engineering accomplishments; in works of art. This explains how it happens that, in a certain sense, man can influence his life and that in this process conscious thinking and wanting can play a part.

Man acquires at birth, through heredity, a biological constitution which we must consider fixed and unalterable, including the natural urges which are characteristic of the human species. In addition, during his lifetime, he acquires a cultural constitution which he adopts from society through communication and through many other types of influences. It is this cultural constitution which, with the passage of time, is subject to change and which determines to a very large extent the relationship between the individual and society. Modern anthropology has taught us, through comparative investigation of so-called primitive cultures, that the social behavior of human beings may differ greatly, depending upon prevailing cultural patterns and the types of organization which predominate in society. It is on this that those who are striving to improve the lot of man may ground their hopes: human beings are not condemned, because of their biological constitution, to annihilate each other or to be at the mercy of a cruel, self-inflicted fate.

If we ask ourselves how the structure of society and the cultural attitude of man should be changed in order to make human life as satisfying as possible, we should constantly be conscious of the fact that there are certain conditions which we are unable to modify. As mentioned before, the biological nature of man is, for all practical purposes, not subject to change. Furthermore, technological and demographic developments of the last few centuries have created conditions which are here to stay. In relatively densely settled populations with the goods which are indispensable to their continued existence, an extreme division of labor and a highly productive apparatus are absolutely necessary. The time -- which, looking back, seems so idyllic -- is gone forever when individuals or relatively small groups could be completely self-sufficient. It is only a slight exaggeration to say that mankind constitutes even now a planetary community of production and consumption.

I have now reached the point where I may indicate briefly what to me constitutes the essence of the crisis of our time. It concerns the relationship of the individual to society. The individual has become more conscious than than ever of his dependence upon society. But he does not dependence as a positive asset, as an organic tie, as a protective force, but rather as a threat to his natural rights, or even to his economic existence. Moreover, his position in society is such that the egotistical drives of his make-up are constantly being accentuated, while his social drives, which are by nature weaker, progressively deteriorate. All human beings, whatever their position in society, are suffering from this process of deterioration. Unknowingly prisoners of their own egotism, they feel insecure, lonely, and deprived of the naive, simple, and unsophisticated enjoyment of life. Man can find meaning in life, short and perilous as it is, only through devoting himself to society.

The economic anarchy of capitalist society as it exists today is, in my opinion, the real source of the evil. We see before us a huge community of producers the members of which are unceasingly striving to deprive each other of the fruits of their collective labor -- not by force, but on the whole in faithful compliance with legally established rules. In this respect, it is important to realize that the means of production -- that is to say, the entire productive capacity that is needed for producing consumer goods as well as additional capital goods -- may legally be, and for the most part are, the private property of individuals.

For the sake of simplicity, in the discussion that follows I shall call "workers" all those who do not share in the ownership of the means of production -- although this does not quite correspond to the customary use of the term. The owner of the means of production is in a position to purchase the labor power of the worker. By using the means of production, the worker produces new goods which become the property of the capitalist. The essential point about this process isthe relation between what the worker produces and what he is paid, both measured in terms of real value. In so far as the labor contract is "free," what the worker receives is determined not by the real value of the goods he produces, but by his minimum needs and by the capitalists' requirements for labor power in relation to the number of workers competing for jobs. It is important to understand that even in theory the payment of the worker is not determined by the value of his product.

Private capital tends to become concentrated in few hands, partly because of competition among the capitalists, and partly because technological development and the increasing division of labor encourage the formation of larger units of production at the expense of the smaller ones. The result of these developments is an oligarchy of private capital the enormous power of which cannot be effectively checked even by a democratically organized political society. This is true since the members of legislative bodies are selected by political parties, largely financed or otherwise influenced by private capitalists who, for all practical purposes, separate the electorate from the legislature. The consequence is that the representatives of the people do not in fact sufficiently protect the interests of the underprivileged sections of the population. Moreover, under existing conditions, private capitalists inevitably control, directly or indirectly, the main sources of information (press, radio, education). It is thus extremely difficult, and indeed in most cases quite impossible, for the individual citizen to come to objective conclusions and to make intelligent use of his political rights.

The situation prevailing in an economy based on the private ownership of capital is thus characterized main principles: first, means of production (capital) are privately owned and the owners dispose of them as they see fit; second, the labor contract is free. Of course, there is no such thing as a pure capitalist society in this sense. In particular, it should be noted that the workers, through long and bitter political struggles, have succeeded in securing a somewhat improved form of the "free labor contract" for certain categories of workers. But taken as a whole, the present-day economy does not differ much from "pure" capitalism. Production is carried on for profit, not for use. There is no provision that all those able and willing to work will always be in a position to find employment; an "army of unemployed" almost always exists. The worker is constantly in fear of losing his job. Since unemployed and poorly paid workers do not provide a profitable market, the production of consumers' goods is restricted, and great hardship is the consequence. Technological progress frequently results in more unemployment rather than in an easing of the burden of work for all. The profit motive, in conjunction with competition among capitalists, is responsible for an instability in the accumulation and utilization of capital which leads to increasingly severe depressions. Unlimited competition leads to a huge waste of labor, and to that crippling of the social consciousness of individuals which I mentioned before.

This crippling of individuals I consider the worst evil of capitalism. Our whole educational system suffers from this evil. An exaggerated competitive attitude is inculcated into the student, who is trained to worship acquisitive success as a preparation for his future career.

I am convinced there is only one way to eliminate these grave evils, namely through the establishment of a socialist economy, accompanied by an educational system which would be oriented toward social goals. In such an economy, the means of production are owned by society itself and are utilized in a planned fashion. A planned economy, which adjusts production to the needs of the community, would distribute the work to be done among all those able to work and would guarantee a livelihood to every man, woman, and child. The education of the individual, in addition to promoting his own innate abilities, would attempt to develop in him a sense of responsibility for his fellow-men in place of the glorification of power and success in our present society.

Nevertheless, it is necessary to remember that a planned economy is not yet socialism. A planned economy as such may be accompanied by the complete enslavement of the individual. The achievement of socialism requires the solution of some extremely difficult socio-political problems: how is it possible, in view of the far-reaching centralization of political and economic power, to prevent bureaucracy from becoming all-powerful and overweening? How can the rights of the individual be protected and therewith a democratic counterweight to the power of bureaucracy be assured?