What hasn't Einstein's equation touched in our world?
It's difficult to separate the enormous legacy of E = mc2 from Einstein's legacy as a whole. After all, the equation grew directly out of Einstein's work on special relativity, which is a subset of what most consider his greatest achievement, the theory of general relativity. But I'm going to give it a try nevertheless.
The equation explained
First, though, a capsule explanation of "energy equals mass times the speed of light squared" might be helpful. On the most basic level, the equation says that energy and mass (matter) are interchangeable; they are different forms of the same thing. Under the right conditions, energy can become mass, and vice versa. We humans don't see them that way-how can a beam of light and a walnut, say, be different forms of the same thing?-but Nature does.
So why would you have to multiply the mass of that walnut by the speed of light to determine how much energy is bound up inside it? The reason is that whenever you convert part of a walnut or any other piece of matter to pure energy, the resulting energy is by definition moving at the speed of light. Pure energy is electromagnetic radiation-whether light or X-rays or whatever-and electromagnetic radiation travels at a constant speed of roughly 670,000,000 miles per hour.
Why, then, do you have to square the speed of light? It has to do with the nature of energy. When something is moving four times as fast as something else, it doesn't have four times the energy but rather 16 times the energy-in other words, that figure is squared. So the speed of light squared is the conversion factor that decides just how much energy lies captured within a walnut or any other chunk of matter. And because the speed of light squared is a huge number-448,900,000,000,000,000 in units of mph-the amount of energy bound up into even the smallest mass is truly mind-boggling (see The Power of Tiny Things.)
Of course, intuitively understanding that energy and matter are essentially one, as well as why and how so much energy can be wrapped up in even minute bits of matter, is another thing. And E = mc2, which focuses on matter at rest, is a simplified version of a more elaborate equation that Einstein devised, which also takes into account matter in motion (more on that in a moment). But I hope that you, like I, now have a basic comprehension with which to appreciate the equation's prodigious influence.
E = mc2 in miniature
Perhaps the equation's most far-reaching legacy is that it provides the key to understanding the most basic natural processes of the universe, from microscopic radioactivity to the big bang itself.
Radioactivity is E = mc2 in miniature. Einstein himself suspected this even as he devised the equation. In the 1905 paper in which he introduced E = mc2 to the world, he suggested that it might be possible to test his theory about the equation using radium, an ounce of which, as Marie Curie had discovered not long before, continuously emits 4,000 calories of heat per hour. Einstein believed that radium was constantly converting part of its mass to energy exactly as his equation specified. He was eventually proved right.
Today we know radioactivity to be a property possessed by some unstable elements, such as uranium, or isotopes, such as carbon 14, of spontaneously emitting energetic particles as their atomic nuclei disintegrate. They are metamorphosing mass into energy in direct accordance with Einstein's equation.
We take advantage of that realization today in many technologies. PET scans and similar diagnostics used in hospitals, for example, make use of E = mc2. "Whenever you use a radioactive substance to illuminate processes in the human body, you're paying direct homage to Einstein's insight," says Sylvester James Gates, a physicist at the University of Maryland. Many everyday devices, from smoke detectors to exit signs, also host an ongoing, invisible fireworks of E = mc2 transformations. Radiocarbon dating, which archeologists use to date ancient material, is yet another application of the formula. "The decay products that we see in carbon dating-that energy is directly obtained from the missing mass that you see in E = mc2," Gates says.
Space technologies owe much to the equation. Unceasing E = mc2 disintegrations from radioactive elements such as plutonium provide everything from power for telecommunications satellites to the heat needed to keep the Mars rovers functioning during the frigid martian winter. Space travel in the distant future may also rely on such radiation-derived power. Photons streaming out from the sun and other stars hold energy that in the vacuum of space can theoretically be harnessed to propel a spaceship. "In the far future," says David Hogg, a cosmologist at New York University, "if you imagine that we're sailing to distant stars with spaceships that are driven by radiation pressure-if that ever happens, that will be a really big legacy of Einstein's kinematics."
Kinematics is the study of motion without reference to mass or force, and it figures in a more elaborate form of Einstein's equation that-unlike plain old E = mc2, which concerns mass at rest-also takes into account mass in motion. (If you must know, it's E2 = m2c4 + p2c2, where p equals momentum.) "His bigger equation plays an enormous part in our understanding of how light works, and how energy and light can be transferred and transformed from one place to another, and that sort of thing," Gates says. "So if you consider the larger context, the part of the equation that's not in the public eye, it has an even larger legacy in science."
One application that draws on this larger equation, Gates says, is the giant neutrino detector now being built in Antarctica. Sunk deep in the ice, it will detect the eerie blue light, known as Cherenkov radiation, that is given off by neutrinos. Neutrinos are subatomic particles so lacking in mass that they pass straight through the Earth unscathed. Studying their light helps cosmologists better understand these mysterious particles and their distant sources, which may include black holes. Thus, says Gates, "as part of the equation's legacy, we'll be using the ice of Antarctica to look at neutrinos and other objects coming from outer space. And without knowing the relationship between the energy, momentum, and mass, that would be inconceivable to do. In fact, it was the use of this equation that led to the realization that neutrinos must exist."
A nuclear world
Einstein's equation also perfectly describes what's happening when we produce nuclear energy. As Arlin Crotts, a professor of astronomy at Columbia University, puts it, "our entire understanding of nuclear processes would be sort of lost without it." Fission reactors in nuclear power plants generate electricity by unlocking the energy tied up in fissionable materials. Fusion also furnishes energy from mass just as the equation posits. When two hydrogen atoms fuse to form a helium atom, the mass of the resulting helium is less than the two hydrogens, with the missing mass manifesting itself as fusion energy. Nuclear weapons, too, operate on the principle defined by the equation. Indeed, the mushroom cloud of an atomic bomb explosion is E = mc2 made visible.
"One of its legacies is very sociological: it just captures the imagination of everyone."
The equation spawned a whole new branch of science-high-energy particle physics. Labs that work in this field thrive on E = mc2 conversions. In fact, proper design of particle accelerators, as well as analysis of the high-speed collisions within them, would be impossible without a thorough comprehension of the equation. Within accelerators, colliding particles are constantly vanishing, leaving only energy, and dollops of energy are constantly transmuting into newly fashioned particles. "Our species has repeatedly used an understanding of the equation to convert E into new forms of m that had never previously been seen," Gates says. "One of the outposts of science for the next century may well be whether the E includes super-E, and m includes super-m-new forms of energy and matter called 'super-partners.'"
A grasp of the equivalence of mass and energy also comes in handy when studying antimatter. When a particle meets its antiparticle, they annihilate eachother, leaving only a pulse of energy; by the same token, a high-energy photon can suddenly become a particle-antiparticle pair. Altogether, says Hogg, "E = mc2 has been very important in diagnosing and understanding properties of antimatter."
Einstein's formula also accounts for the heat in our planet's crust, which is kept warm by a steady barrage of E = mc2 conversions occurring within unstable radioactive elements such as uranium and thorium. "When they decay, some of the mass is lost and a little energy is created, and that keeps the crust warm," says John Rigden, a physicist at Washington University in St. Louis and author of Einstein 1905: The Standard of Greatness (Harvard, 2005). "So the temperature of the outer Earth, the crustal matter, is directly related to E = mc2."
A cosmological constant
A similar process happens far beyond Earth, inside stars. The warmth we feel from the sun, for example, is the result of the energy generated as hydrogen deep within our star continuously fuses to form helium. And stars don't stop there. When they exhaust their hydrogen, they begin to burn new fuels and create new elements, which are spewed out into the universe when the stars eventually explode, as burnt-out stars are wont to do. "The carbon, oxygen, nitrogen, and hydrogen that make up living organisms were baked in the innards of a star," Rigden says. "In terms of what goes on in stars, we owe our existence to E = mc2."
Einstein's equation even tells of what transpires at black holes, which can contain the mass of millions of stars. Here, E = mc2 is taking place on an astronomical-and highly efficient-scale. "In a nuclear process, you convert something like one part in 1,000 of your rest mass into energy, whereas if you fall into a black hole, you can convert something like 20, 30, 40 percent," Hogg says. "So from the point of view of the energetics of the universe, these black holes are important, because they are big converters of rest mass into energy."
On the largest scale of all-the beginning of the universe-E = mc2 is the only accepted explanation for what was going on. In the first seconds after the big bang, energy and matter went back and forth indiscriminately in exact accordance with the equation. "The description of how the big bang unfolds would be much, much different if you couldn't interconvert mass to energy," Crotts says. If it weren't for E = mc2, the universe would have ended up with a completely different collection of particles than we have now. "I'm not sure what we would have, but we definitely wouldn't be here," he says.
The equation's legacy extends into realms well beyond the scientific. David Hogg finds it very useful in teaching, for instance. "I use the equation a lot in class because it's the one equation that all students have definitely heard of," he says. "So one of its legacies is very sociological: it just captures the imagination of everyone." It also helps students remember the units of energy. "A joule is a kilogram meter squared per second squared, and the way you remember that is E = mc2," he says.
Arlin Crotts notes the world Einstein's equation opened up for us. "It just laid bare the fact that all this stuff lying around us is potentially a tremendous reservoir of energy, almost beyond the imagination, if only we could devise ways to get at it," he says. "And that's just an amazing fact." For John Rigden, the equation and Einstein's other leaps of imagination revealed how scientists can be just as visionary as artists, writers, and other "creative" types. "What he did," Rigden says, "has all the creativity in it of Absalom, Absalom or Monet's lily pads."
Jim Gates seconds that. Until Einstein's time, scientists typically would observe things, record them, then find a piece of mathematics that explained the results, he says. "Einstein exactly reverses that process. He starts off with a beautiful piece of mathematics that's based on some very deep insights into the way the universe works and then, from that, makes predictions about what ought to happen in the world. It's a stunning reversal to the usual ordering in which science is done. So that's one of the legacies, that we've learned the power of human creativity in the sciences-or, as Einstein himself might have said, 'to know the mind of God.'"
In the end, the equation's influence, on both scientific and sociological fronts, is indeed hard to separate from Einstein's influence as a whole-which, like E = mc2-derived heat from the sun, shows no sign of diminishing.
13 April 1901
Professor Wilhelm Ostwald
Esteemed Herr Professor!
Please forgive a father who is so bold as to turn to you, esteemed Herr Professor, in the interest of his son.
I shall start by telling you that my son Albert is 22 years old, that ... he feels profoundly unhappy with his present lack of position, and his idea that he has gone off the tracks with his career & is now out of touch gets more and more entrenched each day. In addition, he is oppressed by the thought that he is a burden on us, people of modest means....
I have taken the liberty of turning [to you] with the humble request to ... write him, if possible, a few words of encouragement, so that he might recover his joy in living and working.
If, in addition, you could secure him an Assistant's position for now or the next autumn, my gratitude would know no bounds....
I am also taking the liberty of mentioning that my son does not know anything about my unusual step.
I remain, highly esteemed Herr Professor,
-From the collected papers of Albert Einstein, Volume I. No answer from Professor Ostwald was ever received.
Before the miracle year
The world of 1905 seems distant to us now, but there were many similarities to life today. European newspapers complained that there were too many American tourists, while Americans were complaining that there were too many immigrants. The older generation everywhere complained that the young were disrespectful, while politicians in Europe and America worried about the disturbing turbulence in Russia. There were newfangled "aerobics" classes; there was a trend-setting vegetarian society, and calls for sexual freedom (which were rebuffed by traditionalists standing for family values), and much else.
The year 1905 was also when Einstein wrote a series of papers that changed our view of the universe forever. On the surface, he seemed to have been leading a pleasant, quiet life until then. He had often been interested in physics puzzles as a child, and was now a recent university graduate, easygoing enough to have many friends. He had married a bright fellow student, Mileva Maric, and was earning enough money from a civil service job in the patent office to spend his evenings and Sundays in pub visits, or long walks-above all, he had a great deal of time to think.
Although his father's letter hadn't succeeded, a friend of Einstein's from the university, Marcel Grossman, had pulled the right strings to get Einstein the patent job in 1902. Grossman's help was necessary not so much because Einstein's final university grades were unusually low-through cramming with the ever-useful Grossman's notes, Einstein had just managed to reach a 4.91 average out of a possible 6, which was almost average-but because one professor, furious at Einstein for telling jokes and cutting classes, had spitefully written unacceptable references. Teachers over the years had been irritated by his lack of obedience, most notably Einstein's high school Greek grammar teacher, Joseph Degenhart, the one who has achieved immortality in the history books through insisting that "nothing would ever become of you." Later, when told it would be best if he left the school, Degenhart had explained, "Your presence in the class destroys the respect of the students."
Outwardly Einstein appeared confident and would joke with his friends about the way everyone in authority seemed to enjoy putting him down. The year before, in 1904, he had applied for a promotion from patent clerk third class to patent clerk second class. His supervisor, Dr. Friedrich Haller, had rejected him, writing in an assessment that although Einstein had "displayed some quite good achievements," he would still have to wait "until he has become fully familiar with mechanical engineering."
In reality, though, the lack of success was becoming serious. Einstein and his wife had given away their first child, a daughter born before they were married, and were now trying to raise the second on a patent clerk's salary. Einstein was 26. He couldn't even afford the money for part-time help to let his wife go back to her studies. Was he really as wise as his adoring younger sister, Maja, had told him?
He managed to get a few physics articles published, but they weren't especially impressive. He was always aiming for grand linkages-his very first paper, published back in 1901, had tried to show that the forces controlling the way liquid rises up in a drinking straw were similar, fundamentally, to Newton's laws of gravitation. But he could not quite manage to get these great linkages to work, and he got almost no response from other physicists. He wrote to his sister, wondering if he'd ever make it.
"The idea is amusing and enticing, but whether the Lord is laughing at it ... that I cannot know."
Even the hours he had to keep at the patent office worked against him. By the time he got off for the day, the one science library in Bern was usually closed. How would he have a chance if he couldn't even stay up to date with the latest findings? When he did have a few free moments during the day, he would scribble on sheets he kept in one drawer of his desk-which he jokingly called his department of theoretical physics. But Haller kept a strict eye on him, and the drawer stayed closed most of the time. Einstein was slipping behind, measurably, compared to the friends he'd made at the university. He talked with his wife about quitting Bern and trying to find a job teaching high school. But even that wasn't any guarantee: he had tried it before, only four years earlier, but never managed to get a permanent post.
The turning point
And then, on what Einstein later remembered as a beautiful day in the spring of 1905, he met his best friend, Michele Besso ("I like him a great deal," Einstein wrote, "because of his sharp mind and his simplicity"), for one of their long strolls on the outskirts of the city. Often they just gossiped about life at the patent office, and music, but today Einstein was uneasy. In the past few months a great deal of what he'd been thinking about had started coming together, but there was still something Einstein felt he was very near to understanding but couldn't quite see. That night Einstein still couldn't quite grasp it, but the next day he suddenly woke up feeling "the greatest excitement."
It took just five or six weeks to write up a first draft of the article, filling 30-some pages. It was the start of his theory of relativity. He sent the article to Annalen der Physik to be published, but a few weeks later, he realized that he had left something out. A three-page supplement was soon delivered to the same physics journal. He admitted to another friend that he was a little unsure how accurate the supplement was: "The idea is amusing and enticing, but whether the Lord is laughing at it and has played a trick on me-that I cannot know."
But in the text itself he began confidently: "The results of an electrodynamic investigation recently published by me in this journal lead to a very interesting conclusion, which will be derived here." And then, four paragraphs from the end of this supplement, he wrote it out.
E = mc2 had arrived in the world.
In November of 1919, at the age of 40, Albert Einstein became an overnight celebrity, thanks to a solar eclipse. An experiment had confirmed that light rays from distant stars were deflected by the gravity of the sun in just the amount he had predicted in his theory of gravity, general relativity. General relativity was the first major new theory of gravity since Isaac Newton's more than 250 years earlier.
Einstein became a hero, and the myth-building began. Headlines appeared in newspapers all over the world. On November 8, 1919, for example, the London Times had an article headlined: "The Revolution In Science/Einstein Versus Newton." Two days later, The New York Times' headlines read: "Lights All Askew In The Heavens/Men Of Science More Or Less Agog Over Results Of Eclipse Observations/Einstein Theory Triumphs." The planet was exhausted from World War I, eager for some sign of humankind's nobility, and suddenly here was a modest scientific genius, seemingly interested only in pure intellectual pursuits.
The essence of gravity
What was general relativity? Einstein's earlier theory of time and space, special relativity, proposed that distance and time are not absolute. The ticking rate of a clock depends on the motion of the observer of that clock; likewise for the length of a "yardstick." Published in 1915, general relativity proposed that gravity, as well as motion, can affect the intervals of time and of space. The key idea of general relativity, called the equivalence principle, is that gravity pulling in one direction is completely equivalent to an acceleration in the opposite direction. A car accelerating forwards feels just like sideways gravity pushing you back against your seat. An elevator accelerating upwards feels just like gravity pushing you into the floor.
If gravity is equivalent to acceleration, and if motion affects measurements of time and space (as shown in special relativity), then it follows that gravity does so as well. In particular, the gravity of any mass, such as our sun, has the effect of warping the space and time around it. For example, the angles of a triangle no longer add up to 180 degrees, and clocks tick more slowly the closer they are to a gravitational mass like the sun.
Many of the predictions of general relativity, such as the bending of starlight by gravity and a tiny shift in the orbit of the planet Mercury, have been quantitatively confirmed by experiment. Two of the strangest predictions, impossible ever to completely confirm, are the existence of black holes and the effect of gravity on the universe as a whole (cosmology).
A black hole is a region of space whose attractive gravitational force is so intense that no matter, light, or communication of any kind can escape. A black hole would thus appear black from the outside. (However, gas around a black hole can be very bright.) It is believed that black holes form from the collapse of stars. As long as they are emitting heat and light into space, stars are able to support themselves against their own inward gravity with the outward pressure generated by heat from nuclear reactions in their deep interiors.
Every star, however, must eventually exhaust its nuclear fuel. When it does so, its unbalanced self-gravitational attraction causes it to collapse. According to theory, if a burned-out star has a mass larger than about three times the mass of our sun, no amount of additional pressure can stave off total gravitational collapse. The star collapses to form a black hole. For a nonrotating collapsed star, the size of the resulting black hole is proportional to the mass of the parent star; a black hole with a mass three times that of our sun would have a diameter of about 10 miles.
General relativity may be the biggest leap of the scientific imagination in history.
The possibility that stars could collapse to form black holes was first theoretically "discovered" in 1939 by J. Robert Oppenheimer and Hartland Snyder, who were manipulating the equations of Einstein's general relativity. The first black hole believed to be discovered in the physical world, as opposed to the mathematical world of pencil and paper, was Cygnus X-1, about 7,000 light-years from Earth. (A light-year, the distance light travels in a year, is about six trillion miles.) Cygnus X-1 was found in 1970. Since then, a dozen excellent black hole candidates have been identified. Many astronomers and astrophysicists believe that massive black holes, with sizes up to 10 million times that of our sun, inhabit the centers of energetic galaxies and quasars and are responsible for their enormous energy release. Ironically, Einstein himself did not believe in the existence of black holes, even though they were predicted by his theory.
The start of everything
Beginning in 1917, Einstein and others applied general relativity to the structure and evolution of the universe as a whole. The leading cosmological theory, called the big bang theory, was formulated in 1922 by the Russian mathematician and meteorologist Alexander Friedmann. Friedmann began with Einstein's equations of general relativity and found a solution to those equations in which the universe began in a state of extremely high density and temperature (the so-called big bang) and then expanded in time, thinning out and cooling as it did so. One of the most stunning successes of the big bang theory is the prediction that the universe is approximately 10 billion years old, a result obtained from the rate at which distant galaxies are flying away from each other. This prediction accords with the age of the universe as obtained from very local methods, such as the dating of radioactive rocks on Earth.
According to the big bang theory, the universe may keep expanding forever, if its inward gravity is not sufficiently strong to counterbalance the outward motion of galaxies, or it may reach a maximum point of expansion and then start collapsing, growing denser and denser, gradually disrupting galaxies, stars, planets, people, and eventually even individual atoms. Which of these two fates awaits our universe can be determined by measuring the density of matter versus the rate of expansion. Much of modern cosmology, including the construction of giant new telescopes such as the new Keck telescope in Hawaii, has been an attempt to measure these two numbers with better and better accuracy. With the present accuracy of measurement, the numbers suggest that our universe will keep expanding forever, growing colder and colder, thinner and thinner.
General relativity may be the biggest leap of the scientific imagination in history. Unlike many previous scientific breakthroughs, such as the principle of natural selection, or the discovery of the physical existence of atoms, general relativity had little foundation upon the theories or experiments of the time. No one except Einstein was thinking of gravity as equivalent to acceleration, as a geometrical phenomenon, as a bending of time and space. Although it is impossible to know, many physicists believe that without Einstein, it could have been another few decades or more before another physicist worked out the concepts and mathematics of general relativity.
There is a parlor game physics students play: Who was the greater genius? Galileo or Kepler? (Galileo.) Maxwell or Bohr? (Maxwell, but it's closer than you might think.) Hawking or Heisenberg? (A no-brainer, whatever the best-seller lists might say. It's Heisenberg.) But there are two figures who are simply off the charts. Isaac Newton is one. The other is Albert Einstein. If pressed, physicists give Newton pride of place, but it's a photo finish-and no one else is in the race.
Newton's claim is obvious. He created modern physics. His system described the behavior of the entire cosmos, and while others before him had invented grand schemes, Newton's was different. His theories were mathematical, making specific predictions to be confirmed by experiments in the real world. Little wonder that those after Newton called him lucky-"for there is only one universe to discover, and he discovered it."
But what of Einstein? Well, Einstein felt compelled to apologize to Newton. "Newton, forgive me," Einstein wrote in his Autobiographical Notes. "You found the only way which, in your age, was just about possible for a man of highest thought and creative power." Forgive him? For what? For replacing Newton's system with his own-and, like Newton, for putting his mark on virtually every branch of physics.
That's the difference. Young physicists who play the "who's smarter" game are really asking "How will I measure up?" Is there a shot to match-if not Maxwell, then perhaps Lorentz? But Einstein? Don't go there. Match this:
That's pretty good, but one idea, however spectacular, does not make a demigod. But now add the rest of what Einstein did in 1905:
In sum, an amazing outburst: Einstein's 1905 still evokes awe. Historians call it the annus mirabilis, the miracle year. Einstein ranges from the smallest scale to the largest (for special relativity is embodied in all motion throughout the universe), through fundamental problems about the nature of energy, matter, motion, time, and space-all the while putting in 40 hours a week at the patent office.
Who's smarter? No one since Newton comes close.
And that alone would have been enough to secure Einstein's reputation. But it is what comes next that is almost more remarkable. After 1905, Einstein achieves what no one since has equaled: a 20-year run at the cutting edge of physics. For all the miracles of his miracle year, his best work is still to come:
In sum, Einstein is famous for his distaste for modern quantum theory, largely because its probabilistic nature forbids a complete description of cause and effect. But still he recognizes many of the fundamental implications of the idea of the quantum long before the rest of the physics community does.
The miracle that eluded him
After the quantum mechanical revolution of 1925 through 1927, Einstein spends the bulk of his remaining scientific career searching for a deeper theory to subsume quantum mechanics and eliminate its probabilities and uncertainties. It is the end, as far as his contemporaries believe, of Einstein's active participation in science. He generates pages of equations, geometrical descriptions of fields extending through many dimensions that could unify all the known forces of nature. None of the theories works out. It is a waste of time-and yet:
Contemporary theoretical physics is dominated by what is known as "string theory." It is multidimensional. (Some versions include as many as 26 dimensions, with 15 or 16 curled up in a tiny ball.) It is geometrical: the interactions of one multidimensional shape with another produces the effects we call forces, just as the "force" of gravity in general relativity is what we feel as we move through the curves of four-dimensional space-time. And it unifies, no doubt about it: in the math, at least, all of nature from quantum mechanics to gravity emerges from the equations of string theory.
As it stands, string theory is unproved, and perhaps unprovable, as it involves interactions at energy levels far beyond any we can handle. But to those versed enough in the language of mathematics to follow it, it is beautiful. And in its beauty (and perhaps in its impenetrability), string theory is the heir to Einstein's primitive first attempts to produce a unified field theory.
Between 1905 and 1925, Einstein transformed humankind's understanding of nature on every scale, from the smallest to that of the cosmos as a whole. Now, a century after he began to make his mark, we are still exploring Einstein's universe. The problems he could not solve remain the ones that define the cutting edge, the most tantalizing and compelling.
You can't touch that. Who's smarter? No one since Newton comes close.
Imagine a police officer chasing after a speeding motorist. If he drives fast enough, the officer knows that he can catch the motorist. Anyone who has ever gotten a ticket for speeding knows that. But if we now replace the speeding motorist with a light beam, and an observer witnesses the whole thing, then the observer concludes that the officer is speeding just behind the light beam, traveling almost as fast as light. We are confident that the officer knows he is traveling neck and neck with the light beam.
But later, when we interview him, we hear a strange tale. He claims that instead of riding alongside the light beam as we just witnessed, it sped away from him, leaving him in the dust. He says that no matter how much he gunned his engines, the light beam sped away at precisely the same velocity. In fact, he swears that he could not even make a dent in catching up to the light beam. No matter how fast he traveled, the light beam traveled away from him at the speed of light, as if he were stationary instead of speeding in a police car.
But when you insist that you saw the police officer speeding neck and neck with the light beam, within a hairsbreadth of catching up to it, he says you are crazy; he never even got close. To Einstein, this was the central, nagging mystery: How was it possible for two people to see the same event in such totally different ways? If the speed of light was really a constant of nature, then how could a witness claim that the officer was neck and neck with the light beam, yet the officer swears that he never even got close?
Einstein had realized earlier that the Newtonian picture (where velocities can be added and subtracted) and the Maxwellian picture (where the speed of light was constant) were in total contradiction. Newtonian theory was a self-contained system, resting on a few assumptions. If only one of these assumptions were changed, it would unravel the entire theory in the same way that a loose thread can unravel a sweater. That thread would be Einstein's daydream of racing a light beam.
Special relativity is born
One day around May of 1905, Einstein went to visit his good friend Michele Besso, who also worked at the patent office, and laid out the dimensions of the problem that had puzzled him for a decade. Using Besso as his favorite sounding board for ideas, Einstein presented the issue: Newtonian mechanics and Maxwell's equations, the two pillars of physics, were incompatible. One or the other was wrong. Whichever theory proved to be correct, the final resolution would require a vast reorganization of all of physics. He went over and over the paradox of racing a light beam. Einstein would later recall, "The germ of the special relativity theory was already present in that paradox." They talked for hours, discussing every aspect of the problem, including Newton's concept of absolute space and time, which seemed to violate Maxwell's constancy of the speed of light. Eventually, totally exhausted, Einstein announced that he was defeated and would give up the entire quest. It was no use; he had failed.
Although Einstein was depressed, his thoughts were still churning in his mind when he returned home that night. In particular, he remembered riding in a streetcar in Bern and looking back at the famous clock tower that dominated the city. He then imagined what would happen if his streetcar raced away from the clock tower at the speed of light. He quickly realized that the clock would appear stopped, since light could not catch up to the streetcar, but his own clock in the streetcar would beat normally.
Then it suddenly hit him, the key to the entire problem. Einstein recalled, "A storm broke loose in my mind." The answer was simple and elegant: time can beat at different rates throughout the universe, depending on how fast you moved. Imagine clocks scattered at different points in space, each one announcing a different time, each one ticking at a different rate. One second on Earth was not the same length as one second on the moon or one second on Jupiter. In fact, the faster you moved, the more time slowed down. (Einstein once joked that in relativity theory, he placed a clock at every point in the universe, each one running at a different rate, but in real life he didn't have enough money to buy even one.) This meant that events that were simultaneous in one frame were not necessarily simultaneous in another frame, as Newton thought. He had finally tapped into "God's thoughts." He would recall excitedly, "The solution came to me suddenly with the thought that our concepts and laws of space and time can only claim validity insofar as they stand in a clear relation to our experiences.... By a revision of the concept of simultaneity into a more malleable form, I thus arrived at the theory of relativity."
"Thank you, I've completely solved the problem."
For example, remember that in the paradox of the speeding motorist, the police officer was traveling neck and neck with the speeding light beam, while the officer himself claimed that the light beam was speeding away from him at precisely the speed of light, no matter how much he gunned his engines. The only way to reconcile these two pictures is to have the brain of the officer slow down. Time slows down for the policeman. If we could have seen the officer's wristwatch from the roadside, we would have seen that it nearly stopped and that his facial expressions were frozen in time. Thus, from our point of view, we saw him speeding neck and neck with the light beam, but his clocks (and his brain) were nearly stopped. When we interviewed the officer later, we found that he perceived the light beam to be speeding away, only because his brain and clocks were running much slower.
The paper that changed everything
The day after this revelation, Einstein went back to Besso's home and, without even saying hello, he blurted out, "Thank you, I've completely solved the problem." He would proudly recall, "An analysis of the concept of time was my solution. Time cannot be absolutely defined, and there is an inseparable relation between time and signal velocity." For the next six weeks, he furiously worked out every mathematical detail of his brilliant insight, leading to a paper that is arguably one of the most important scientific papers of all time. According to his son, he then went straight to bed for two weeks after giving the paper to his wife Mileva to check for any mathematical errors. The final paper, "On the Electrodynamics of Moving Bodies," was scribbled on 31 handwritten pages, but it changed world history.
In the paper, he does not acknowledge any other physicist; he only gives thanks to Michele Besso. It was finally published in Annalen der Physik in September 1905, in volume 17. In fact, Einstein would publish three of his pathbreaking papers in that famous volume 17. His colleague Max Born has written, volume 17 is "one of the most remarkable volumes in the whole scientific literature. It contains three papers by Einstein, each dealing with a different subject and each today acknowledged to be a masterpiece." (Copies of that famous volume sold for $15,000 at an auction in 1994.)
With almost breathtaking sweep, Einstein began his paper by proclaiming that his theories worked not just for light, but were truths about the universe itself. Remarkably, he derived all his work from two simple postulates applying to inertial frames (i.e., objects that move with constant velocity with respect to each other):
These two deceptively simple principles mark the most profound insights into the nature of the universe since Newton's work. From them, one can derive an entirely new picture of space and time.
Length, like time, is relative
First, in one masterful stroke, Einstein elegantly proved that if the speed of light was indeed a constant of nature, then the most general solution was the Lorentz transformation*. He then showed that Maxwell's equations did indeed respect that principle. Last, he showed that velocities add in a peculiar way. Although Newton, observing the motion of sailing ships, concluded that velocities could add without limit, Einstein concluded that the speed of light was the ultimate velocity in the universe. Imagine, for a moment, that you are in a rocket speeding at 90 percent the speed of light away from Earth. Now fire a bullet inside the rocket that is also going at 90 percent the speed of light. According to Newtonian physics, the bullet should be going at 180 percent the speed of light, thus exceeding light velocity. But Einstein showed that because meter sticks are shortening and time is slowing down, the sum of these velocities is actually close to 99 percent the speed of light. In fact, Einstein could show that no matter how hard you tried, you could never boost yourself beyond the speed of light. Light velocity was the ultimate speed limit in the universe.
We never see these bizarre distortions in our experience because we never travel near the speed of light. For everyday velocities, Newton's laws are perfectly fine. This is the fundamental reason why it took over 200 years to discover the first correction to Newton's laws. But now imagine that the speed of light is only 20 miles per hour. If a car were to go down the street, it might look compressed in the direction of motion, being squeezed like an accordion down to perhaps one inch in length, for example, although its height would remain the same. Because the passengers in the car are compressed down to one inch, we might expect them to yell and scream as their bones are crushed. In fact, the passengers see nothing wrong, since everything inside the car, including the atoms in their bodies, is squeezed as well.
As the car slows down to a stop, it would slowly expand from one inch to about 10 feet, and the passengers would walk out as if nothing happened. Who is really compressed? You or the car? According to relativity, you cannot tell, since the concept of length has no absolute meaning.
The greatest afterthought in history
Einstein then pushed further and made the next fateful leap. He wrote a small paper, almost a footnote, late in 1905 that would change world history. If meter sticks and clocks became distorted the faster you moved, then everything you can measure with meter sticks and clocks must also change, including matter and energy. In fact, matter and energy could change into each other. For example, Einstein could show that the mass of an object increased the faster it moved. (Its mass would in fact become infinite if you hit the speed of light-which is impossible, which proves the unattainability of the speed of light.) This meant that the energy of motion was somehow being transformed into increasing the mass of the object. Thus, matter and energy are interchangeable. If you calculated precisely how much energy was being converted into mass, in a few simple lines you could show that E = mc2, the most celebrated equation of all time. Since the speed of light was a fantastically large number, and its square was even larger, this meant that even a tiny amount of matter could release a fabulous amount of energy. A few teaspoons of matter, for example, has the energy of several hydrogen bombs. In fact, a piece of matter the size of a house might be enough to crack the Earth in half.
"Imagine the audacity of such a step ... every speck of dust becoming a prodigious reservoir of untapped energy."
Einstein's formula was not simply an academic exercise, because he believed that it might explain the curious fact discovered by Marie Curie, that just an ounce of radium emitted 4,000 calories of heat per hour indefinitely, seemingly violating the first law of thermodynamics (which states that the total amount of energy is always constant or conserved). He concluded that there should be a slight decrease in its mass as radium radiated away energy (an amount too small to be measured using the equipment of 1905). "The idea is amusing and enticing; but whether the Almighty is laughing at it and is leading me up the garden path-that I cannot know," he wrote. He concluded that a direct verification of his conjecture "for the time being probably lies beyond the realm of possible experience."
Why hadn't this untapped energy been noticed before? He compared this to a fabulously rich man who kept his wealth secret by never spending a cent.
Banesh Hoffman, a former student, wrote, "Imagine the audacity of such a step.... Every clod of earth, every feather, every speck of dust becoming a prodigious reservoir of untapped energy. There was no way of verifying this at the time. Yet in presenting his equation in 1907 Einstein spoke of it as the most important consequence of his theory of relativity. His extraordinary ability to see far ahead is shown by the fact that his equation was not verified ... until some twenty-five years later."
Once again, the relativity principle forced a major revision in classical physics. Before, physicists believed in the conservation of energy, the first law of thermodynamics, which states that the total amount of energy can never be created or destroyed. Now physicists considered the total combined amount of matter and energy as being conserved.