views updated

# Physics: Special and General Relativity

## Introduction

Even if you know very little about science you've probably heard of the theories of relativity—the words alone almost certainly make you think of Albert Einstein (1879–1955). And because Einstein is such an iconic genius, most people think that relativity is a very difficult mathematical concept that only a brilliant physicist could understand.

Einstein developed his theories between 1905 and 1911, but simpler ideas of relativity date back almost 400 years, to the time of Galileo Galilei (1564–1642). Everyone has a simple grasp of relativity that is based on everyday experience: moving around in cars, trains, and planes.

The central question of any theory of relativity is simple: How does a person know if they are moving or standing still? And if they are moving, how do their observations of the world compare with those of a person who is not?

## Historical Background and Scientific Foundations

Moving or Standing Still?

Answering the question “Am I moving or standing still?” is not as simple as it might seem. When we look around us, there are plenty of things we think are stationary—trees, buildings, the sidewalk. When we drive down the street, it is obvious to us that our car is moving, while the street and the buildings are not. But remember: We are on the surface of a moving planet. Earth's rotation spins us at nearly 1,000 miles per hour (1,609 km/hr), yet we don't notice this motion at all.

When we look up in the sky, we see the sun and moon rise and set, and the stars spin in the heavens. For thousands of years people assumed that Earth sat still while everything in the universe circled around it. But in 1543 Polish astronomer Nicolaus Copernicus (1473–1543) realized that stellar and planetary motions could be explained more simply and accurately if Earth moved as well. Earth, he believed, spins on its axis once per day and orbits the sun once per year; these combined motions explain everything from the rising and setting of the sun to the changing of the seasons to the intricate paths of the planets across the sky.

For many years Copernicus's ideas were of interest to only a handful of astronomers, who recognized their power for understanding and predicting the motions of the planets. To most people, however, it all seemed too outlandish to be true. The real uproar over a sun-centered universe erupted more than half-century later, when Galileo Galilei (1564–1642) provided solid proof that Copernicus was, in fact, correct. Only then did the intellectual and religious authorities see these new ideas as a threat. In Galileo's time, Copernicus's book was banned, teaching the sun-centered model was forbidden, and Galileo himself was tried for heresy. While these ideas seem unremarkable to us today, at the time they were truly revolutionary. Not only did they turn the known universe on its head, but they challenged accepted religious and intellectual orthodoxy as well.

One reason many people didn't take Copernicus's new theory seriously was because they found it impossible to believe that Earth was moving without being able to sense it. Wouldn't they be thrown off their feet by such rapid motion? Wouldn't there be a 1,000-mile-perhour wind outside? If they jumped in the air, wouldn't they land hundreds of feet away as the planet moved out from underneath them?

Of course the answer to all of these questions is “no.” In 1543 people had no experience that would allow them to understand what it feels like to move at hundreds of miles an hour. But today we do—if you've ever been on an airplane you've done so. And as long as the plane is in level steady flight it's easy to forget that you are moving at all. You can stand up, walk around the cabin, pour yourself a drink, all with no more difficulty than when you are standing still. The situation changes dramatically when the plane turns or climbs or experiences turbulence.

Galileo was the first to recognize this. A strong supporter of Copernican ideas, he went to great lengths to prove that the sun-centered model of the solar system was correct. To do so he developed an entirely new understanding of motion, starting with this simple fact: Moving at a constant speed feels just like sitting still.

Once we accept that both stationary and moving observers have a similar experience of the world, we can address the question of how their observations compare. A theory of relativity is basically a set of rules that allows us to compare the observations of two people who are moving at different speeds relative to one another. For example, imagine a car driving past a park where some kids are playing baseball. Say the pitcher is facing south, and the car is driving north at 40 miles per hour (64 km/h). The coach, standing behind the catcher with a radar gun, clocks the pitcher's throw at 50 mph (80 km/h). The question that any theory of relativity attempts to answer is this: What speed would the driver of the moving car record for the pitch as they drove by?

The answer seems straightforward and obvious to most people. If the car was driving north at 40 mph and the ball is being thrown south at 50 mph, then relative to the driver, the ball is moving at 90 mph (145 km/h). If a wild pitch sent the ball flying into the car's windshield, the effect of the 50-mph pitch on the car would be the same as if it were sitting still and hit with a 90-mph Major League fastball.

This commonsense answer is the cornerstone of what physicists call classical or Galileian relativity. According to this theory, in order for two people who are moving relative to one another to compare their measurements of the speeds of various objects, all they have to do is add their own relative velocity to the speed measured by the other observer.

Relativity of Velocity

So what is the baseball's “real” velocity? Is it the speed measured relative to the players on the field? Or the speed measured relative to the car driving by? You may be tempted to answer that it is the baseball players who measure the actual speed of the ball, since they are the ones who are standing still. But this argument goes out the window when you realize that the baseball players are not standing still at all. They are standing on an Earth spinning at nearly 1,000 mph (1,609 km/h), and hurtling around the sun at more than 60,000 mph (96,561 km/h)! To an observer “at rest” on the moon or on Mars or at the center of the Milky Way, the ball could appear to be moving 500, or 5,000, or 500,000 mph. Which is the “true” velocity of the baseball? There is no way to tell. Or perhaps more accurately there simply is no true velocity. Every speed in the universe is relative to something else. This is the essence of any theory of “relativity.”

This version of relativity was first expressed formally by Galileo in the early 1600s; it became an integral part of Isaac Newton's (1642–1727) more complete description of motion a generation later. Even today the ideas of classical relativity seem to work just fine for baseballs and cars, even planes and rockets. But our commonsense notion of how to add velocities together begins to fail when we look at the fastest object in the universe—light.

The Motion of Light

For centuries, scientists and philosophers had wondered about the nature of light, including how fast it moves—which is clearly very fast. When we turn on a lamp, the room fills with light immediately. We don't see it move outward gradually to the far corners of the room; it just seems to come on instantaneously. But is it really instantaneous or just very, very fast?

## IN CONTEXT: GALILEO AND INERTIAL REFERENCE FRAMES

Galileo Galilei laid out his support for the new Copernican astronomical system in his work Dialogue Concerning the Two Chief World Systems, Ptolemaic and Copernican, published in 1632. To make his case, Galileo had to silence critics who objected to the idea of a moving Earth and insisted that surely they would be able to feel this motion. But Galileo knew that motion at a constant speed is undetectable. To prove to his detractors that Earth could be spinning rapidly and we would not feel it, Galileo compared our situation on the moving Earth to the following scenario:

Shut yourself up with some friend in the main cabin below decks on some large ship, and have with you there some flies, butterflies, and other small flying animals. Have a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it. With the ship standing still, observe carefully how the little animals fly with equal speed to all sides of the cabin. The fish swim indifferently in all directions; the drops fall into the vessel beneath; and, in throwing something to your friend, you need throw it no more strongly in one direction than another, the distances being equal; jumping with your feet together, you pass equal spaces in every direction. When you have observed all these things carefully (though there is no doubt that when the ship is standing still everything must happen in this way), have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still. In jumping, you will pass on the floor the same spaces as before, nor will you make larger jumps toward the stern than toward the prow even though the ship is moving quite rapidly, despite the fact that during the time that you are in the air the floor under you will be going in a direction opposite to your jump. In throwing something to your companion, you will need no more force to get it to him whether he is in the direction of the bow or the stern, with yourself situated opposite. The droplets will fall as before into the vessel beneath without dropping toward the stern, although while the drops are in the air the ship runs many spans. The fish in their water will swim toward the front of their bowl with no more effort than toward the back, and will go with equal ease to bait placed anywhere around the edges of the bowl. Finally the butterflies and flies will continue their flights indifferently toward every side, nor will it ever happen that they are concentrated toward the stern, as if tired out from keeping up with the course of the ship. The cause of all these correspondences of effects is the fact that the ship's motion is common to all the things contained in it.

A modern physicist would call Galileo's ship cabin an inertial frame of reference. According to both Galileo and Einstein, any observer in an inertial reference frame should see all of the laws of physics obeyed.

Galileo proposed an experiment to measure the speed of light by stationing two observers with lanterns atop two hills several miles apart. By flashing their lights at one another and awaiting a reply, the speed of light could be determined from the delay. But the speed of light is so fast that no delay was observed. Even a distance of a few miles was traversed in the blink of an eye. To measure the speed of light, much larger, interplanetary distances must be used. A beam of light travels from Earth to the moon in about 2 seconds and to the sun in about 8 minutes. Only by observing astronomical events separated by hundreds of millions of miles can we see the delays that Galileo tried in vain to measure.

These sorts of delays were first observed by Danish mathematician and astronomer Ole Rømer (1644–1710) in 1677. Rømer was observing the moons of Jupiter, discovered by Galileo only a generation before, and watching and timing them as they passed behind Jupiter itself. He found that if you measured the timing of an eclipse when Earth's orbit was near Jupiter, then used this information to predict an eclipse six months later, when Earth was far from Jupiter, your answer would be off—it would happen 15 or 16 minutes later than you expected. Why? Rømer realized that this happened because the light had to travel further. From the amount of the delay and the size of Earth's orbit, Rømer was able to calculate the speed of light—around 186,000 miles per second (300,000 kilometers per second).

Light and the Ether

By 1700 it was clear that light moved very fast, but the question remained—what was light itself? What was it “made of?” Isaac Newton suggested that light was a stream of tiny particles. But others believed it was a kind of wave, like water or sound. Experiments in 1803 by Thomas Young (1773–1829) and others supported this view.

But if light were a wave, there had to be some substance that was doing the “waving.” A wave is not an object, a wave is a vibration or disturbance in some other material. Ocean waves, for example, are a disturbance in water, and sound waves are a disturbance in air. If light waves traveled throughout the universe, from the sun to Earth and out to the distant stars, there had to be some substance in space whose vibrations carried them. This invisible and purely hypothetical substance was named the “luminiferous æther,” or ether.

If all of space really were filled with some sort of material, wouldn't there be some way to detect it? In 1887 Albert Michelson (1852–1931) and Edward Morley (1838–1923) devised an experiment to do so. Their experiment was not designed to detect the ether directly, but Earth's motion through it.

To understand the effect Michelson and Morley sought, imagine a fast ship moving across a rough ocean. As the ship crashes through the waves, an observer aboard the ship would see the waves passing by faster than if the ship were sitting still. Likewise, as Earth moves through space in its orbit around the sun, they presumed they would notice an effect on the speed of light—a sort of “ether wind”—caused by Earth's motion through the ether.

Michelson and Morley set up a very sensitive experiment consisting of an arrangement of mirrors that split a beam of light into two parts—one part traveling in the direction of Earth's motion through space, the other traveling perpendicular to it. By comparing the motion of these two beams of light, they hoped to detect the effect of the ether wind on one of the beams. The result? They found no effect. The speed of light was not affected at all by Earth's motion. This was a strange result indeed.

Light and Electromagnetism

While it took some time, the Michelson-Morley experiment eventually caused the “luminiferous ether” theory to fall out of favor. But if space was not filled with a light-carrying medium, then what was a light wave?

Luckily, a new idea was waiting to take over. It had been discovered more than a decade earlier by James Clerk Maxwell (1831–1879).

Maxwell wasn't working on the problem of light at all. He was studying the properties of electricity and magnetism and the relationships between them. Scientists had known for some time that electric currents could create magnetic fields. (You may have done this yourself in science class by wrapping wire around a nail or a bolt and connecting it to a battery to make an electromagnet.) Researchers had also discovered that moving magnets could be used to generate electricity. Maxwell expressed these connections between electricity and magnetism in four simple equations, summarizing

Maxwell then used his equations to study what would happen to an electrically charged particle moving back and forth in space. Since the particle has an electric charge, this would create an electric field in space around it. And since the particle is moving, the strength of its electric field would change from place to place over time. But Maxwell's equations told him that such a changing electric field would also create a magnetic field that would also change over time as the electron moved back and forth. Another equation told him that this changing magnetic field would create its own changing electric field in space.

Maxwell had stumbled on the remarkable possibility that an electric field might create a magnetic field that would create an electric field that would create a disturbance traveling through space—a disturbance that was made of electric and magnetic fields. The mathematical form of this disturbance was identical to the equation for a wave. When Maxwell calculated what speed his wave of electricity and magnetism would have as it moved through space, he made an even more remarkable discovery. Based on the numbers that were known to describe the strengths of electric and magnetic fields, this electromagnetic wave should move outwards in space at a speed of about 300,000 kilometers per second (186,000 miles per second): Exactly the speed of light!

The Science: Physics Faces a Dilemma

Maxwell's picture of light as an eletromagnetic wave was a huge success. It unified everything that was known about electricity, magnetism, and light at the time, and also predicted new phenomena such as radio waves and other electromagnetic radiation that wouldn't be discovered for decades to come. But one feature of Maxwell's discovery was unsettling. The equations predicted an exact value for the speed of light—a first in the history of physics. Never before had an equation in physics said—“the speed of some object is this particular number.” According to Galileo and the classical theory of relativity, an object could not have one exact speed—it depends on who is measuring it. If Maxwell and his equations tell us the speed of light is 300,000 km/sec, it's fair to ask—as measured by whom?

Let's explore this using what Einstein called a gedankenexperiment a “thought experiment.” Suppose a rocket was traveling through space at 1,000 km/s. (As you know, rockets can't travel anywhere near that fast. At the turn of the twentieth century, in fact, scientists could hardly have imagined a rocket at all! Einstein placed most of his own thought experiments aboard fast-moving trains.) Inside the rocket, the passenger points a flash-light from the rear of the ship to the front. The light travels at the speed of light according to the occupants of the ship. But what would someone outside of the ship see?

From an outsider's point of view, everything in the ship is moving at 1,000 km/s. When the flash-light is turned on, the light moves at the speed of light, 300,000 km/s. But since the flashlight is already moving, the light should appear to be moving 301,000 km/s to the observer. At least, this is what classical relativity tells us should happen. But if the outside observer tried to use Maxwell's equations to calculate the speed of the light, he or she would get an answer (300,000 km/s) that didn't match their observations (301,000 km/s). Something is wrong here.

So, as the twentieth century approached, physicists were faced with a problem. Everything they understood about motion told them that velocity is a relative concept, and that objects in the universe have no one true velocity. But Maxwell's equations seemed to disprove this. They predicted a single number for the speed of light that was based not on the motion of any particular observer, but on the properties of electric and magnetic fields. So who was right—Galileo or Maxwell? It was a difficult problem that puzzled some of the great scientists of the day. The solution to the dilemma would come from the virtually unknown, 26-year-old patent clerk named Albert Einstein.

Einstein's Solution: Special Relativity

Einstein's solution was simple, but the implications were revolutionary. He began with a simple idea—that all moving observers should agree on the laws of physics. He then accepted Maxwell's equations and the speed of light they predicted as laws of physics. Then he imagined a situation very much like the rocket ship example above. How would observers inside and outside the ship measure the speed of the light?

The observers inside the rocket would see the light travel from the back to the front of the ship. They could divide the length of the ship by the time it took the light to travel and use that to calculate the speed. But an outside observer would see the light travel a longer distance—from the back of the ship to the front, which has moved some distance forwards from where it started. If the light moved a greater distance in the same time, it must have a greater speed. But this violates Einstein's principle that all observers must agree on the laws of physics. How do we fix our thought experiment to get both observers to measure the same speed for the light?

Einstein realized that the only way that two observers moving at different speeds could record the same speed for the light beam was if they recorded different values for the time that the light takes to travel the length of the ship. Even though this seems counterintuitive—how can two people watching the same thing happen disagree on how long it takes?—Einstein accepted this surprising conclusion and used it as the basis for constructing a new theory of relativity.

Until this point, scientists had always considered measurements of time and distance to be absolute and universal—something that all observers could agree on, no matter where they were or how fast they were moving. Issac Newton made this explicit in his Principia Mathematica in 1687:

Absolute, true, and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration…. Absolute space, in its own nature, without regard to anything external, remains always similar and immovable.

This view agrees with our everyday understanding of time and space. But according to Einstein, space and time are not absolute. The only true absolutes in the universe are the laws of physics; the speed of light, according to Maxwell's equations, is one such law. Einstein built his whole theory of relativity around this idea—that all observers must agree on the laws of physics, including the speed of light, even if doing so means that they must disagree on such things as the flow of time and the measurement of space.

The implications of Einstein's idea are stunning. They suggest that when a person is moving very fast, he or she will experience time differently than an observer who is stationary. These effects are negligible when we travel at the relatively slow speeds of cars, trains, or planes, but if we were to travel faster and faster, approaching the speed of light, the effect would become more and more noticeable.

Imagine a spaceship that could travel very fast—say, 90% of the speed of light. If a traveler were to board this ship and take off into space very fast, he would notice nothing particularly strange from his point of view. Time would appear to flow normally, objects in the spaceship would appear just as they did before the trip began. But outside observers watching him zip past would notice some very strange things. First of all, were they to peek into the ship's windows as it streaked by, they would see that, although the ship itself is moving very quickly, everything inside seems to be moving in slow motion. Everything from the movements of the space traveler to the ticking of his watch would be slowed down to less than half its normal rate. Compared to the observers outside, inside the ship time has slowed down.

## IN CONTEXT: IT'S ALL RELATIVE

Einstein's special theory of relativity suggests that when a person moves very fast, time slows down for him, and measurements of distances in space are shortened along the direction in which he is traveling. But in any given situation, the question of who is moving complicates matters. If a rocket streaks past Earth at nearly the speed of light, people on Earth will see the rocket “squished” in the direction of motion, and observe that clocks aboard the rocket seem to be running slowly compared to our own. But remember that all velocities are relative, and that all observers have the right to consider themselves stationary (as long as they are in an inertial reference frame). This means that to an observer aboard the ship, the earthbound clocks seem to be running slowly, and Earth appears flattened like a pancake as it streaks by the ship's windows at nearly the speed of light!

Many people have misrepresented Einstein's contribution to physics by boiling it down to “everything is relative.” But this is a gross oversimplification of Einstein's theories. In fact, while it is true that many measurements in Einstein's theory are relative, the most important aspect of the theory revolves around what is not relative—the laws of physics and the speed of light, which are the same for everyone everywhere in the universe.

That's not all they would see. As the ship passed by the stationary observers, the ship and everything within it would have a sort of flattened appearance. This would not be apparent to the traveler inside the rocket, because the flattening would apply to everything around him. According to Einstein, the traveler's measurements of space itself are altered due to his movement through it.

The Implications and Impact of Relativity

These two effects, called time dilation and length contraction are still surprising to us, since no one has ever traveled even close to the speed of light. One can only imagine how strange these ideas must have seemed in 1905. Here was a patent clerk from outside of the academic establishment, with no credentials to speak of, publishing a paper that challenged everything known about the nature of space and time. The reaction at first was similar to the reaction to Copernicus 350 years earlier—silence. It seemed as if scientists simply didn't know what to make of Einstein's ideas. But over the next few years, they increasingly realized the power of Einstein's new theory of relativity. Within a decade he was recognized as one of the brightest minds in physics.

Einstein's predictions about space and time were far ahead of their time. Today they are confirmed daily by physicists working with particle accelerators and observing high-energy particles that bombard Earth from space. These unstable subatomic particles can live for only a microsecond when sitting still, but can exist for several seconds or minutes when traveling close to the speed of light, when time slows down and stretches out their brief lifespans (when observed by the stationary scientists in their labs).

In 1971 J.C. Hafele and Richard E. Keating tested this concept of time dilation in an experiment that used very precise atomic clocks accurate to a few billionths of a second. They placed several of these sensitive clocks aboard airplanes and compared their times to an identical clock that remained on the ground. They found that time aboard the moving planes slowed down by a few hundred nanoseconds during their flights—just the amount that Einstein's equations predicted.

This slowing down of time aboard a moving airplane is obviously negligible at the speed of a commercial aircraft, which moves at a crawl compared to the speed of light. The few nanoseconds you gain during a long airplane flight don't amount to much no matter how often you fly. Even a professional airline pilot who flies back and forth across the Atlantic every day wouldn't extend his lifespan by so much as a microsecond. But if you could go faster and faster you would begin to notice dramatic effects on your experiences of space and time.

Suppose you built the very fast rocket we discussed earlier—one that could travel 270,000 km/s or 90% of the speed of light (even though no rocket or satellite built so far can travel faster than 62.14 miles/s, or 100 km/s). Now imagine you wanted to travel to a distant star, say Vega, which lies about 20 light-years from Earth. The trip would take you just over 20 years—22.2to be exact. But that's only as measured by a stationary observer on Earth. Because of time dilation, time aboard your rocket would move more slowly, and from your point of view, the trip would take less than 10 years!

The Ultimate Speed Limit

What would happen if you traveled faster than the speed of light? Would time stop? Would it flow backwards? We don't have to worry about such questions, fortunately, because Einstein's relativity equations make such situations impossible. Only an object with no mass, such as light, can travel at the speed of light. Material objects can approach the speed of light very closely, but never exceed it. As an object gets closer and closer to the speed of light, c, it takes more and more energy to speed up. A rocket can travel 90% or 99% or even 99.99% of the speed of light, but gaining that last little bit of speed would take an infinite amount of energy! The effect is almost as if the rocket gets heavier and heavier (and harder and harder to push) the closer it gets to c. This new relationship between force, mass, and acceleration revealed yet another revolutionary implication of Einstein's theory—an unexpected connection between energy and mass.

Energy and Mass: E = mc2

What Einstein's theory did for our understanding of space and time, it also did for our understanding of matter and energy. For most of the 200 years before Einstein, chemists and physicists had gone to great lengths to prove some important facts about the changes that occur in nature. During the 1700s chemists painstakingly demonstrated that whenever a chemical change occurs in nature, matter is conserved—that is, not created or lost. The chemical elements or atoms that make up the substance are merely rearranged and recombined to make new compounds. If you were to carefully weigh the reactants that go into a chemical reaction, and then weigh the products of that reaction, you would get the same result.

During the 1800s physicists discovered much the same thing about energy. Whenever a process occurs in nature that transforms energy from one kind to another, the total amount of energy in the universe remains constant. For example, when you drive a car, the chemical energy in the gasoline is converted to kinetic energy—the energy of the motion of the car. When you put on the brakes, the friction in the brake pads converts the kinetic energy of the car into heat. If you were to add up the total amount of chemical energy that went into the car, it would be equal to the total amount of heat energy that comes out of the car. Energy, like matter, can never be created or destroyed.

These two laws of nature—the law of conservation of matter and the law of conservation of energy—were fundamental to our understanding of the world at the turn of the twentieth century. But just as Einstein showed that space and time are really two aspects of a single entity called space-time, he demonstrated that there is a fundamental connection between matter and energy.

## ALBERT EINSTEIN (1879–1955)

Albert Einstein was born in Ulm, Württemberg, Germany, on March 14, 1879. After dropping out of high school, at 17 he enrolled at the Swiss Federal Polytechnic School in Zurich. He graduated in 1901, but, unable to find a teaching post, was forced to accept a position as a technical assistant in the Swiss patent office. During his years there, Einstein continued to work on physics in his spare time. He married Mileva Maric, a fellow student of mathematics and physics, in 1903. Two years later he earned his doctoral degree, but not before he had already written a handful of papers that would change physics, and our understanding of the universe, forever.

Nineteen hundred five is often referred to as Einstein's “miracle year.” During this single year, he published not only his revolutionary work on relativity, but a paper on the photoelectric effect (an important milestone in the development of quantum mechanics) and papers on the size and motion of molecules. In fact, it was his work on the photoelectric effect, and not his papers on relativity, which was specifically cited when Einstein was awarded the Nobel Prize in physics 16 years later.

In 1912 Einstein returned to the Polytechnic School in Zurich as a full professor. By this time he and Mileva had two sons, Hans Albert and Eduard, and Einstein himself had made substantial progress in expanding his original work on relativity to include accelerated motion and gravity. This work was finally published in 1916 as Die grundlagen der allgemeinen Relativitätstheorie (Foundation of the general theory of relativity). By this time Einstein had moved to Germany, accepting positions at the Kaiser Wilhelm Physical Institute and University of Berlin.

As Einstein's theories were confirmed by experiment in 1919, he rose to worldwide fame, earning the Nobel Prize for physics in 1921. But he was also Jewish, and in Nazi Germany fame was not enough to protect him from the rising tide of anti-Semitism. He fled Germany for the United States in 1933, landing at Princeton's prestigious Institute for Advanced Study.

In 1939 Einstein wrote a now-famous letter to President Franklin D. Roosevelt that warned of German experiments that had split the uranium atom, unleashing the potential of devastatingly destructive power. Ironically, this research had been made possible by Einstein's own theories and his now-famous equation E = mc 2. Forgoing his normally pacifist principles, Einstein urged Roosevelt to work on an atomic bomb if only to ensure that the Germans did not acquire such a weapon first.

While Einstein's work made the atomic bomb possible, he never worked directly on its development. In fact, his political views made the government view him with suspicion; he was deemed a security risk and denied the clearance that would have allowed him to work on the Manhattan Project. Those working on the project were even forbidden to discuss their research with him. When World War II ended in 1945 with the bombings of Hiroshima and Nagasaki, Japan, and the nuclear tension of the Cold War began, Einstein became more politically active and outspoken than ever, devoting much of his later life to the cause of peace and the fight against the proliferation of nuclear weapons.

Einstein's most famous equation (perhaps the most famous in all of science), E = mc 2 suggested that matter could be destroyed and converted to energy. Likewise, energy could vanish and become bound up in matter. To Einstein, mass was simply another kind of energy.

How much energy is produced when mass is converted into energy via E = mc2? A lot. The speed of light, c, is a very big number, and squaring it gives us a bigger number still. To find out how much energy is contained in an object, we multiply its mass by the speed of light (the speed of light = 299,792,458 m/s, and so the squared value is approximately 8.99 × 1016 m2 / s2).

If the book you are holding in your hands right now were converted entirely into energy, it could supply the electrical power needs of a large city like New York or Los Angeles for several months.

The implications of this discovery were far-reaching. The enormous amounts of energy locked inside of matter made a vast resource of previously unimagined energy available. Scientists soon realized that converting matter into energy by nuclear fusion was the fuel that powered the sun and the distant stars. By 1939 they began to look for ways to harness this power through nuclear fission—the splitting of atomic nuclei, converting a tiny fraction of the mass of a uranium atom into energy. This is the process that underlies both nuclear weapons and atomic power plants.

General Relativity

The final task facing Einstein in his development of relativity was to find a complete treatment of all kinds of motion—not just inertial reference frames and objects moving at constant speeds, but reference frames that change speeds and direction and objects that move under the influence of external forces, such as gravity. In fact, Einstein recognized a symmetry between acceleration through space and gravity that led him to formulate a whole new theory about how gravity works.

Imagine a passenger inside a closed automobile with all of the widows painted black. As far as he can tell the car is sitting perfectly still. All of a sudden his head snaps back and he feels pushed back into the seat. What does he think just happened? Since most people know what it

feels like to be in a moving car, they would probably assume that the car had just accelerated forward abruptly. But Einstein recognized another possibility. If a very massive object like a large comet or asteroid passed behind the car, the passenger would feel its gravitational pull tugging it backward. With the windows blacked out, Einstein claimed that there was no way to tell the difference between the feeling of accelerating forward and the sensation of gravity pulling backward. Acceleration and gravity are, in some sense, equivalent.

The same effect occurs inside an elevator. When the elevator accelerates upwards, you briefly feel heavier. If you were to take a bathroom scale with you into an elevator and stand on it, you would notice that the scale reads a slightly heavier weight when the elevator begins moving up. If you didn't know the elevator was moving, you might imagine that for a split second that Earth's gravitational pull had increased slightly, temporarily increasing your weight.

Einstein considered this apparent equivalence between acceleration and gravity to be of great significance. Since he believed that observers in different reference frames should agree on all fundamental laws of physics, this thought experiment suggested to him that an observer accelerating through space and an observer sitting still in a gravitational field should be able to use the same equations to describe all their observations about the world. And since we already know from special relativity that moving through space affects measurements of space and time, Einstein argued that gravity must also affect space and time. In fact, he developed a whole new theory of gravitational attraction based on the idea that gravity was nothing more than a kind of curvature of space-time itself.

In the old picture of gravity developed by Isaac Newton, gravity was a force of attraction between all objects with mass. Newton provided no explanation for why two massive objects attracted one another, the force

of gravity was simply there. It was invisible, infinite in range, and more than a little mysterious. But Einstein's picture eliminated the need for an invisible force. In the general theory of relativity, a massive object causes space-time to bend or curve in its vicinity, and other objects appear to be attracted to it as they travel through this curved space. Imagine placing two heavy bowling balls on a trampoline. The bowling balls will bend the trampoline's surface, and if they are close enough together, they will roll toward each other. But there is no mysterious invisible “force” between the bowling balls, they are simply rolling along the curved surface of the trampoline.

The general theory of relativity predicted entirely new phenomena—from black holes to twisted space to ripples in the fabric of the cosmos. The first such prediction—that light should be bent by gravity when it passed a massive object—was tested and confirmed in 1919. But many of general relativity's predictions are still being examined and tested.

## Modern Cultural Connections

Einstein's ideas, while they can seem unbelievable and strange, have become an indispensable part of our understanding of how the universe works. Scientists also realize that they are incomplete. While Einstein's theories are very good at describing space, time, and gravity for very large-scale objects like stars and galaxies, they fail when applied to problems of curved space and matter on the scale of atoms and smaller particles. In the realm of quantum mechanics, the science of the tiniest particles of matter, the intrusion of relativity can wreak havoc—producing nonsensical results, wrong answers, and infinities.

Much like the conflict between the theories of Galileo and Maxwell a century ago, scientists face a similar dilemma as they try to reconcile relativity with theories of subatomic particles. New approaches with exotic-sounding names like “string theory” and “supergravity” are taking Einstein's ideas to places he would never have imagined—expanding space-time into a universe with 11 dimensions. But while scientific progress may revise and extend the ideas of relativity, the profound changes in our concepts of space, time, and matter wrought by Einstein's theories cannot be undone.

## Primary Source Connection

The following article was written by Peter N. Spotts, a science and technology writer for the Christian Science Monitor. Founded in 1908, the Christian Science Monitor is an international newspaper based in Boston, Massachusetts. The article describes how the American physicist Albert Einstein introduced, and then later disregarded, a mathematical cosmological constant that scientists now say provides a clue to understanding the structure and future of the universe.

EINSTEIN WAS RIGHT! (FOR THE WRONG REASON)

Michael Levi is finding a golden opportunity in Albert Einstein's “greatest blunder.”

In 1917, Einstein pulled a fudge factor out of thin air to coax his equations on general relativity into describing a universe astronomers actually saw.

Three years ago, two teams of astronomers startled the scientific world with evidence that this figment of Einstein's chalk board—which the legendary physicist later repudiated—has a measurable impact on the universe.

Now, what Einstein called a cosmological constant appears to be “the largest form of energy in the universe,” Dr. Levi, a physicist, says. And, he laments, “we know nothing about it.” That is about to change.

On June 30, the National Aeronautics and Space Administration is slated to launch a spacecraft that will map the afterglow of the big bang in unprecedented detail. Data from the craft are expected to carry further clues about the “dark energy” Einstein's fudge factor describes.

Meanwhile, at the Lawrence Berkeley National Laboratory in Berkeley, Calif., Levi and colleague Saul Perlmutter are designing a space-based telescope that will use light from exploding stars in distant galaxies to trace the history of this energy's influence on the cosmos.

These projects are two among several aimed at unraveling the mysteries of dark energy, which has earned that moniker less for its lack of luminosity than for the ignorance surrounding it, some researchers say.

Fundamentally bizarre phenomenon

Indeed, the very idea of dark energy in the cosmos “is so bizarre from a fundamental-physics point of view that in their heart of hearts, people are still extremely skeptical,” says Scott Dodelson, an astrophysicist and theoretician at the Fermi National Accelerator Laboratory in Batavia, Ill. “They say: ‘You've got to prove it to me again and again—and you've got to prove it in different ways—or I won't believe it.’”

For his part, Einstein invoked dark energy out of expedience.

As he watched his equations on general relativity unfold, they led to the conclusion that the fabric of space-time is not holding steady, but could either expand or contract, depending on the universe's shape and on how densely it is packed with matter. Above a certain threshold, a densely packed universe would collapse under the pull of its combined gravity. Below that threshold, gravity grip loosens and the universe expands.

At the time, however, astronomers saw no large-scale motion. So Einstein added the cosmological constant, which applied brakes to the universe his equations described. When Edwin Hubble published his evidence in 1925 that the universe was expanding, and distant objects were receding from us at faster rates than close ones, Einstein tossed the cosmological constant out the window.

“Einstein was pulling something out of a hat,” says Sean Carroll, an assistant professor of physics at the University of Chicago. “He thought of it as an extra term in his equations changing the response of spacetime to ordinary matter.” But, he adds, “We know now that the term he added is precisely equivalent in all ways” to a form of energy that has come to be known as vacuum energy.

Take a volume of space, he continues, strip it of every form of matter, and general relativity still allows the vacuum to contain energy. Its density would be constant: The amount of vacuum energy in a cubic inch of space in our solar system would match that of a cubic inch of space billions of light-years away. Depending on the value assigned to it, this energy could either retard or accelerate the expansion of the cosmos.

Many cosmologists hold that the universe got its kick-start with the sudden release of vast amounts of pent-up vacuum energy. During the universe's first billion trillion trillionth of a second, it burst from subatomic size to nearly its current volume. The result was the big bang, the primordial explosion that scientists say gave birth to the universe.

Yet only in 1998 were astronomers able to spot what looked to be the action of vacuum energy on the universe.

Two teams—one led by Dr. Perlmutter, the other by Brian Schmidt, with the Mt. Stromlo Siding Springs Observatories in Australia—reported that light from distant supernovae was dimmer than inflation theories said it should be. Currently, inflation holds that all the “stuff” in the universe is just dense enough to prevent collapse, but that expansion will slow without ever reaching a stop.

Yet light measurements taken from the supernovae, roughly 7 billion light-years away, indicated that the galaxies hosting the supernovae were farther away then they should have been if the universe was decelerating.

Last month, Lawrence Berkeley's Peter Nugent and Adam Riess of the Space Telescope Science Institute bolstered the 1998 results with data from a supernova more distant yet, which does fit with the expected rate of deceleration.

One explanation, researchers say, is that scientists have now bracketed the period in the universe's history when matter thinned sufficiently for gravity to give way to the universe's residual vacuum energy, which counteracts gravity and pushes clusters and superclusters of galaxies away from each other.

The most recent observation virtually eliminates objections that the 1998 data might merely be showing the effect of dust obscuring the supernovae, or other measurement errors, says Dr. Nugent, who also is a member of Perlmutter's team.

The Hubble Space Telescope result Dr. Riess and Nugent reported also “gives us a look at the epoch when gravity was dominant,” Nugent says.

This distance scale is likely to be one of the most fruitful for followup studies of vacuum energy—if that's what it is—LBL's Levi says, because farther out, when the universe was younger and smaller, matter's higher density would give gravity the advantage over the much weaker vacuum energy. Any closer than about 7 billion light-years, and the vacuum energy's effect would be swamped by “local” regions of space where matter is relatively dense.

This rough distance is the target region for SNAP, a space telescope Perlmutter and Levi have proposed to tease more information out of supernovae. Known as type-1A supernovae, these stellar explosions yield consistent levels and changes of brightness as they evolve.

But type-1A explosions are rare, so researchers say they must gather repeat images of thousands of galaxies in less than two weeks to ensure they can spot an explosion soon enough to track it through its entire cycle.

With initial funding from the Department of Energy, the team is designing a 1.8-meter orbiting telescope with a million-pixel camera to fill that role. If all goes well, Levi estimates that the telescope could be ready for launch in 2008.

Next month, NASA is scheduled to launch the Microwave Anisotropy Probe, a spacecraft that will map the microwave background radiation from the big bang with extreme accuracy.

Tiny changes in the density of the radiation are thought to be the seeds from which galaxies and larger cosmic structures evolved. Buried in those fingerprints of the early universe are signatures that will help cosmologists refine their estimates of the universe's density and the share of that density that different forms of “stuff” account for, says MAP lead scientist Charles Bennett, with the Goddard Space Flight Center in Greenbelt, Md.

Density Defines Future of the Cosmos

Each cosmological theory predicts a certain pattern in the radiation, he says, turning density measurements into “a powerful tool” for pointing toward the correct theory.

Recent microwave background measurements from balloon-borne instruments in Antarctica have provided stunning confirmations of the inflation theories, researchers say. They yield a “flat” universe in which 5 percent of its density consists of matter and forms of energy humans can detect, 25 percent dark matter, which is inferred from the movement of galaxies, clusters, and super clusters. The remaining 65 percent consists of vacuum energy or its equivalent.

For Dodelson, it's an amazing time for astrophysics. “The time scale for change in cosmology is typically 500 years,” he says.

“Five years ago, if someone told you there's a cosmological constant, you'd say he's crazy. Today it's just the Physics: Special and General Relativity reverse. It might take 100 years to figure out what this stuff is. But it's remarkable we're living at this time.”

Peter N. Spotts

spotts, peter n. “einstein was right! (for the wrong reason.)” christian science monitor (may 10, 2001).

bibliography

Books

Bodanis, David. E = mc2: A Biography of the World's Most Famous Equation. New York: Berkley Trade, 2001.

Fölsing, Albrecht Albert Einstein: A Biography. New York: Penguin Books, 1998.

Galilei, Galileo. Dialogue Concerning the Two Chief World Systems: Ptolemaic & Copernican. Translated by Stillman Drake. Berkeley: University of California Press, 1953.

Greene, Brian. The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory. New York: Vintage, 2000.

Newton, Isaac. The Principia: Mathematical Principles of Natural Philosophy. Translated by I. Bernard Cohen and Anne Whitman. Berkeley: University of California Press, 1999.

Wolfson, Richard. Simply Einstein: Relativity Demystified. New York: Norton & Company, 2003.

Periodicals

Spotts, Peter N. “Einstein was Right! (For the Wrong Reason.)” Christian Science Monitor (May 10, 2001).

Web Sites

American Institute of Physics. “World Year of Physics 2005: Einstein in the 21st Century.” http://www.physics2005.org/ (accessed March 24, 2007).

Hebrew University of Jerusalem, and California Institute of Technology. “The Einstein Archives Online.” http://www.alberteinstein.info/ (accessed March 24, 2007).

NOVA. “Einstein's Big Idea.” http://www.pbs.org/wgbh/nova/einstein/ (accessed March 24, 2007).

David L. Morgan