Chapter 9
In This Chapter
Measuring the speed of light through the ether
Studying an inconsistency in electromagnetism
Extending Galileo’s principle of relativity
Realizing that the speed of light is fixed
E instein’s brand of relativity rests on two ideas:
The laws of physics are the same in all nonaccelerated frames of reference.
The speed of light is always constant.
These ideas began growing in Einstein when, as a 16 year old, he tried to imagine what he would see were he to ride alongside a beam of light, moving at its same speed. Would he be able to see the edge of the beam? Would the light beam stop at some point (looking like a light saber from Star Wars)?
In this chapter, I show you the developments that helped Einstein continue to think about this problem for the next ten years. I explain the “failed” experiment by Albert Michelson and Edward Morley that attempted to measure the speed of the Earth in the ether,the stuff that supposedly filled space. I show how Einstein used Galilean relativity to help solve the problems with mechanics and electromagnetism. And, finally, I show you how his answer to these problems came in the form of his special theory of relativity.
Accounting for the Ether
During his junior year in college, Einstein wanted to set up an experiment to detect the motion of the Earth through the ether, the stuff that supposedly filled the entire universe and allowed light to travel. By the time he was a senior, he had designed the experiment. But (as I explain in Chapter 2) Professor Heinrich Weber, the physics department chair at the Zurich Polytechnic, wouldn’t let him set up the experiment in the school’s lab.
At the time, neither Weber nor Einstein knew that Michelson and Morley had performed a landmark experiment in 1886 to try to accomplish the same goal. Michelson and Morley had come up with a clever way to measure the motion of the Earth through the ether by measuring the speed of light at different times during the Earth’s orbit around the sun.
Michelson had invented the instrument to perform this experiment when he worked in Hermann von Helmholtz’s laboratory in Germany. The method that he had in mind was actually proposed by James Clerk Maxwell in 1875. It was simple. Because the ether fills space, the motion of the Earth in its orbit around the sun must create a wind (as shown in Figure 9-1). It’s not too different from when you stick your hand out the window when you’re riding in a car down the highway.
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Figure 9-1: The Earth moving through the ether as it orbits around the sun. |
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To see how you’d conduct such an experiment, think about how you’d measure your speed when swimming upstream and downstream in a river. If you know that you swim at 2 meters per second (m/s), about 120 yards a minute, in calm waters and are now swimming downstream in a river that’s running at 1 m/s, you really are advancing at 3 m/s relative to shore. When you turn around, you’ll be swimming upstream, advancing at only 1 m/s relative to the shore.
Michelson and Morley believed you could do essentially the same thing to measure the speed of light in the ether:
If you measured the speed of light in the direction of motion of the Earth around the sun, you’d be going against the ether wind and get a speed equal to the speed of light in the ether minus the speed of the ether wind.
If you measured the speed of light in the opposite direction, you’d get a value equal to the speed of light relative to the ether plus the speed of the ether wind.
Michelson did his experiment in Germany in 1881. He knew that his interferometer — as his instrument is called — was sensitive enough to measure the difference between the speed of light in the ether (300,000 kilometers per second [kps]) and the speed of light relative to the Earth moving upstream in the ether wind. The speed of the ether wind was the speed of the Earth in its orbit around the sun, which he knew to be 30 kps. He expected to measure the speed of light at 299,970 kps. He got 300,000 kps, as if there were no ether wind.
Some time later, Michelson accepted an offer to be a professor at the Case School of Applied Science in Cleveland, Ohio (now Case Western Reserve University). There, he met Edward Morley, a chemistry professor. The two redesigned Michelson’s experiment with increased accuracy.
Michelson and Morley measured the speed of light in the direction of the ether wind (opposite to the direction of motion of the Earth in its orbit) and across the ether wind simultaneously. Using a two-way mirror, they split a light beam so that it could travel along those two directions (see Figure 9-2). The two beams met and fell on a screen where they were superimposed. Because the two beams came from a single beam, they were in lockstep, or coherent. (I discuss the importance of this fact in Chapter 7, where I describe Thomas Young’s experiment.) Therefore, when they met, they formed an interference pattern that the scientists used to calculate the speed of light with extreme precision (see Figure 9-3).
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Figure 9-2: The setup of the Michelson–Morley experiment. |
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Figure 9-3: An interference pattern obtained with a modern Michelson and Morley interferometer. |
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Courtesy E. Arens, NASA
The two scientists believed that their experiment failed, because they didn’t see any difference in the measurements in the two directions. They believed that the interference pattern should’ve shifted.
The negative results of the Michelson–Morley experiment puzzled scientists all over the world. According to their experiment, the speed of light didn’t change regardless of how fast you moved.
Einstein was 7 years old when Michelson and Morley first did their experiment. He learned about it only after he graduated from college. His special theory of relativity would provide the final solution to the puzzle. But he didn’t develop it with their experiment in mind. He was more concerned with electromagnetism and with Galileo’s principle of relativity.
Struggling with an Inconsistency
Einstein developed his special theory of relativity during a few weeks in 1905, his miracle year, when he was 26 years old. The word “special” wasn’t originally part of the theory’s name; Einstein added it later to distinguish this early theory from an important extension that he developed (which he called the general theory of relativity). The relativity paper was the fourth of five incredible papers he published in 1905. With these papers, he changed physics at its roots. Check out Chapter 3 for the details about what he accomplished during this extraordinary time period.
What led Einstein to develop the special theory of relativity? As I explain in Chapters 3 and 6, Einstein was fascinated by electromagnetism and studied it on his own throughout college. He continued his studies after graduation. In doing so, he discovered that Galileo’s principle of relativity (which I explain in Chapter 8) worked for mechanics but not for electromagnetism. He set out to figure out why.
Discovering that you’re moving
Isaac Newton had adopted Galileo’s principle of relativity when he formulated his mechanics (see Chapter 4). The principle of relativity says that the laws of mechanics don’t change just because you’re moving. According to Newton and Galileo, if you are inside the cabin of a ship moving at a constant speed on smooth waters, for example, you can’t tell if you are moving or docked at port. Things behave the same in either case.
In 1905, Einstein found out that electromagnetism, as presented by Maxwell, gives you a way to discover if you are in uniform motion or at rest, without stepping out of your cabin or looking out the window. He started his special relativity paper by pointing out this inconsistency.
Focusing on electric fields
If you take a magnet and move it toward or away from a stationary wire, the moving magnet produces an electric field in the wire that generates a current (see Figure 9-4). That’s Faraday’s law — and one of Maxwell’s four equations, as I explain in Chapter 6. With his experiments (which I also explain in Chapter 6), Michael Faraday showed that to produce an electric field in the wire, the magnetic field has to change. In this case, the field from the moving magnet changes at the location of the wire. It becomes stronger and stronger if the magnet is approaching, or weaker and weaker if the magnet is moving away.
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Figure 9-4: Move a magnet toward a wire (or away from it), and you can detect a current in the wire. |
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Now, what happens if you keep the magnet at rest and move the wire? According to Maxwell, because the magnetic field in the area around the magnet isn’t changing, there is no electric field that can create a current in the wire — see Figure 9-5. (The current still appears in the wire, but according to Maxwell, that occurs for an entirely different reason.)
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Figure 9-5: There is no electric field in the wire when you move it toward a magnet. |
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In one case, when the magnet moves, there is an electric field. In the other case, when the magnet is at rest, there is no electric field. So, according to Maxwell’s electromagnetism, you have a way to tell if you’re moving or not. Just bring a magnet along. And an electric field sensor.
The law in Betelgeuse
What difference does it make if the laws of physics are the same everywhere? Why all the fuss about whether all motion is relative or whether absolute motion exists?
The big deal is that if things don’t work the same everywhere, the universe is unpredictable. You couldn’t discover anything, because the laws here wouldn’t apply somewhere like Betelgeuse, the red supergiant star in the constellation of Orion. If the laws of physics change when you change locations, for all we know the apples on Betelgeuse might fall up.
If, on the other hand, you agree with Einstein that the laws of physics are the same everywhere, you can discover something on Earth (like the way objects heat up) and then look at the sun and use your discovery to study it. Eventually, a satellite is sent there, and you find out that the sun works the way you predicted. You can then start to make predictions about solar flares and other phenomena that disturb communications and climate here on Earth.
Being at rest in the universe
If you can distinguish motion, if you can tell when you are at rest, then motion is not relative. You could take your motion-detector device into space and slow down until your device tells you that you are at rest. Or you could use it on the ground and start moving in the direction opposite to the Earth’s rotation and revolution around the sun, trying to balance all the possible motions of the Earth and the solar system until your meter indicator showed zero. Then you would be at rest in the universe.
From this vantage point, you could see everything else moving around you with their true motions, their absolute motions, as scientists call them.
Siding with Galileo
Einstein didn’t like the implications of this aspect of electromagnetism. As formulated by Maxwell, electromagnetism applied only to objects that didn’t move relative to the ether. That was actually the reason why no electric field appeared in the moving wire; the wire wasn’t at rest in the ether.
Einstein didn’t believe that absolute motion existed. He thought that Galileo was right in believing that all motion was relative, that the laws of mechanics were the same everywhere. But he wanted to go beyond mechanics. Einstein believed that the laws of physics were the same everywhere in the universe.
Laying the Cornerstones of Relativity
In his 1905 paper, Einstein made Galileo’s principle of relativity universal. Galileo and Newton had applied it to mechanics (the only physics they ever knew), and Einstein extended it to the rest of physics.
Dispelling absolute motion
Einstein made his extended principle one of the cornerstones of his new theory. He called it a postulate, and it reads as follows:
The principle of relativity: The laws of physics are the same in all nonaccelerated frames of reference.
His extended principle of relativity means that
The laws of physics are the same everywhere; everything works the same regardless of how fast you’re moving.
You can’t distinguish rest from motion; this means that all reference frames are the same, and there is no absolute motion.
Without a reference point at rest, all uniform motion is relative.
Armed with his postulate, Einstein was able to reformulate electromagnetism. In the second part of his 1905 paper, he showed that all electric and magnetic effects remain unchanged in all reference frames in uniform motion. In his paper, Einstein fixed electromagnetism so that it would depend on relative motion.
What about the moving wire and the stationary magnet? According to Einstein, there is only relative motion between the magnet and the wire. If you stay with the wire, the magnet moves toward you, and if you stay with the magnet, the wire moves toward you. The situation is identical, and everything you measure should be identical. If you measure an electric field in one case, you should also measure it in the other case.
I mention in the “Focusing on electric fields” section that Maxwell’s electromagnetism indicated that an effect other than an electric field causes a current when you move a wire toward a magnet that’s at rest. But Einstein showed that Maxwell was wrong; an electric field creates the current in that situation as well.
A modern physicist will not even bother to decide what’s moving. She will simply consider the magnet and the wire to be in relative motion. For today’s physicists, there is no confusion. But that’s because Einstein proved that there is no absolute motion.
Thanks to Einstein’s correction, electromagnetism and mechanics are on equal footing. The principle of relativity applies to both. The motion-detection device based on the absence of an electric field in one case doesn’t work. There is no difference in what you measure in either case. You really can’t distinguish rest from motion.
But Einstein didn’t just solve the inconsistency with electromagnetism and mechanics. He extended the principle of relativity to all of physics.
Struggling with the speed of light
According to Maxwell’s equations, light moves at a fixed speed relative to the ether. But Einstein didn’t have a need for the ether. With his principle of relativity, he did away with an absolute standard of rest. He believed that light moves as independent electric and magnetic fields vibrating through empty space.
Without an ether, with respect to what is light moving? Einstein’s answer was unexpected: Light travels at the same speed with respect to everything.
That simple answer contained the key to relativity. But Einstein didn’t just arrive at this conclusion one day. He struggled with it.
Why should light be different?
Einstein was saying that light travels at the same speed — 300,000 kps, or c (the letter Einstein used for the speed of light), regardless of how you move. The problem was, this idea is crazy.
Think of it this way: If you ran at 10 kilometers per hour (kph) after a bus that’s moving at 30 kph, you’d clock the bus moving at 20 kph. And if you sped up, you could match the bus’s speed and hop on. So, if you run up to a beam of light at one-third of c — at 100,000 kps — and measure its speed from your moving vehicle, shouldn’t you get 200,000 kps? Why can’t you use the same type of calculation for the speed of light that you use for the speed of the bus?
The Olympic Academy
As I explain in Chapter 3, Einstein struggled to find a job after he graduated from the Zurich Polytechnic. He finally secured a job as a patent examiner in the Bern patent office, but he found out that the position wasn’t going to be available for several months. He had a temporary job as a math tutor at an institute but was extremely unhappy about the institute’s militaristic director and his meager salary. To make ends meet, he placed an ad in the paper offering tutoring in physics and math.
Two people called in, Maurice Solovine and Conrad Habicht. Solovine was a philosophy and physics major at the University of Bern. Habicht was an old friend of Einstein’s who had studied physics and math and was now getting his PhD in math at the University of Bern.
Einstein didn’t lecture to the two men. Instead, the three of them held discussions; Solovine and Habicht would ask questions that Einstein would answer and explain. They also discussed physics and philosophy books. The three became good friends, and they often held discussions while hiking to a nearby village, climbing a mountain, or going on a trip to a lake. They decided to call their group the “Olympic Academy,” partly as a joke, but also because they felt that during their discussions, they learned more that they ever did in any formal class.
The discussions with his two friends helped Einstein figure out things in his own mind. Solovine and Habicht (as well as Einstein’s other friends) were sounding boards for the ideas that he was developing.
The meetings of the Olympic Academy continued even after Einstein married Mileva Maric (see Chapter 2). Mileva joined in but, according to Solovine, was not a very active participant and never joined them when the discussions took place outdoors.
The Olympic Academy lasted for a few years until Solovine and Habicht left to accept job offers. The men continued their friendship throughout their lives.
Einstein had extended the principle of relativity to include all the laws of physics. But by doing this he was creating a problem. He’d opened a new hole by trying to plug another.
Plugging the new hole
At the time Einstein was formulating many of his famous theories, he worked at the Bern patent office with his old friend Michelangelo (Michele) Besso. Besso was an engineer with a good grasp of physics. Einstein talked to Besso about his ideas regarding the principle of relativity. On their daily walks to and from work, they discussed Einstein’s struggle with the conflict between the speed of light and the speeds of ordinary objects.
The nagging conflict kept bothering Einstein. One day, he went to visit Besso to see if he could help him think the problem through. They talked late into the night, but Einstein got no closer to solving the problem. However, when he woke up the next morning, the answer came to him. He greeted Besso on their way to work by saying, “I’ve completely solved the problem.”
“My solution was really for the very concept of time,” Einstein said some time later. What Einstein realized is that time is relative. And space is relative. Time and space aren’t fixed, like Newton believed they were. For Einstein, time and space change when you move, but they adjust themselves so that the speed of light stays the same, regardless of how you move.
After Einstein made this startling discovery, he was ready to finish his theory. “Five weeks after my recognition of this, the present theory of special relativity was completed,” he later said. Einstein made his discovery that light always travels at the same speed into the second cornerstone of his theory, his second postulate. This postulate says:
The principle of light: The speed of light is a universal constant. All observers in uniform (nonaccelerated) motion measure the same value c for the speed of light.
The two postulates were the cornerstones upon which he built his theory.
From here on, space stopped being the stage where things happen, and time no longer flowed at the same rate for everyone. Space and time became relative, but the speed of light was absolute. (I expand on this strange idea in the next chapter.)
You See, Light Always Travels at c
Einstein developed his special theory of relativity from beginning to end in five weeks. He submitted it for publication in June of 1905, and it was received at the offices of the prestigious journal Annalen der Physik on June 30th.
Finally, Einstein had his answer to the question about what he would see if he rode alongside a beam of light. The answer was that he couldn’t ever catch up to it. Light would always be traveling at c, no matter how fast he moved. There is a front of the wave, an edge to the beam, but no one can ever move along with it. Light moves at c with respect to anything.
This remarkable and completely unexpected idea was the key to relativity, the stroke of genius. This idea was what differentiated Einstein’s relativity from Poincaré’s (see Chapter 8). Einstein took the crucial step. That step didn’t even cross Poincaré’s mind, or anybody else’s. Einstein’s step changed our ideas of space and time.
With his special theory of relativity, Einstein also solved the problem of the Michelson–Morley experiment. The problem had bothered physicists for almost 20 years. As I explain in Chapter 8, Hendrik Antoon Lorentz and George FitzGerald had proposed the strange idea of length contraction so that objects would shrink as they moved, with the shrinking matching exactly what was needed to make the Michelson–Morley experiment work. Scientists were not happy with this too-convenient idea. Lorentz had also added the idea of time stretching and contracting as you moved. But to him and to everyone else, his equations didn’t apply to the real world. They were tools to explain the Michelson–Morley experiment.
Einstein’s solution was even stranger. As with Lorentz and FitzGerald’s solution, time and lengths change as you move. But for Einstein, these changes are real, not just mathematical tools. Einstein’s equations represent the real world.
But, if time and space change when you move, as Einstein said, why hadn’t anyone noticed? Why don’t we notice it now? Because the changes are extremely small at ordinary speeds. They become noticeable only if you move at speeds close to the speed of light.
In his 1905 paper, Einstein gave us equations to correctly calculate the relative speeds of objects in motion, and they’re slightly different than the speeds you would normally measure. For example, say you’re driving down the highway at 90 kph in a 90 kph zone and a car passes you at 97 kph. Wouldn’t you clock the other car going 7 kph faster than you? Not exactly. If you had a very precise instrument, you’d clock it going 7.0000000000001 kph faster than you. Obviously, the difference is tiny at such a speed.
When you apply Einstein’s equations to spaceships moving at speeds close to the speed of light, the correction becomes important. Say you’re on a spaceship traveling at 0.97c relative to the Earth in a mission to the center of the galaxy. You pass the slower Expedition One ship that left earlier and is traveling at 0.90c relative to Earth. Will the Expedition One crew see you pulling past it at 0.07c? No. The crew will see you speeding away at 0.5c (see Figure 9-6).
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Figure 9-6: The spaceships are relativistic. |
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It you try to measure the speed of a ray of light moving at c relative to Earth from your spaceship that’s moving at 0.97c relative to Earth, you won’t measure it at 0.07c relative to you, but at c relative to you. Light travels at c as measured from anywhere.
Making Physics Beautiful
Einstein came up with the equations that I used to calculate the speeds in this thought experiment. He worked them out from his theory. What’s remarkable is that they came out to be the same as the Lorentz transformations that had been introduced to make the Michelson–Morley experiment work.
Einstein wasn’t trying to make the Michelson–Morley experiment work. Extending the principle of relativity beyond mechanics, he was looking to make physics simpler, more beautiful.
Although the equations that he obtained were the same as the Lorentz– FitzGerald transformations, Einstein’s interpretation was different. I discuss the implications of the special theory in Chapter 10.
