10
A Myth about the Speed of Light
EINSTEIN kept some secrets, and he often shunned attention as if the details of his life were quite inconsequential. He wrote: “the essential in the being of a man of my type lies precisely in what he thinks and how he thinks, not in what he does or suffers.”1 Although he was a relatively self-isolating person, people flocked to him, reporters and photographers chased him around for decades, converting him into an icon. We see him in posters, magazines, toys, postage stamps, cereal boxes. As he complained in 1949: “my accomplishments have been overvalued beyond all bounds for incomprehensible reasons. Humanity needs a few romantic idols as spots of light in the drab field of earthly existence. I have been turned into such a spot of light. The particular choice of person is inexplicable and unimportant.”2
Still, there were some fair reasons why he first won attention, one of which is that he managed to convince many people of some seemingly unbelievable ideas. Suppose that you sit on a spaceship traveling in a straight line, say, at 160,000 miles per second. According to Einstein's physics, the length of planet Earth as judged by you will be about half of its original length. And, allegedly, this is not an optical illusion. Does the entire planet really contract when you move?
Suppose also that as you're zipping away from Earth at 160,000 miles per second (mps), you aim a flashlight in the forward direction and turn it on. Light shoots out at about 186,282 mps away from you. How fast does that same light ray move away from Earth? We might expect that since it moves at 186,282 mps away from the ship and the ship moves at 160,000 mps away from Earth, the light moves at about 346,282 miles per second away from Earth. But according to Einstein's physics, that ray of light moves at 186,282 mps away from Earth. We might think that the light ray must move away relative to Earth at a greater speed, and we'd expect that just flying away on a rocket cannot possibly cause the contraction of the entire planet. Otherwise, the world is bizarre. Common sense seems to fly out the window as physics becomes unbelievable and esoteric.
Such notions crystallized in Einstein's theory of relativity and they became accepted by many physicists. His theory was all based on the idea of the relativity of time, the relativity of simultaneity. Yet for centuries, philosophers had theorized various ideas about time, without generating any intense public interest. For example, according to one source, the prominent religious leader and philosopher “Pythagoras believed that time is the encompassing sphere.”3 In the late 1700s, Immanuel Kant denied that time had any absolute or objective reality.4 In 1902 the prominent mathematician Henri Poincaré echoed a growing conviction that “There is no absolute time.”5 While such various arguments did not generate widespread attention, somehow, the imaginative conjectures of a lowly patent clerk in 1905 eventually generated immense public acclaim.
Einstein reached his theory by a long and complicated trajectory, but instead of tracing a broad overview, let's take a close view of just one of its seminal aspects: the relations between speed, time, and length. I'll discuss the kind of explanation that we don't find in a physics class. Then in the next two chapters, I will discuss some controversial and historical speculations—myths—about the origins of Einstein's theory. How did Einstein come to think about relativity?
For ten years, from 1895 until 1905, Einstein was trying to understand the motion of light.6 Physicists conceived of light as an electromagnetic wave in an invisible medium, like air, but much more subtle and intangible, which they called “the ether.” When Einstein was just sixteen years old, he was puzzled because he wondered what a light wave would look like if one could catch up to it.7 It's analogous to waves in the ocean; you constantly see them moving. Why don't we ever see a stationary mountain of water on the ocean? One would be perplexed to see such a thing, a standing bump of water. Yet if you fly alongside a wave at its same speed, and look at it, then relative to you, it would look like a bump in the otherwise flat water. Likewise, Einstein was puzzled by the idea of what light would look like if one could catch up to it.8 Nobody had ever reported seeing a flash of light that stands still.
While in college, Einstein was fascinated by questions about ether, electrons, atoms, and light. He learned that several experiments on light had given puzzling results.9 Even though scientists were sure of the existence of the ether (because light behaves like waves; causing effects of interference and diffraction), they failed to measure the speed of Earth relative to the ether. We can measure the speed of a boat relative to the water, so, why not the Earth relative to the ether?
After exhausting and nearly traumatic final exams, Albert graduated college in 1900.10 He failed to get a university job, though he said that he applied to every job in Europe. Meanwhile, his parents faced immense financial difficulties. His mother came from a wealthy family, but his father's business with his uncle, an electrical company, collapsed, destroying all their capital. So Albert lived in considerable poverty.
In 1902, Einstein moved to Bern, the capital of Switzerland, and took a low-level job at the Federal Office of Intellectual Property, evaluating patent applications. In 1903, he married his college girlfriend. He smoked a lot. He drank a lot of coffee, but rarely alcohol, and not beer, saying that “beer makes one dumb and lazy.”11 He continued his struggles to understand light and electromagnetism. He worked on the puzzles of light and motion for two more years. He recalled: “I was plagued by all sorts of nervous conflicts; I went around confused for weeks.”12 Einstein continually obsessed over the problem, until he “feared for his health,” and “wondered if this was the path to insanity.”13 After struggling for years, he had no results. By spring 1905, when he was twenty-six years old, he had reached a roadblock, frustrated.
He then visited his friend Michele Besso, a coworker. Besso was an absentminded mechanical engineer who knew about many topics, including physics, and was often attentive to petty details. Einstein and his shorter, bearded friend discussed every aspect of the light problem.14 And right then they realized that there was something ambiguous about the measurement of time. It suddenly occurred to Einstein that the reason he wasn't making much progress was because he had taken the notion of time for granted.15
In the equations of electricity and magnetism, there appears a term identified as the speed of light, and since speed is distance over time, it raises a question: how is this measurement of time made? Einstein had believed that any concept in physics earns its right to be used only if it can be connected clearly to experience.16 He had been influenced by the writer Ernst Mach, who sought to rid physics of all traces of metaphysics. One of the notions that Mach had singled out was Newton's concept of “absolute time.” Newton had argued that in addition to the apparent measures of time that we obtain with clocks and observations, there exists an exact and true time that flows constantly, uniformly, and independently of anything.17 Nearly all physicists agreed with him. But Mach, in his 1883 book called Mechanics, had complained: “With just as little justice, also, may we speak of an ‘absolute time’—of a time independent of change. This absolute time can be measured by comparison with no motion; it has therefore neither a practical nor scientific value; and no one is justified in saying that he knows aught about it. It is an idle metaphysical conception.”18 Besso gifted Mach's book to Einstein in 1897, and Einstein read it while he was in college, and again in Bern before 1905.19 Now Einstein suddenly realized that there was something obscure, ambiguous, about the measurement of time when we consider, specifically, bodies in motion.20 After his helpful conversation with Besso, he went home frustrated that he still had not solved the problem, but sensing that he had pinpointed the crux of the matter, the notion of time—the key to the solution.21 We don't know exactly what he thought, but we can piece together some relevant notions in order to explain his key insight.
We know that sometimes, often actually, clocks disagree. We usually decide which ones are right by referring to the best and most accurate clocks. Consider clocks at the Royal Observatory at Greenwich in south
-east England or at the National Institute of Standards and Technology in Maryland. They have precise clocks, but how well do they agree with each other?
We can well bring two clocks together and adjust one so that it marks the same time as the other. And that seems to work well enough. But how do we synchronize clocks that are far away from one another? We might, for example, synchronize the clocks together and then move one clock far away. But how do we know whether the clock that we moved remains synchronized with the stationary clock? What if moving it disturbs the rates of motion of its parts, even slightly? We might make the effect smaller by making the distance smaller, or the motion smoother. But there's still an effect, quite likely, however small.
One way to verify that the clocks are synchronized is to bring them back together. Then, either they do mark the same time, or they don't. If they mark the same time, then either they were indeed synchronized all along, or, they became synchronized only when we brought them back together. The problem of just moving one clock or both is that we know, in fact, that accelerated motion can and does affect the rate of clocks. (To accelerate a body is equivalent to hitting it with hammers, even extremely small hammers.) This was known for decades, as clockmakers tried to devise ever-improved chronometers for traveling.
So, to synchronize distant clocks, we should try to avoid moving them. Instead, we might connect such distant clocks with a long rigid beam, such that when we yank the beam the clocks start ticking. For example, given a beam connecting two clocks, both may be activated to start ticking by yanking the beam to one side. The problem is that we don't know whether the effect of yanking the beam is transmitted in the same way along both of its sides. On one side, the parts of the beam (molecules and atoms) are pushed together, on the other they are pulled, and we don't know if both distortions travel at equal speeds along the beam.
So what about pushing down the beam at the center? The same problem occurs. If the force does not travel in the exact same way along both sides, then one side will activate the clock first, and the two won't really be synchronized. How can we check whether the “push” traveling along both sides of the beam reaches both extremities at once?
And there's another problem: what if the beam tilts as you push it down? Even if it tilts very slightly, the two clocks won't be exactly synchronized. The only way to ensure that the beam does not tilt is to confirm, as it moves down, that both of its extremities are at the same height at the same time. But for that we need at least two more clocks, and those clocks need to be synchronized. But we're trying to synchronize distant clocks in the first place!
Another plausible procedure is to synchronize clocks by sending a signal of some sort, such as a light ray, from one to the other. Light travels extremely quickly, so we send the light ray and expect that it synchronizes the clocks. But wait, the clocks are not quite synchronized precisely, because light takes a little bit of time to travel from one clock to the other; there's a very slight delay because light is not infinitely fast.
We might account for this delay by making the first clock start ticking a few moments after the light ray is sent outward from it, just long enough for light to have reached the other clock. Then we expect that the two clocks start at once. But to do so, we need to know, for a fact, how long it takes light to travel from one clock to another. So how do we measure the speed of light?
Back in 1676, a Danish astronomer, Ole Rømer (sometimes written Olaf Roemer), measured the speed of light and presented his results at the French Academy of Sciences in Paris.22 Rømer measured the speed of light using one of Jupiter's moons. As the innermost moon, Io, moves behind Jupiter (its orbit takes about 42.5 hours), its moonlight is eclipsed, so from Earth we don't see it for a while. After a time t, Jupiter's moon becomes visible again.
But later in the year, when Earth had moved to the other side of the sun, Rømer again looked at the eclipse of Jupiter's moon and found that it did not reappear after the same time t. Instead it took a longer time. He inferred that Jupiter's moon took longer to become visible because its moonlight had to travel a greater distance, across Earth's orbit, to reach Earth. By comparing the two time delays, Rømer found a value for the speed of light. Newton and other scientists were impressed.
But do we really therefore know the speed of light? Notice that the only thing we have directly measured are the time delays for the eclipses. But, what if there is any change of speed in Jupiter's moon? To make Rømer's procedure work, we have to assume that the speed of Jupiter's moon is constant. But it isn't. Also, Jupiter itself is moving, so what if the speed of Jupiter changes? The only way we can observationally know the speeds of Jupiter and its moons are by measuring the light that comes from them. To do that, we need to know the speed of all those light rays. Moreover, sunlight bounces off of Jupiter and its moons, but physicists did not know whether the motions of Jupiter and its moons, as they move away from the sun or toward it, affect the speed of the reflected light.
How do we know that light rays all have the same constant speed? Rømer didn't know from his observations, he just assumed it. Thus, consider the critical words of the French mathematician and physicist, Henri Poincaré, writing in 1898: “When an astronomer tells me that some stellar phenomenon…happened [at a certain time]…I seek his meaning, and to that end I shall ask him first how he knows it, that is, how he has measured the velocity of light. He has begun by supposing that light has a constant velocity, and in particular that its velocity is the same in all directions. That is a postulate without which no measurement of this velocity could be attempted. This postulate could never be verified directly by experiment.”23 Accordingly, Rømer's observations are insufficient to ascertain the speed of light, contrary to the claims of many textbooks that fail to explain this matter.
One alternative was to carry out some sort of terrestrial measurement of the speed of light rays. In 1849, the French physicist Armand Fizeau successfully carried out an experiment using a rotating gear wheel with 720 teeth. Fizeau placed the first mirror on the high belvedere of a house in Suresnes, a suburb west of Paris, and he placed the other mirror on a belvedere on Montmartre hill, north of the center of Paris. The distance between the two mirrors was 8.63 kilometers (5.4 miles). Using the first mirror, he sent a narrow beam of light toward the spinning gear wheel, at a position we may call A. The light beam crossed between a gap in the teeth of the spinning wheel at a time t1, it traveled the 8.63 kilometers and there bounced against a mirror at B, making it go in the opposite direction, returning at a time t2 back to the spinning wheel at A.
By varying the speed of rotations of the wheel, Fizeau controlled whether or not the light beam, having crossed the wheel once, made it back through on its return. At first, for various speeds, light crossed a gap in the moving wheel and returned right through the same gap. But at 12.6 revolutions per second, light did not make it back through; that is, the returning ray was blocked by a tooth of the moving wheel. By taking into account the total distance light traveled, 2AB = 17.26 kilometers (10.7 miles), and the total travel time, Fizeau calculated the speed of light.24 We may write it as:
So here we have a terrestrial experiment, and a value for the speed of light. It would seem that finally, knowing the speed of light, we're ready to synchronize those clocks!
Notice, however, that we have not really measured the velocity of light, we have only measured the round-trip average speed. That is, we now know, pretty much, the time t it took a light ray traveling from A to B and back to A, but we do not know the time it took to travel from A to B alone.
We might perhaps assume that the speed of light from A to B alone is the same as the round-trip speed. That sounds reasonable. But that is just an assumption, we have not proven by experiment whether the speeds in opposite directions are truly equal.
Someone might think: “That's weird! Why the heck would light take two different times to travel equal distances in opposite directions?” Mainly, because the distances might not really be equal. As
Earth moves in a given direction, the mirror in Fizeau's experiment moves, for example, away from the approaching light ray. Once the light is reflected, it travels toward the source that approaches it as well, carried by Earth. Hence the distance light traversed to meet the mirror is longer than the distance back to the source. In that case, it takes longer for light to travel from A to B than from B to A. It does not help that the source of light moves as well, carried by Earth, because that would not make light move any faster toward the receding mirror. (Physicists expected that the speed of light is independent of the motion of its source.25) So, contrary to many textbooks, Fizeau's experiment says nothing about the one-way velocity of light.
Suppose we synchronize clocks by sending light from a lamp in opposite directions, to activate the clocks, to start them in synchrony. This procedure would work if light rays have the same speed in opposite directions. But does light take the same travel time in opposite directions? To know that, we have to measure the speeds of light rays and then compare them. In order to measure any such speed, we need two more clocks.
But to measure a speed, those clocks need to be synchronized. How? Let's place a light bulb at the center between them, and turn it on. But that only works if light takes the same speed in opposite directions. So how do we test that? We need two more clocks. And how do we synchronize those clocks?
There is a circularity here! To synchronize distant clocks you need to know a velocity. To know a velocity you need to have synchronized clocks. Thus, in spring 1905, Einstein realized, “there is an inseparable relation between time and signal velocity.”26 He wasn't the first to notice this circularity. For example, Poincaré also noticed it earlier and wrote about it in a paper of 1898 that was cited in a book that Einstein read before 1905.27
Science Secrets Page 19