by Brian Greene
Again, the proposal holds for all kinds of accelerated motion, not just spinning. When the airplane you are on is accelerating down the runway, when the car you are in screeches to a halt, when the elevator you are in starts to climb, Mach's ideas imply that the force you feel represents the combined influence of all the other matter making up the universe. If there were more matter, you would feel greater force. If there were less matter, you would feel less force. And if there were no matter, you wouldn't feel anything at all. So, in Mach's way of thinking, only relative motion and relative acceleration matter. You feel acceleration only when you accelerate relative to the average distribution of other material inhabitingthe cosmos. Without other material—without any benchmarks for comparison—Mach claimed there would be no way to experience acceleration.
For many physicists, this is one of the most seductive proposals about the cosmos put forward during the last century and a half. Generations of physicists have found it deeply unsettling to imagine that the untouchable, ungraspable, unclutchable fabric of space is really a something—a something substantial enough to provide the ultimate, absolute benchmark for motion. To many it has seemed absurd, or at least scientifically irresponsible, to base an understanding of motion on something so thoroughly imperceptible, so completely beyond our senses, that it borders on the mystical. Yet these same physicists were dogged by the question of how else to explain Newton's bucket. Mach's insights generated excitement because they raised the possibility of a new answer, one in which space is not a something, an answer that points back toward the relationist conception of space advocated by Leibniz. Space, in Mach's view, is very much as Leibniz imagined—it's the language for expressing the relationship between one object's position and another's. But, like an alphabet without letters, space does not enjoy an independent existence.
Mach vs. Newton
I learned of Mach's ideas when I was an undergraduate, and they were a godsend. Here, finally, was a theory of space and motion that put all perspectives back on an equal footing, since only relative motion and relative acceleration had meaning. Rather than the Newtonian benchmark for motion—an invisible thing called absolute space—Mach's proposed benchmark is out in the open for all to see—the matter that is distributed throughout the cosmos. I felt sure Mach's had to be the answer. I also learned that I was not alone in having this reaction; I was following a long line of physicists, including Albert Einstein, who had been swept away when they first encountered Mach's ideas.
Is Mach right? Did Newton get so caught up in the swirl of his bucket that he came to a wishy-washy conclusion regarding space? Does Newton's absolute space exist, or had the pendulum firmly swung back to the relationist perspective? During the first few decades after Mach introduced his ideas, these questions couldn't be answered. For the most part, the reason was that Mach's suggestion was not a complete theory or description, since he never specified how the matter content of the universe would exert the proposed influence. If his ideas were right, how do the distant stars and the house next door contribute to your feeling that you are spinning when you spin around? Without specifying a physical mechanism to realize his proposal, it was hard to investigate Mach's ideas with any precision.
From our modern vantage point, a reasonable guess is that gravity might have something to do with the influences involved in Mach's suggestion. In the following decades, this possibility caught Einstein's attention and he drew much inspiration from Mach's proposal while developing his own theory of gravity, the general theory of relativity. When the dust of relativity had finally settled, the question of whether space is a something—of whether the absolutist or relationist view of space is correct—was transformed in a manner that shattered all previous ways of looking at the universe.
3 - Relativity and the Absolute
IS SPACETIME AN EINSTEINIAN ABSTRACTION
OR A PHYSICAL ENTITY?
Some discoveries provide answers to questions. Other discoveries are so deep that they cast questions in a whole new light, showing that previous mysteries were misperceived through lack of knowledge. You could spend a lifetime—in antiquity, some did—wondering what happens when you reach earth's edge, or trying to figure out who or what lives on earth's underbelly. But when you learn that the earth is round, you see that the previous mysteries are not solved; instead, they're rendered irrelevant.
During the first decades of the twentieth century, Albert Einstein made two deep discoveries. Each caused a radical upheaval in our understanding of space and time. Einstein dismantled the rigid, absolute structures that Newton had erected, and built his own tower, synthesizing space and time in a manner that was completely unanticipated. When he was done, time had become so enmeshed with space that the reality of one could no longer be pondered separately from the other. And so, by the third decade of the twentieth century the question of the corporeality of space was outmoded; its Einsteinian reframing, as we'll talk about shortly, became: Is spacetime a something? With that seemingly slight modification, our understanding of reality's arena was transformed.
Is Empty Space Empty?
Light was the primary actor in the relativity drama written by Einstein in the early years of the twentieth century. And it was the work of James Clerk Maxwell that set the stage for Einstein's insights. In the mid-1800s, Maxwell discovered four powerful equations that, for the first time, set out a rigorous theoretical framework for understanding electricity, magnetism, and their intimate relationship. 1 Maxwell developed these equations by carefully studying the work of the English physicist Michael Faraday, who in the early 1800s had carried out tens of thousands of experiments that exposed hitherto unknown features of electricity and magnetism. Faraday's key breakthrough was the concept of the field. Later expanded on by Maxwell and many others, this concept has had an enormous influence on the development of physics during the last two centuries, and underlies many of the little mysteries we encounter in everyday life. When you go through airport security, how is it that a machine that doesn't touch you can determine whether you're carrying metallic objects? When you have an MRI, how is it that a device that remains outside your body can take a detailed picture of your insides? When you look at a compass, how is it that the needle swings around and points north even though nothing seems to nudge it? The familiar answer to the last question invokes the earth's magnetic field, and the concept of magnetic fields helps to explain the previous two examples as well.
I've never seen a better way to get a visceral sense of a magnetic field than the elementary school demonstration in which iron filings are sprinkled in the vicinity of a bar magnet. After a little shaking, the iron filings align themselves in an orderly pattern of arcs that begin at the magnet's north pole and swing up and around, to end at the magnet's south pole, as in Figure 3.1. The pattern traced by the iron filings is direct evidence that the magnet creates an invisible something that permeates the space around it—a something that can, for example, exert a force on shards of metal. The invisible something is the magnetic field and, to our intuition, it resembles a mist or essence that can fill a region of space and thereby exert a force beyond the physical extent of the magnet itself. A magnetic field provides a magnet what an army provides a dictator and what auditors provide the IRS: influence beyond their physical boundaries, which allows force to be exerted out in the "field." That is why a magnetic field is also called a force field.
Figure 3.1 Iron filings sprinkled near a bar magnet trace out its magnetic field.
It is the pervasive, space-filling capability of magnetic fields that makes them so useful. An airport metal detector's magnetic field seeps through your clothes and causes metallic objects to give off their own magnetic fields—fields that then exert an influence back on the detector, causing its alarm to sound. An MRI's magnetic field seeps into your body, causing particular atoms to gyrate in just the right way to generate their own magnetic fields—fields that the machine can detect and decode into a picture of internal tissues. Th
e earth's magnetic field seeps through the compass casing and turns the needle, causing it to point along an arc that, as a result of eons-long geophysical processes, is aligned in a nearly south-north direction.
Magnetic fields are one familiar kind of field, but Faraday also analyzed another: the electric field. This is the field that causes your wool scarf to crackle, zaps your hand in a carpeted room when you touch a metal doorknob, and makes your skin tingle when you're up in the mountains during a powerful lightning storm. And if you happened to examine a compass during such a storm, the way its magnetic needle deflected this way and that as the bolts of electric lightning flashed nearby would have given you a hint of a deep interconnection between electric and magnetic fields—something first discovered by the Danish physicist Hans Oersted and investigated thoroughly by Faraday through painstaking experimentation. Just as developments in the stock market can affect the bond market which can then affect the stock market, and so on, these scientists found that changes in an electric field can produce changes in a nearby magnetic field, which can then cause changes in the electric field, and so on. Maxwell found the mathematical underpinnings of these interrelationships, and because his equations showed that electric and magnetic fields are as entwined as the fibers in a Rastafarian's dreadlocks, they were eventually christened electromagnetic fields, and the influence they exert the electromagnetic force.
Today, we are constantly immersed in a sea of electromagnetic fields. Your cellular telephone and car radio work over enormous expanses because the electromagnetic fields broadcast by telephone companies and radio stations suffuse impressively wide regions of space. The same goes for wireless Internet connections; computers can pluck the entire World Wide Web from electromagnetic fields that are vibrating all around us—in fact, right through us. Of course, in Maxwell's day, electromagnetic technology was less developed, but among scientists his feat was no less recognized: through the language of fields, Maxwell had shown that electricity and magnetism, although initially viewed as distinct, are really just different aspects of a single physical entity.
Later on, we'll encounter other kinds of fields—gravitational fields, nuclear fields, Higgs fields, and so on—and it will become increasingly clear that the field concept is central to our modern formulation of physical law. But for now the critical next step in our story is also due to Maxwell. Upon further analyzing his equations, he found that changes or disturbances to electromagnetic fields travel in a wavelike manner at a particular speed: 670 million miles per hour. As this is precisely the value other experiments had found for the speed of light, Maxwell realized that light must be nothing other than an electromagnetic wave, one that has the right properties to interact with chemicals in our retinas and give us the sensation of sight. This achievement made Maxwell's already towering discoveries all the more remarkable: he had linked the force produced by magnets, the influence exerted by electrical charges, and the light we use to see the universe—but it also raised a deep question.
When we say that the speed of light is 670 million miles per hour, experience, and our discussion so far, teach us this is a meaningless statement if we don't specify relative to what this speed is being measured. The funny thing was that Maxwell's equations just gave this number, 670 million miles per hour, without specifying or apparently relying on any such reference. It was as if someone gave the location for a party as 22 miles north without specifying the reference location, without specifying north of what. Most physicists, including Maxwell, attempted to explain the speed his equations gave in the following way: Familiar waves such as ocean waves or sound waves are carried by a substance, a medium. Ocean waves are carried by water. Sound waves are carried by air. And the speeds of these waves are specified with respect to the medium. When we talk about the speed of sound at room temperature being 767 miles per hour (also known as Mach 1, after the same Ernst Mach encountered earlier), we mean that sound waves travel through otherwise still air at this speed. Naturally, then, physicists surmised that light waves—electromagnetic waves—must also travel through some particular medium, one that had never been seen or detected but that must exist. To give this unseen light-carrying stuff due respect, it was given a name: the luminiferous aether, or the aether for short, the latter being an ancient term that Aristotle used to describe the magical catchall substance of which heavenly bodies were imagined to be made. And, to square this proposal with Maxwell's results, it was suggested that his equations implicitly took the perspective of someone at rest with respect to the aether. The 670 million miles per hour his equations came up with, then, was the speed of light relative to the stationary aether.
As you can see, there is a striking similarity between the luminiferous aether and Newton's absolute space. They both originated in attempts to provide a reference for defining motion; accelerated motion led to absolute space, light's motion led to the luminiferous aether. In fact, many physicists viewed the aether as a down-to-earth stand-in for the divine spirit that Henry More, Newton, and others had envisioned permeating absolute space. (Newton and others in his age had even used the term "aether" in their descriptions of absolute space.) But what actually is the aether? What is it made of? Where did it come from? Does it exist everywhere?
These questions about the aether are the same ones that for centuries had been asked about absolute space. But whereas the full Machian test for absolute space involved spinning around in a completely empty universe, physicists were able to propose doable experiments to determine whether the aether really existed. For example, if you swim through water toward an oncoming water wave, the wave approaches you more quickly; if you swim away from the wave, it approaches you more slowly. Similarly, if you move through the supposed aether toward or away from an oncoming light wave, the light wave's approach should, by the same reasoning, be faster or slower than 670 million miles per hour. In 1887, however, when Albert Michelson and Edward Morley measured the speed of light, time and time again they found exactly the same speed of 670 million miles per hour regardless of their motion or that of the light's source. All sorts of clever arguments were devised to explain these results. Maybe, some suggested, the experimenters were unwittingly dragging the aether along with them as they moved. Maybe, a few ventured, the equipment was being warped as it moved through the aether, corrupting the measurements. But it was not until Einstein had his revolutionary insight that the explanation finally became clear.
Relative Space, Relative Time
In June 1905, Einstein wrote a paper with the unassuming title "On the Electrodynamics of Moving Bodies," which once and for all spelled the end of the luminiferous aether. In one stroke, it also changed forever our understanding of space and time. Einstein formulated the ideas in the paper over an intense five-week period in April and May 1905, but the issues it finally laid to rest had been gnawing at him for over a decade. As a teenager, Einstein struggled with the question of what a light wave would look like if you were to chase after it at exactly light speed. Since you and the light wave would be zipping through the aether at exactly the same speed, you would be keeping perfect pace with the light. And so, Einstein concluded, from your perspective the light should appear as though it wasn't moving. You should be able to reach out and grab a handful of motionless light just as you can scoop up a handful of newly fallen snow.
But here's the problem. It turns out that Maxwell's equations do not allow light to appear stationary—to look as if it's standing still. And certainly, there is no reliable report of anyone's ever actually catching hold of a stationary clump of light. So, the teenage Einstein asked, what are we to make of this apparent paradox?
Ten years later, Einstein gave the world his answer with his special theory of relativity. There has been much debate regarding the intellectual roots of Einstein's discovery, but there is no doubt that his unshakable belief in simplicity played a critical role. Einstein was aware of at least some experiments that had failed to detect evidence for the existence of the aether. 2 S
o why dance around trying to find fault with the experiments? Instead, Einstein declared, take the simple approach: The experiments were failing to find the aether because there is no aether. And since Maxwell's equations describing the motion of light—the motion of electromagnetic waves—do not invoke any such medium, both experiment and theory would converge on the same conclusion: light, unlike any other kind of wave ever encountered, does not need a medium to carry it along. Light is a lone traveler. Light can travel through empty space.
But what, then, are we to make of Maxwell's equation giving light a speed of 670 million miles per hour? If there is no aether to provide the standard of rest, what is the what with respect to which this speed is to be interpreted? Again, Einstein bucked convention and answered with ultimate simplicity. If Maxwell's theory does not invoke any particular standard of rest, the most direct interpretation is that we don't need one. The speed of light, Einstein declared, is 670 million miles per hour relative to anything and everything.
Well, this is certainly a simple statement; it fit well a maxim often attributed to Einstein: "Make everything as simple as possible, but no simpler." The problem is that it also seems crazy. If you run after a departing beam of light, common sense dictates that from your perspective the speed of the departing light has to be less than 670 million miles per hour. If you run toward an approaching beam of light, common sense dictates that from your perspective the speed of the approaching light will be greater than 670 million miles per hour. Throughout his life, Einstein challenged common sense, and this time was no exception. He forcefully argued that regardless of how fast you move toward or away from a beam of light, you will always measure its speed to be 670 million miles per hour—not a bit faster, not a bit slower, no matter what. This would certainly solve the paradox that stumped him as a teenager: Maxwell's theory does not allow for stationary light because light never is stationary; regardless of your state of motion, whether you chase a light beam, or run from it, or just stand still, the light retains its one fixed and never changing speed of 670 million miles per hour. But, we naturally ask, how can light possibly behave in such a strange manner?
