Now suppose we repeat the experiment, this time shining lights on the slits so that we know an intermediate point, C, through which the particle passed. (C is the position of either one of the slits or the other.) This is called “which-path” information because it tells us whether each particle went from A to slit 1 to B, or from A to slit 2 to B. Since we now know through which slit each particle passed, the paths in our sum for that particle will now include only paths that travel through slit 1, or only paths that travel through slit 2. It will never include both the paths that go through slit 1 and the paths that pass through slit 2. Because Feynman explained the interference pattern by saying that paths that go through one slit interfere with paths that go through the other, if you turn on a light to determine which slit the particles pass through, thereby eliminating the other option, you will make the interference pattern disappear. And indeed, when the experiment is performed, turning on a light changes the results from the interference pattern, to a pattern like that! Moreover, we can vary the experiment by employing very faint light so that not all of the particles interact with the light. In that case we are able to obtain which-path information for only some subset of the particles. If we then divide the data on particle arrivals according to whether or not we obtained which-path information, we find that data pertaining to the subset for which we have no which-path information will form an interference pattern, and the subset of data pertaining to the particles for which we do have which-path information will not show interference.
This idea has important implications for our concept of “the past.” In Newtonian theory, the past is assumed to exist as a definite series of events. If you see that vase you bought in Italy last year lying smashed on the floor and your toddler standing over it looking sheepish, you can trace backward the events that led to the mishap: the little fingers letting go, the vase falling and exploding into a thousand pieces as it hits. In fact, given complete data about the present, Newton’s laws allow one to calculate a complete picture of the past. This is consistent with our intuitive understanding that, whether painful or joyful, the world has a definite past. There may have been no one watching, but the past exists as surely as if you had taken a series of snapshots of it. But a quantum buckyball cannot be said to have taken a definite path from source to screen. We might pin down a buckyball’s location by observing it, but in between our observations, it takes all paths. Quantum physics tells us that no matter how thorough our observation of the present, the (unobserved) past, like the future, is indefinite and exists only as a spectrum of possibilities. The universe, according to quantum physics, has no single past, or history.
The fact that the past takes no definite form means that observations you make on a system in the present affect its past. That is underlined rather dramatically by a type of experiment thought up by physicist John Wheeler, called a delayed-choice experiment. Schematically, a delayed-choice experiment is like the double-slit experiment we just described, in which you have the option of observing the path that the particle takes, except in the delayed-choice experiment you postpone your decision about whether or not to observe the path until just before the particle hits the detection screen.
Delayed-choice experiments result in data identical to those we get when we choose to observe (or not observe) the which-path information by watching the slits themselves. But in this case the path each particle takes—that is, its past—is determined long after it passed through the slits and presumably had to “decide” whether to travel through just one slit, which does not produce interference, or both slits, which does.
Wheeler even considered a cosmic version of the experiment, in which the particles involved are photons emitted by powerful quasars billions of light-years away. Such light could be split into two paths and refocused toward earth by the gravitational lensing of an intervening galaxy. Though the experiment is beyond the reach of current technology, if we could collect enough photons from this light, they ought to form an interference pattern. Yet if we place a device to measure which-path information shortly before detection, that pattern should disappear. The choice whether to take one or both paths in this case would have been made billions of years ago, before the earth or perhaps even our sun was formed, and yet with our observation in the laboratory we will be affecting that choice.
In this chapter we have illustrated quantum physics employing the double-slit experiment. In what follows we will apply Feynman’s formulation of quantum mechanics to the universe as a whole. We will see that, like a particle, the universe doesn’t have just a single history, but every possible history, each with its own probability; and our observations of its current state affect its past and determine the different histories of the universe, just as the observations of the particles in the double-slit experiment affect the particles’ past. That analysis will show how the laws of nature in our universe arose from the big bang. But before we examine how the laws arose, we’ll talk a little bit about what those laws are, and some of the mysteries that they provoke.
The most incomprehensible thing about the universe is that it is comprehensible.
—ALBERT EINSTEIN
HE UNIVERSE IS COMPREHENSIBLE because it is governed by scientific laws; that is to say, its behavior can be modeled. But what are these laws or models? The first force to be described in mathematical language was gravity. Newton’s law of gravity, published in 1687, said that every object in the universe attracts every other object with a force proportional to its mass. It made a great impression on the intellectual life of its era because it showed for the first time that at least one aspect of the universe could be accurately modeled, and it established the mathematical machinery to do so. The idea that there are laws of nature brings up issues similar to that for which Galileo had been convicted of heresy about fifty years earlier. For instance, the Bible tells the story of Joshua praying for the sun and moon to stop in their trajectories so he would have extra daylight to finish fighting the Amorites in Canaan. According to the book of Joshua, the sun stood still for about a day. Today we know that that would have meant that the earth stopped rotating. If the earth stopped, according to Newton’s laws anything not tied down would have remained in motion at the earth’s original speed (1,100 miles per hour at the equator)—a high price to pay for a delayed sunset. None of this bothered Newton himself, for as we’ve said, Newton believed that God could and did intervene in the workings of the universe.
The next aspects of the universe for which a law or model was discovered were the electric and magnetic forces. These behave like gravity, with the important difference that two electric charges or two magnets of the same kind repel each other, while unlike charges or unlike magnets attract. Electric and magnetic forces are far stronger than gravity, but we don’t usually notice them in everyday life because a macroscopic body contains almost equal numbers of positive and negative electrical charges. This means that the electric and magnetic forces between two macroscopic bodies nearly cancel each other out, unlike the gravitational forces, which all add up.
Our current ideas about electricity and magnetism were developed over a period of about a hundred years from the mid-eighteenth to the mid-nineteenth century, when physicists in several countries made detailed experimental studies of electric and magnetic forces. One of the most important discoveries was that electrical and magnetic forces are related: A moving electrical charge causes a force on magnets, and a moving magnet causes a force on electrical charges. The first to realize there was some connection was Danish physicist Hans Christian Ørsted. While setting up for a lecture he was to give at the university in 1820, Ørsted noticed that the electric current from the battery he was using deflected a nearby compass needle. He soon realized that moving electricity created a magnetic force, and coined the term “electromagnetism.” A few years later British scientist Michael Faraday reasoned that—expressed in modern terms—if an electric current could cause a magnetic field, a magnetic field should be able to produce
an electric current. He demonstrated that effect in 1831. Fourteen years later Faraday also discovered a connection between electromagnetism and light when he showed that intense magnetism can affect the nature of polarized light.
Faraday had little formal education. He had been born into a poor blacksmith’s family near London and left school at age thirteen to work as an errand boy and bookbinder in a bookshop. There, over the years, he learned science by reading the books he was supposed to care for, and by performing simple and cheap experiments in his spare time. Eventually he obtained work as an assistant in the laboratory of the great chemist Sir Humphry Davy. Faraday would stay on for the remaining forty-five years of his life and, after Davy’s death, succeed him. Faraday had trouble with mathematics and never learned much of it, so it was a struggle for him to conceive a theoretical picture of the odd electromagnetic phenomena he observed in his laboratory. Nevertheless, he did.
One of Faraday’s greatest intellectual innovations was the idea of force fields. These days, thanks to books and movies about bug-eyed aliens and their starships, most people are familiar with the term, so maybe he should get a royalty. But in the centuries between Newton and Faraday one of the great mysteries of physics was that its laws seemed to indicate that forces act across the empty space that separates interacting objects. Faraday didn’t like that. He believed that to move an object, something has to come in contact with it. And so he imagined the space between electric charges and magnets as being filled with invisible tubes that physically do the pushing and pulling. Faraday called those tubes a force field. A good way to visualize a force field is to perform the schoolroom demonstration in which a glass plate is placed over a bar magnet and iron filings spread on the glass. With a few taps to overcome friction, the filings move as if nudged by an unseen power and arrange themselves in a pattern of arcs stretching from one pole of the magnet to the other. That pattern is a map of the unseen magnetic force that permeates space. Today we believe that all forces are transmitted by fields, so it is an important concept in modern physics—as well as science fiction.
For several decades our understanding of electromagnetism remained stalled, amounting to no more than the knowledge of a few empirical laws: the hint that electricity and magnetism were closely, if mysteriously, related; the notion that they had some sort of connection to light; and the embryonic concept of fields. At least eleven theories of electromagnetism existed, every one of them flawed. Then, over a period of years in the 1860s, Scottish physicist James Clerk Maxwell developed Faraday’s thinking into a mathematical framework that explained the intimate and mysterious relation among electricity, magnetism, and light. The result was a set of equations describing both electric and magnetic forces as manifestations of the same physical entity, the electromagnetic field. Maxwell had unified electricity and magnetism into one force. Moreover, he showed that electromagnetic fields could propagate through space as a wave. The speed of that wave is governed by a number that appeared in his equations, which he calculated from experimental data that had been measured a few years earlier. To his astonishment the speed he calculated equaled the speed of light, which was then known experimentally to an accuracy of 1 percent. He had discovered that light itself is an electromagnetic wave!
Today the equations that describe electric and magnetic fields are called Maxwell’s equations. Few people have heard of them, but they are probably the most commercially important equations we know. Not only do they govern the working of everything from household appliances to computers, but they also describe waves other than light, such as microwaves, radio waves, infrared light, and X-rays. All of these differ from visible light in only one respect—their wavelength. Radio waves have wavelengths of a meter or more, while visible light has a wavelength of a few ten-millionths of a meter, and X-rays a wavelength shorter than a hundred-millionth of a meter. Our sun radiates at all wavelengths, but its radiation is most intense in the wavelengths that are visible to us. It’s probably no accident that the wavelengths we are able to see with the naked eye are those in which the sun radiates most strongly: It’s likely that our eyes evolved with the ability to detect electromagnetic radiation in that range precisely because that is the range of radiation most available to them. If we ever run into beings from other planets, they will probably have the ability to “see” radiation at whatever wavelengths their own sun emits most strongly, modulated by factors such as the light-blocking characteristics of the dust and gases in their planet’s atmosphere. So aliens who evolved in the presence of X-rays might have a nice career in airport security.
Maxwell’s equations dictate that electromagnetic waves travel at a speed of about 300,000 kilometers a second, or about 670 million miles per hour. But to quote a speed means nothing unless you specify a frame of reference relative to which the speed is measured. That’s not something you usually need to think about in everyday life. When a speed limit sign reads 60 miles per hour, it is understood that your speed is measured relative to the road and not the black hole at the center of the Milky Way. But even in everyday life there are occasions in which you have to take into account reference frames. For example, if you carry a cup of tea up the aisle of a jet plane in flight, you might say your speed is 2 miles per hour. Someone on the ground, however, might say you were moving at 572 miles per hour. Lest you think that one or the other of those observers has a better claim to the truth, keep in mind that because the earth orbits the sun, someone watching you from the surface of that heavenly body would disagree with both and say you are moving at about 18 miles per second, not to mention envying your air-conditioning. In light of such disagreements, when Maxwell claimed to have discovered the “speed of light” popping out of his equations, the natural question was, what is the speed of light in Maxwell’s equations measured relative to?
There is no reason to believe that the speed parameter in Maxwell’s equations is a speed measured relative to the earth. His equations, after all, apply to the entire universe. An alternative answer that was considered for a while is that his equations specify the speed of light relative to a previously undetected medium permeating all space, called the luminiferous ether, or for short, simply the ether, which was Aristotle’s term for the substance he believed filled all of the universe outside the terrestrial sphere. This hypothetical ether would be the medium through which electromagnetic waves propagate, just as sound propagates through air. If the ether existed, there would be an absolute standard of rest (that is, rest with respect to the ether) and hence an absolute way of defining motion as well. The ether would provide a preferred frame of reference throughout the entire universe, against which any object’s speed could be measured. So the ether was postulated to exist on theoretical grounds, setting some scientists off on a search for a way to study it, or at least to confirm its existence. One of those scientists was Maxwell himself.
If you race through the air toward a sound wave, the wave approaches you faster, and if you race away, it approaches you more slowly. Similarly, if there were an ether, the speed of light would vary depending on your motion relative to the ether. In fact, if light worked the way sound does, just as people on a supersonic jet will never hear any sound that emanates from behind the plane, so too would travelers racing quickly enough through the ether be able to outrun a light wave. Working from such considerations, Maxwell suggested an experiment. If there is an ether, the earth must be moving through it as it orbits the sun. And since the earth is traveling in a different direction in January than, say, in April or July, one ought to be able to observe a tiny difference in the speed of light at different times of the year—see the figure below.
Maxwell was talked out of publishing his idea in Proceedings of the Royal Society by its editor, who didn’t think the experiment would work. But in 1879, shortly before he died at age forty-eight of painful stomach cancer, Maxwell sent a letter on the subject to a friend. The letter was published posthumously in the journal Nature, where it was read by, among others, an
American physicist named Albert Michelson. Inspired by Maxwell’s speculation, in 1887 Michelson and Edward Morley carried out a very sensitive experiment designed to measure the speed at which the earth travels through the ether. Their idea was to compare the speed of light in two different directions, at right angles. If the speed of light were a fixed number relative to the ether, the measurements should have revealed light speeds that differed depending on the direction of the beam. But Michelson and Morley observed no such difference.
The outcome of the Michelson and Morley experiment is clearly in conflict with the model of electromagnetic waves traveling through an ether, and should have caused the ether model to be abandoned. But Michelson’s purpose had been to measure the speed of the earth relative to the ether, not to prove or disprove the ether hypothesis, and what he found did not lead him to conclude that the ether didn’t exist. No one else drew that conclusion either. In fact, the famous physicist Sir William Thomson (Lord Kelvin) said in 1884 that the ether was “the only substance we are confident of in dynamics. One thing we are sure of, and that is the reality and substantiality of the luminiferous ether.”
How can you believe in the ether despite the results of the Michelson-Morley experiment? As we’ve said often happens, people tried to save the model by contrived and ad hoc additions. Some postulated that the earth dragged the ether along with it, so we weren’t actually moving with respect to it. Dutch physicist Hendrik Antoon Lorentz and Irish physicist George Francis FitzGerald suggested that in a frame that was moving with respect to the ether, probably due to some yet-unknown mechanical effect, clocks would slow down and distances would shrink, so one would still measure light to have the same speed. Such efforts to save the aether concept continued for nearly twenty years until a remarkable paper by a young and unknown clerk in the patent office in Berne, Albert Einstein.