The God Particle
Page 17
We have already discussed his electrolysis research, which prepared the way for the discovery of the electrical structure of chemical atoms and, indeed, for the existence of the electron. Now I want to describe Faraday's two most remarkable contributions: electromagnetic induction and his almost mystical concept of "field."
The route to the modern understanding of electricity (more properly, electromagnetism or the electromagnetic field) is akin to the famous baseball double-play combination linker to Evers to Chance. In this case it's Oersted to Ampère to Faraday. Oersted and Ampère made the first steps in understanding electric currents and magnetic fields. Electric currents flowing in wires, like those in your house, make magnetic fields. Thus you can make as powerful a magnet as you want, from the tiny battery-operated magnets that drive small fans to the giant ones used in particle accelerators, by organizing currents. This understanding of electromagnets illuminates our understanding of natural magnets as containing atomic-scale current elements that cooperate to generate a magnet. Nonmagnetic materials also have these Amperian atomic currents, but their random orientation produces no net magnetism.
Faraday struggled for a long time to unify electricity and magnetism. If electricity can make magnetic fields, he wondered, can magnets make electricity? Why not? Nature loves symmetry. But it took him more than ten years (1820–1831) to prove it. This was probably his greatest achievement.
Faraday's experimental discovery is called electromagnetic induction, and the symmetry he sought emerged in a surprising form. The road to fame is paved with good inventions. Faraday first wondered whether a magnet could make a current-carrying wire move. Visualizing the forces, he rigged up a device that consisted of a wire connected to a battery at one end, with the other end hanging in a beaker of mercury. The electric wire hung free so that it could revolve around an iron magnet in the beaker. When the current was turned on, the wire moved in a circle around the magnet. We know this odd invention today as an electric motor. Faraday had converted electricity to motion, which could do work.
Let's jump to 1831 and another invention. Faraday wrapped a large number of turns of copper wire on one side of a soft iron doughnut, then connected the two ends of the coil to a sensitive current-measuring device called a galvanometer. He wrapped a similar length of wire on the other side of the doughnut, connecting these ends to a battery so that current could flow in the coil. This device is now called a transformer. Let's review. We have two coils wound on opposite sides of a doughnut. One, let's call it A, is connected to a battery; the other (B) is connected to a galvanometer. What happens when you turn on the juice?
The answer is important to the history of science. When the current flows in coil A, the electricity produces magnetism. Faraday reasoned that this magnetism should induce a current in coil B. But instead he got a strange effect. When he turned on the current, the needle in the galvanometer connected to coil B deflected—voila! electricity!—but only momentarily. After the sudden jump, the needle remained pointed maddeningly to zero. When he disconnected the battery, the needle deflected briefly in the opposite direction. Increasing the sensitivity of the galvanometer had no effect. Increasing the number of turns in each coil had no effect. Using a much stronger battery had no effect. And then the Eureka moment (in England it is called the By Jove moment): Faraday figured out that current in the first coil had induced a current in the second, but only when the first current was changing. So, as the next thirty years or so of research showed, a changing magnetic field generates an electric field.
The technology that emerged in due course was the electric generator. By rotating a magnet mechanically, one can produce a constantly changing magnetic field, which will generate an electric field and, if connected to a circuit, an electric current. One can rotate a magnet by turning a crank, by using the force of a waterfall, or by harnessing a steam turbine. Now we had a way of generating electricity to turn night into day and to energize those electrical outlets in home and factory.
But we pure scientists ... we are on the track of the a-tom and the God Particle; we dwell on the technology only because it would have been awfully hard to make particle accelerators without Faraday's electricity. As for Faraday, he probably wouldn't have been impressed with the electrification of the world except that now he could work at night.
Faraday built the first hand-cranked electrical generator himself; it was called a dynamo in those days. But he was too involved in the "discovery of new facts ... being assured that the latter [practical applications] would find their full development hereafter" to figure out what to do with it. The story is often told that the British prime minister visited Faraday's laboratory in 1832 and, pointing to the funny machine, asked what use it was. "I know not, but I wager that one day your government will tax it," said Faraday. A tax on electrical generation was levied in England in 1880.
THE FIELD BE WITH YOU
Faraday's major conceptual contribution, crucial to our history of reductionism, was the field. To prepare for this, we must go back to Roger Boscovich, who published a radical hypothesis some seventy years before Faraday's time, carrying the a-tom an important step forward. How do a-toms collide? he asked. When billiard balls collide, they deform; their elastic recovery pushes the balls apart. But a-toms? Can one imagine a deformed a-tom? What would deform? What recover? Boscovich was led by such thinking to reduce a-toms to a dimensionless, structureless mathematical point. This point is the source of forces, both attractive and repulsive. He constructed a detailed geometric model that treated atomic collisions very plausibly. The point a-tom did everything that Newton's "hard, massy atom" did but offered advantages. Although it had no extension, it did have inertia (mass). Boscovich's a-tom reached out into space via forces radiating from it. This is an extremely prescient concept. Faraday also was convinced that a-toms were points, but since he could not offer proof, his support was muted. The Boscovich/Faraday view was this: matter consists of point a-toms surrounded by forces. Newton had said force acts on mass, so this was clearly an extension of his idea. How does this force manifest itself?
"Lets play a game," I say to the students in a large lecture hall. "When the student to your left lowers his hand, you raise and lower your hand." At the end of the row we pass the signal up one row and switch to "student on your right." We begin with the student at the extreme left of the front row, who raises her hand. Soon the "hand-up" wave travels across the room, up, back across, and so on until it peters out at the top of the hall. What we have is a disturbance propagating with some speed through a medium of students. It's the same principle as the wave, seen in football stadiums across the land. A water wave has the same properties. Although the disturbance propagates, the water particles stay put, bobbing up and down but not involved in the horizontal velocity of the disturbance. The "disturbance" is the height of the wave. The medium is water. The velocity depends on the properties of water. Sounds propagate through air in much the same way. But how does a force reach out from atom to atom through intervening empty space? Newton punted. "I frame no hypothesis," he said. Framed or not, the common hypothesis for how a force propagate was the mysterious action-at-a-distance, a kind of placeholder for a future understanding of how gravity is supposed to work.
Faraday introduced the concept of field, the ability of space to be disturbed because of a source somewhere. The most common example is a magnet reaching for iron nails. Faraday pictured the space around the magnet or coil as being "strained" because of the source. The field concept emerged painfully over many years in many writings, and historians enjoy differing on how, what, and when it all came out. Here is a note from Faraday in 1832: "When a magnet acts upon a distant magnet or piece of iron, the influencing cause ... proceeds gradually from magnetic bodies and requires time for its transmission [emphasis mine]." Thus the concept is that a "disturbance"—for example a magnetic field strength of 0.1 tesla—can travel through space and notify a grain of iron powder not only that it is there but that it ca
n exert a force. This is what a strong water wave does to an unwary bather. The water wave—say it's three feet high—needs water in which to propagate. We must still wrestle with what the magnetic field needs. Later.
Magnetic lines of force are revealed in the old experiment you did in school by sprinkling iron powder on a sheet of paper placed over a magnet. You gave the paper a tap to break the surface friction, and the iron powder clustered in a definite pattern of lines connecting the poles of the magnet. Faraday thought these lines were real manifestations of his field concept. The important issue is not so much Faraday's ambiguous descriptions of this alternative to action-at-a-distance but the way the concept was altered and used by our next electrician, Scotsman James Clerk (pronounced "klark") Maxwell (1831–1879).
Before we leave Faraday, we should clarify his attitude toward atoms. He left us two gemlike quotes from 1839:
Although we know nothing of what an atom is, yet we cannot resist forming some idea of a small particle which represents it to the mind—there is an immensity of facts which justify us in believing that the atoms of matter are in some way associated with electrical powers, to which they owe their most striking qualities, and amongst them their chemical affinity [attraction of atom to atom].
and
I must confess that I am jealous of the term atom, for although it is very easy to talk of atoms, it is very difficult to form a clear idea of their nature when compound bodies are under consideration.
Abraham Pais, citing these statements in his book Inward Bound, concludes: "That is the true Faraday, exquisite experimentalist, who would only accept what he was forced to believe on experimental grounds."
AT THE SPEED OF LIGHT
If the first play was Oersted to Ampère to Faraday, the next was Faraday to Maxwell to Hertz. Although Faraday the inventor changed the world, his science could not stand by itself and would have dead-ended if it were not for Maxwell's synthesis. For Maxwell, Faraday provided a semiarticulate (that is, nonmathematical) insight. Maxwell played Kepler to Faraday's Brahe. Faraday's magnetic lines of force acted as a steppingstone to the field concept, and his extraordinary comment in 1832 that electromagnetic actions are not transmitted instantaneously but require a well-defined time played a key role in Maxwell's great discovery.
Maxwell gave full credit to Faraday, even admiring his mathematical illiteracy because it forced him to express his ideas in "natural, untechnical language." Maxwell asserted that his primary motivation was to translate Faraday's view of electricity and magnetism to mathematical form. But the treatise that evolved went far beyond Faraday.
In the years 1860–1865 Maxwell's papers—models of dense, difficult, complicated mathematics (ugh!)—emerged as the crowning glory of the electrical period of science that had begun in dim history with amber and lodestones. In this final form Maxwell not only set Faraday to mathematical music (albeit atonal) but in so doing established the existence of electromagnetic waves moving through space at some finite velocity, as Faraday had predicted. This was an important point; many of Faraday and Maxwell's contemporaries thought forces were transmitted instantaneously. Maxwell specified how Faraday's field would work. Faraday had found experimentally that a changing magnetic field generates an electric field. Maxwell, struggling for symmetry and consistency in his equations, postulated that a changing electric field would generate a magnetic field. This produced, in the mathematical stuff, a surging back and forth of electric and magnetic fields, which, in Maxwell's notebooks, took off through space, speeding away from their sources at a velocity that depended on all kinds of electrical and magnetic quantities.
But there was a surprise. Not predicted by Faraday, and essentially Maxwell's major discovery, was the actual velocity of these electromagnetic waves. Maxwell pored over his equations, and after he plugged in the proper experimental numbers, out came 3 × 108 meters per second. "Gor luv a duck!" he said, or whatever Scotsmen say when they're surprised. Because 3 × 108 meters per second is the speed of light (which had been measured for the first time a few years earlier). As we learned with Newton and the mystery of the two kinds of masses, there are few real coincidences in science. Maxwell concluded that light is but one example of an electromagnetic wave. Electricity need not be confined to wires but can disseminate through space as light does. "We can scarcely avoid the inference," wrote Maxwell, "that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena." Maxwell opened the possibility, which Heinrich Hertz seized, of verifying his theory by experimentally generating electromagnetic waves. It was left to others, including Guglielmo Marconi and a host of more modern inventors, to develop the second "wave" of electromagnetic technology: radio, radar television, microwave, and laser communications.
Here is the way it works. Consider an electron at rest. Because of its electric charge, an electric field exists everywhere in space, stronger near the electron, weaker as we go farther away. The electric field "points" toward the electron. How do we know there is a field? Simple: place a positive charge anywhere, and it will feel a force pointing toward the electron. Now force the electron to accelerate up a wire. Two things happen. The electric field changes, not instantly but as soon as the information arrives at the point in space where we are measuring it. Also, a moving charge is a current, so a magnetic field is created.
Now apply forces on the electron (and on many of its friends) so that it surges up and down the wire at a regular cycle. The resulting change in electric and magnetic fields propagates away from the wire with a finite velocity—the velocity of light. This is an electromagnetic wave. We often call the wire an antenna and the force driving the electron a radio frequency signal. Thus the signal, with whatever message is contained in it, propagates away from the antenna at the speed of light. When it reaches another antenna, it will find plenty of electrons, which it will, in turn, force to jiggle up and down, creating an oscillating current that can be detected and converted to video and audio information.
Despite his monumental contribution, Maxwell was anything but an overnight sensation. Let's look at what the critics said of Maxwell's treatise:
"A somewhat gross conception."—Sir Richard Glazebrook
"A feeling of uneasiness, often even of mistrust is mingled with admiration..."—Henri Poincaré
"Found no foothold in Germany and was scarcely even noticed."—Max Planck
"I may say one thing about it [the electromagnetic theory of light]. I do not think it is admissible."—Lord Kelvin
With reviews like these it is hard to become a superstar. It took an experimenter to make Maxwell a legend, though not in his own time, for he died about a decade too soon.
HERTZ TO THE RESCUE
The true hero (to this highly biased student of historians) is Heinrich Hertz who, in a series of experiments spanning more than a decade (1873–1888), confirmed all the predictions of Maxwell's theory.
Waves have a wavelength, which is the distance between crests. The crests of water waves in the ocean typically may be twenty to thirty feet apart. Sound wavelengths range around inches. Electromagnetism also comes in waves. The difference between various electromagnetic waves—infrared, microwave, x-rays, radio waves—is simply a matter of their wavelengths. Visible light—blue, green, orange, red—is in the middle of the electromagnetic spectrum. Radio waves and microwaves have longer wavelengths. Ultraviolet, x-rays, and gamma rays have shorter wavelengths.
Using a high-voltage coil and a detection device, Hertz found a way to generate electromagnetic waves and measure their speed. He showed that these waves had the same reflection, refraction, and polarization properties as light waves and that they could be focused. Despite the bad reviews, Maxwell was right. Hertz, in subjecting Maxwell's theory to rigorous experiment, clarified and simplified it to a "system of four equations," which we'll get to in a moment.
After Hertz, Maxwell's ideas became generally accepted, and the old problem of action-at-a-dista
nce was put to rest. Forces in the form of fields propagated through space with a finite velocity, the speed of light. Maxwell felt that he needed a medium to support his electric and magnetic fields, so he adapted the Faraday-Boscovich notion of an all-pervading aether in which the electric and magnetic fields vibrated. Just like Newton's discarded aether, this aether had weird properties and would soon play a crucial role in the next scientific revolution.
The Faraday-Maxwell-Hertz triumph spelled another success for reductionism. No longer did universities have to hire a professor of electricity, a professor of magnetism, and a professor of light or optics. These are all unified, and only one position is now needed (more money for the football team). A vast set of phenomena is encompassed: both things created by science and things natural—like motors and generators, transformers, and an entire electrical power industry, like sunlight and starlight, radio and radar and microwaves, and infrared and ultraviolet light and x-rays and gamma rays and lasers. The propagation of all of these is explained by Maxwell's four equations, which in their modern form, applied to electricity in free space, are written:
In these equations, £ stands for the electric field, £ stands for the magnetic field, and c, the velocity of light, stands for a combination of electric and magnetic quantities that can be measured on a lab bench. Note here the symmetry of E and B. Never mind the incomprehensible doodles; for our purposes it's not important to explain the workings of these equations. The point is, this is the scientific summons: "Let there be light!"