The God Particle: If the Universe Is the Answer, What Is the Question?
Page 17
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 can 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 si
mply 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-distance 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!"
Physics and engineering students the world over wear T-shirts sporting these four crisp equations. Maxwell's original equations, however, looked nothing like the above. These simple versions are the work of Hertz, a rare example of someone who was more than the usual experimenter with only a working grasp of theory. He was exceptional in both areas. Like Faraday, he was aware of, but uninterested in, the immense practical importance of his work. He left that to lesser scientific minds, such as Marconi and Larry King. Hertz's theoretical work consisted largely of cleaning up Maxwell, reducing and popularizing his theory. Without Hertz's efforts, physics students would have to lift weights so they could wear triple-extra-large T-shirts in order to accommodate Maxwell's clumsy mathematics.
True to our tradition and our promise to Democritus, who recently faxed us a reminder, we have to interview Maxwell (or his estate) on atoms. Of course he believed. He was also the author of a very successful theory that treated gases as an assembly of atoms. He believed, correctly, that chemical atoms were not just tiny rigid bodies, but had some complex structure. This belief came out of his knowledge of optical spectra, which became important, as we shall see, in the development of quantum theory. Maxwell believed, incorrectly, that his complex atoms were uncuttable. He said it so beautifully in 1875: "Though in the course of ages catastrophies have occurred and may yet occur in the heavens, though ancient systems may be dissolved and new systems evolved out of their ruins, the [atoms] out of which these systems [earth, solar system, and so on] are built—the foundation stones of the material universe—remain unbroken and unworn." If only he had used the terms "quarks and leptons" instead of "atoms."
The ultimate judgment on Maxwell comes again from Einstein, who stated that Maxwell made the single most important contribution of the nineteenth century.
THE MAGNET AND THE BALL
We have glossed over some important details in our story. How do we know that fields propagate at a fixed speed? How did physicists in the nineteenth century even know what the speed of light was? And what is the difference between instantaneous action-at-a-distance and time-delayed response?
Consider a very powerful electromagnet at one end of a football field and, at the other end, an iron ball suspended by a thin wire from a very high support. The ball tilts ever so slightly toward the faraway magnet. Now suppose we very rapidly turn the current off in the electromagnet. Precise observations of the ball and its wire would record a response as the ball relaxes back to its equilibrium position. But is the response instantaneous? Yes, say the action-at-a-distance folk. The connection between magnet and iron ball is tight and, when the magnet disappears, the ball instantaneously begins to move back to zero tilt. "No!" say the finite-velocity people. The information "magnet is turned off, you can relax now" travels across the gridiron with a definite velocity, so the ball's response is delayed.
Today we know the answer. The ball has to wait, not very long because the information travels at the speed of light, but there is a measurable delay. But in Maxwell's time this problem was at the heart of a raging debate. At stake was the validity of the field concept. Why didn't scientists just do an experiment and settle the issue? Because light is so fast that it takes only one millionth of a second to cross the football field. In the 1800s that was a difficult delay to measure. Today it is trivial to measure time intervals a thousand rimes shorter so the finite propagation of electromagnetic happenings is easily gauged. For example, we bounce laser signals off a new reflector on the moon to measure the distance between earth and moon. The round trip takes about 1.0 second.
An example on a larger scale: On February 23, 1987, at exactly 7:36 UT Greenwich mean time, a star was observed to explode in the southern sky. This supernova event took place in the Large Magellanic Cloud, a cluster of stars and dust located 160,000 light-years away. In other words, it took 160,000 years for the electromagnetic information from the supernova to arrive at planet earth. And Supernova 87A was a relatively near neighbor. The most distant object observed is about 8 billion light-years old. Its light set out for our telescope rather close to the Beginning.
The velocity of light was first measured in an earthbound laboratory by Armand-Hippolyte-Louis Fizeau, in 1849. Lacking oscilloscopes and crystal-controlled clocks, he used an ingenious arrangement of mirrors (to extend the length of the light path) and a rapidly rotating toothed wheel. If we know how fast the wheel is turning, and we know the radius of the wheel, we can calculate the time it takes for a gap to be replaced by a tooth. We can adjust the rotation speed so that this time is precisely the time a light beam takes to proceed from gap to distant mirror and back to gap, and then through gap to the eyeball of M. Fizeau. Mon dieu! I see it! Now gradually speed up the wheel (shorten the time) until the light is blocked. There. Now we know the distance the beam traveled—from light source through gap to mirror and back to wheel tooth—and we know the time it took. Fiddling with this arrangement gave Fizeau the famous number 300 million (3 × 108) meters per second or 186,000 miles per second.
I am continually surprised at the philosophical depth of all these guys during this electromagnetic renaissance. Oersted believed (contrary to Newton) that all forces of nature (at the time: gravity, electricity, and magnetism) were different manifestations of one primordial force. This is s-o-o-o modern! Faraday's efforts to establish the symmetry of electricity and magnetism invokes the Greek heritage of simplicity and unification, 2 of the 137 goals at Fermilab in the 1990s.
TIME TO GO HOME?
In these past two chapters we've covered more than three hundred years of classical physics, from Galileo to Hertz. I've left out some good people. The Dutchman Christiaan Huygens, for example, told us a lot about light and waves. The Frenc
hman René Descartes, the founder of analytical geometry, was a leading advocate of atomism, and his sweeping theories of matter and cosmology were imaginative but unsuccessful.
We've looked at classical physics from an unorthodox point of view, that of searching for Democritus's a-tom. Usually the classical era is viewed as an examination of forces: gravity and electromagnetism. As we've seen, gravitation derives from the attraction between masses. In electricity Faraday recognized a different phenomenon; matter is irrelevant here, he said. Let's look at force fields. Of course, once you have a force you must still invoke Newton's second law (F = ma) to find the resultant motion, and here inertial matter really matters. Faraday's matter-doesn't-matter approach was derived from the intuition of Boscovich, a pioneer in atomism. And, of course, Faraday provided the first hints about "atoms of electricity." Perhaps one isn't supposed to look at science history this way, as a search for a concept, the ultimate particle. Yet, it's there beneath the surface in the intellectual lives of many of the heroes of physics.