I.

Introduction

Thematic Essay: Physics, from Leonardo to Hertz

Thematic Essays combine a broad survey of a particular topic with key supplementary readings to create a comprehensive learning experience. In this essay, Nobel Prize-winning physicist Leon Lederman traces the development of classical physics. Accompanying the essay are Sidebars consisting of excerpts from the works of some of the world’s most influential scientific thinkers.

By Leon M. Lederman

The great English physicist Sir Isaac Newton once remarked, “If I have seen further it is by standing on the shoulders of giants.” Indeed, much of what physicists know today can be traced to the giants who lived during a period of scientific discovery often referred to as “classical physics”—a period that runs roughly from the time of Leonardo da Vinci in the 15th century to the time of Heinrich Hertz in the late 19th century. During this nearly 400-year period, many of the key concepts in physics, such as the notion of inertia and the ideas of gravity, electricity, magnetism, and light, were formulated and explained in a few simple equations. Looking back on this period in history and reviewing its accomplishments enable us to understand not only the physics of today but also the modern world we live in.

The period before the beginning of the Renaissance in the 15th century is often referred to as Western Europe's Dark Ages. The principal intellectual accomplishment during the Dark Ages was the preservation of the writings of the ancient Greeks, many of whom made important contributions to the study of science. This preservation was aided by the Egyptians in Alexandria and by the Arabs, who had translated some of the Greek scientists and philosophers, particularly Aristotle and Plato. With the blessing of the Roman Catholic Church, friars translated the Arabic versions of Greek science into Latin, the language of all educated people in Western Europe.

Largely through the work of the friars, the church accepted the teachings of Aristotle, the greatest of ancient Greek scholars. Unfortunately, Aristotle’s writings on astronomy and physics were misguided, and the church blindly adopted these errors. This uncritical approach made things difficult for Italian astronomer Galileo Galilei and others who created modern physics. By opposing Aristotle, they were opposing the Catholic Church, which was then all-powerful in Europe.

The spirit of intellectual curiosity during the Renaissance era, however, prompted a renewed study of nature without preconceived ideas. One of the most important figures in the Renaissance was Italian artist and scientist Leonardo da Vinci.

II.

Leonardo da Vinci

Leonardo is regarded as the consummate Renaissance man not primarily for his scientific accomplishments but because of his extraordinary range of achievements. Leonardo was a painter, sculptor, engineer, architect, physicist, biologist, and philosopher—and he was outstanding in each of these fields. Science influenced all of Leonardo’s activities; he believed in observing nature and carrying out experiments. As a painter, Leonardo studied the laws of optics and the optical structure of the eye; he studied human anatomy with the thoroughness of a medical surgeon to understand how to paint the torso. Leonardo’s ability to solve physics problems in the fields of static (stationary) and dynamic (moving) mechanics fortified his civil and military engineering work.

Leonardo excelled at physics. He anticipated the principle of inertia, which would be demonstrated by Galileo nearly a century later. The inertia principle is the idea that an isolated body, not in contact with anything, will continue moving at a constant velocity forever. Understanding this concept required deep insight since it is not at all easy to imagine an abstract idea such as an “isolated body.” Leonardo knew that the speed of a falling body increases over time. He knew that perpetual motion was impossible as a source of power, and he invented a mathematical scheme for proving the law of the lever. Leonardo worked on the flow of water through pipes, designing an irrigation system and channels. He studied wave motion on water and extended this study to waves in the air and the laws of sound.

Leonardo dismissed with contempt all the work of alchemists, astrologers, and magicians. To him, nature was orderly and subject to logical laws. In most of his scientific work, Leonardo was 100 years ahead of his time.

III.

Copernicus

The first major scientific breakthrough in the mid-1500s was called the Copernican revolution, and it revolutionized science. Nicolaus Copernicus, a Polish mathematician and astronomer, was dissatisfied with the accepted picture of our solar system as developed by the ancient Egyptian astronomer Ptolemy, who did his work around 150 ad. Ptolemy had carefully studied the motion of the planets, but he did so under the assumption that Earth is at rest while the Sun and all the planets somehow move around it. Other early astronomers had noticed that the planets sometimes moved across the sky ahead of the stars, but that they also sometimes reversed themselves. Ptolemy explained this motion as the result of a set of small circles, called epicycles, on which the planets moved. He hypothesized that the epicycles moved on larger circles called deferents, which were centered on Earth, and that the combination of these motions caused the planets’ forward and reverse movements. Ptolemy did not have instruments to make precise observations of planetary motions, and his data were skewed by his failure to realize that Earth also moves.

Copernicus made the bold, courageous assumptions that Earth is just another planet and that it revolves around the Sun. Why bold? Because it seemed absurd to assume that our solid, stable Earth could actually be speeding through space. Why courageous? Because religious authorities had adopted the satisfying idea that the entire universe was centered on Earth, and to refute that idea was to go against the church.

Copernicus’ description of his theory of the universe, written near the time of his death in 1540, is typical of the way modern physicists think and how they strive for simplicity in the description of nature. Copernicus describes his theory of the universe thusly:

As the modern physicist-historian Thomas Kuhn points out, Copernicus’s finding was “an ‘epochal’ turning point in the intellectual development of Western man.” Unlike more modern scientific revolutions, Copernicus’s system of a central Sun orbited by the seven known planets did not immediately affect science, but its social, cultural, moral, and political influence was rapid and profound. Copernicus’s paper was published in 1543, but its influence on physics had to wait for German astronomer Johannes Kepler, Italian astronomer Galileo Galilei, and English physicist and mathematician Sir Isaac Newton. The conceptual challenge centered on the need to understand the new idea that Earth actually moved.

By centering motions around the Sun, the Copernican system made the orbits of planets simpler, whereas the Earth-centric Ptolemaic system created the need for complex epicycles. Still, the overall accuracy of the two systems turned out to be about the same given the relatively low accuracy of astronomical measurements at the time. Consequently, observational precision played a key role in the advance of physics and astronomy. The champion of accuracy in the late 16th century was the Danish astronomer Tycho Brahe, who had valuable help from Kepler.

IV.

Tycho Brahe and Johannes Kepler

Outfitted by the king of Denmark on an island totally dedicated to precise astronomical measurements, Brahe outfitted his laboratory with ingeniously fabricated, beautifully constructed astronomical instruments designed on a large scale. He supplemented the new equipment with a new ethic of continuous and repeated measurement, and he eventually obtained an unprecedented level of precision.

Kepler was Brahe’s assistant. Whereas Brahe was fascinated by the art of making careful measurements of the motion of the planets, Kepler was more interested in trying to arrive at a mathematical picture of the solar system. In the beginning, he followed Copernicus and assumed that the planets performed circular orbits around the Sun, but he soon realized that Brahe’s measurements indicated that the geometric shape of the planets’ orbits could not be a circle.

Kepler converted the calculation of the orbits, described in Brahe’s notebooks as a long string of carefully transcribed numbers, into a figure studied in all geometry classes: the ellipse. Kepler also wrote down several mathematical relations that all planet motions would obey. Kepler’s three laws of planetary motion became famous by the early 1600s and proved to be crucial to the great work of Newton. Kepler’s laws of planetary motion were the direct predecessors of Newton’s theory of gravitation. However, between Kepler’s Sun-centered ellipses and Newton’s revolution, the physics of Galileo and French philosopher René Descartes played crucial roles.

V.

Galileo Galilei

Contemporary scientists regard Galileo as the model of the new scientist. He made major advances in physics, helped popularize physics, and became even more famous when he was arrested and tried by papal authorities. For his discoveries, which directly defied the teachings of the Catholic Church, Galileo was convicted and sentenced to house arrest. This sentence turned out to be a lot better than being jailed or burned at the stake, fates met by many other early scientists who defied church authority.

The story of Galileo starts with his telescope. Galileo reportedly constructed many telescopes after hearing about one built by a Dutch optician. Lenses were quite common in Galileo’s time, and it did not cost him great effort to calculate the separation of lenses that would produce proper magnification. Technology has advanced enormously, of course, and Galileo’s best telescope would not rival a pair of good binoculars today. Nevertheless, the telescope enabled Galileo to make profound discoveries.

First, he determined that the Moon’s surface had mountains and craters and that, like Earth, it was craggy and corrugated. He discovered that, like the Moon, Earth also shines. He then looked at Jupiter, and in one glorious week of careful observations, discovered Jupiter’s moons in orbit around the planet. This finding contradicted the prevailing Aristotelian belief that everything orbited Earth. Galileo opened the heavens to observation. Anyone could look through Galileo’s telescope and conclude, as Copernicus had, that Earth was just another planet. Some prominent philosophers who were critics of Galileo refused to look through the telescope, afraid that their safe conclusions about the way the world worked would be jeopardized.

Galileo’s discoveries of the laws of motion were also revolutionary. By experiment and mathematical analysis, he demonstrated a style of science that has been the model for physicists ever since. Galileo made two major contributions to physics: He advanced the use of mathematics to understand “how nature is,” and he pioneered difficult experiments to test the consequences. Galileo wrote, “Philosophy [science] is written in this grand book, the universe, which stands continually open to our gaze … but this book cannot be understood unless one learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics and its characters are triangles, circles and other geometric figures without which it is humanly impossible to understand nature.”

VI.

Isaac Newton

Newton is considered the greatest physicist of all time, with the debatable exception of German-born American physicist Albert Einstein. Newton carried Galileo’s study of motion forward in a major way. Galileo carried out experiments and described mathematically how objects moved, but he did not address the issue of why they moved. For example, Galileo described the distance an object will fall after a particular amount of time has passed by the equation x = 1/2at².

The x represents the distance moved, and t is the time the object has been falling. The a in the equation stands for the acceleration of the object, which Galileo had defined as a measure of how velocity changes. This quantity depends on conditions. For example, a ball dropped from a tower falls with a particular value of a, whereas a ball sliding down an inclined plane has a much smaller value of a, depending on the angle of the tilt of the plane. But why?

Newton carried Galileo’s equation forward by introducing the concept of force. He began by restating Galileo’s law of inertia as a situation applying to the absence of force. Newton’s first law states “A body in motion remains in motion (with constant velocity) unless acted upon by an external force.” Rest, in Newton’s laws, is merely an example of motion with zero velocity. So force is defined as the agency that changes the state of motion, and thus the velocity, of a body.

Newton’s famous second law relates a to a force acting on the object via the equation F = ma. The quantity m is the “stuff” inside the object, which Newton called inertial mass. The bigger the value of m, the larger the force required to get the object moving—that is, accelerating. Applied to Galileo’s experiments, F is the force of gravity tugging at the object and aimed toward the center of Earth. F is carefully defined as the sum of all forces.

Forces can be exerted by a variety of things—air, surfaces, walls, or hammers. But forces can also be exerted by electric fields and by magnetic fields. Many scientists who explored nature after Newton applied his equation to their own studies of electric and magnetic fields.

Newton’s second law accounted for the motion of planets pulled by the Sun’s gravitational force; the motion of projectiles, influenced by air and the pull of gravity; and the tides, which are caused by ocean waters pulled by the Sun and the Moon. Newton proved mathematically what Kepler had concluded from observations—that planets move in elliptical paths. To make this proof, he had to know the precise form of F. F must change, depending on the distance of the planet from the Sun. So Newton had to guess the way the force of the Sun on a planet grows weaker as the distance between these two objects increases. His guess was an inverse square law, which states that the force of gravity is inversely proportional to the square of the distance between the two objects.

Newton’s equations also took into account the fact that objects have two kinds of masses: inertial mass that resists motion and gravitational mass that encourages motion. He wrote another equation illustrating that for any object, whether it be a steel ball, a wood block, water, or a planet, the two types of masses—gravitational mass and inertial mass—are equal. Einstein would return to this idea in his general theory of relativity, wherein he made the equality of inertia and gravitational masses a key point.

This equality accounts for many curious results. For example, Galileo had discovered that heavy objects and light objects fall with the same speeds. Aristotle was sure that heavy objects would fall faster, although he never tried it. We now can see why Galileo’s discovery is true. The Earth pulls harder on a heavy thing, but the inertial mass of a heavy thing is higher; the two effects cancel out, and all bodies fall with the same speed. Of course, the influence of air complicates the experiment.

The curious behavior of objects in space capsules, which we call weightlessness, works on the same principle. The astronaut, his sandwich, and his drink all float together, apparently without gravity. But gravity is still pulling on the astronaut, and the capsule, and the sandwich. They respond according to their inertia, and the two effects cancel each other out.

Newton’s work was vital to the evolution of modern physics. In fact, many of his theories and conclusions remained free of revisions until the 20th century.

VII.

Electricity and Magnetism

The final stage in the development of classical physics involved the study of electricity. In the 19th century, electricity was considered almost a science unto itself.

Electricity was a mysterious force. At first appearance, it did not seem to occur naturally, except in the frightening form of lightning. Researchers had to do an unnatural thing to study electricity; they had to manufacture the phenomenon before they could analyze it. We have come to realize that electricity is everywhere and that all matter is electrical in nature. In the 19th century, however, electricity was considered quite exotic.

Many heroes in the study of electricity and magnetism emerged between the late 1700s and the early 1800s, many of whom left their names on various electrical units. These scientists include Charles Augustin de Coulomb (the unit of charge), André Ampère (current), Georg Ohm (resistance), James Watt (electrical power), and James Joule (energy). Luigi Galvani gave us the galvanometer, a device for measuring currents, and Alessandro Volta gave us the volt, a unit of potential, or electromotive force. Similarly C. F. Gauss, Hans Christian Oersted, and W. E. Weber all made their mark and left their names on electrical engineering. Only Benjamin Franklin failed to get his name on any electrical unit, despite his significant contributions. All of these scientists contributed to the study of electricity. But the real giants in the field were two 19th-century Englishmen, Michael Faraday and James Clerk Maxwell.

The story of electricity begins in the late 1700s with Galvani’s invention of the battery, which was later improved by Volta, another Italian. Galvani studied frog reflexes by hanging frog muscles on a metal latticework outside his window and watching them twitch during thunderstorms. Volta called this a demonstration of “animal electricity.” Volta discovered that the frog electricity was caused by the action of an electrical current through two dissimilar metals separated by animal tissues, for Galvani’s frogs had hung on brass hooks attached to an iron latticework. Volta was able to produce an electrical current without the frog parts by experimenting with different pairs of metals separated by pieces of leather soaked in brine. He then created a “pile” of zinc and copper plates, realizing that the larger the pile, the more current he could drive through an external circuit. Crucial to this work was Volta’s invention of an electrometer for measuring the current. This research yielded two important results: a laboratory tool for producing currents and a realization that electricity could be produced by chemical reactions.

Another important development was Coulomb’s measurement of the strength and behavior of the electrical force between two charge balls. In 1777 Coulomb invented the torsion balance, a measuring device that was exquisitely sensitive to tiny forces. The force he was after, of course, was electricity. In the mid-1700s Benjamin Franklin had explained that there are two kinds of electricity, which he named plus (+) and minus (-). Franklin called the amount of electricity on an object electric charge. Coulomb discovered that objects with opposite electric charge (+ and -) attract each other and objects with the same electric charge (+ and +) repel one another. Using his torsion balance, he determined that the force between electrical charges varied inversely as the square of the distance between them. This determination, subsequently known as Coulomb’s law, would play a crucial role in our understanding of the atom.

In a brief period from 1820 to 1870, scientists conducted a series of experiments on what they first believed to be the separate phenomena of electricity and magnetism. These experiments led to an understanding that electricity and magnetism were the same phenomenon, which they called electromagnetism, and that light was a form of electromagnetic energy.

VIII.

Secret of the Chemical Bond

Much of the early knowledge of electricity emerged from discoveries in chemistry, specifically in what is now called electrochemistry. Volta’s battery taught scientists that an electrical current can flow around a circuit in a wire that reaches from one pole of the battery to the other. When the circuit is interrupted by wires attached to pieces of metal immersed in a liquid, the current flows through the liquid. The current in the liquid, they found, creates a chemical process called decomposition. If the liquid is water, hydrogen gas appears near one piece of metal, and oxygen near the other. The proportion of two parts hydrogen to one part oxygen indicated that water was being decomposed into its constituent elements, since a molecule of water is made up of two atoms of hydrogen and one atom of oxygen. Similarly, a solution of sodium chloride resulted in a plating of sodium on one terminal and the appearance of the greenish gas chlorine at the other.

The decomposition of chemical compounds by an electrical current indicated a profound connection between electricity and the way atoms bind to each other. This connection led to the theory that the attractions between atoms—that is, the affinity one chemical has for another—were electrical in nature.

IX.

A Shock in Copenhagen

The next steps in understanding electricity unfolded in Copenhagen, Denmark. In 1820 Hans Christian Oersted made a key discovery. Oersted created an electric current in the usual manner, with wires connecting one terminal of a battery to the other. He placed a compass needle, a magnet, near the circuit. When the current flowed, the compass needle veered from pointing to Earth’s magnetic North Pole—its normal position—to taking an odd position at right angles to the wire. Oersted worried about this effect until it dawned on him that, after all, a compass is designed to detect magnetic fields. He realized that the current in the wire must be producing a magnetic field. Oersted had discovered a connection between electricity and magnetism: Currents produce magnetic fields. Magnets, of course, also produce magnetic fields, and their ability to attract pieces of iron had been well studied. The news traveled across Europe and created a great stir.

Using this information, Parisian scientist André Marie Ampère found a mathematical relationship between a current and its magnetic field. The strength and direction of the magnetic field depended upon the strength and direction of the current and on the shape of the wire carrying the current. By a combination of mathematical reasoning and hastily executed experiments, Ampère generated a storm of controversy. Out of this controversy eventually emerged a prescription for calculating the magnetic field produced by an electric current through any configuration of wire, whether the wire was straight, bent, formed into a circular loop, or wound densely on a cylindrical form. Ampère found that a current passing through two straight wires produces two magnetic fields, and these fields can push on each other. This discovery was profound, as it made possible Faraday's experiments with magnetic induction, which is the creation of a current in a conductor when the conductor is moved through a magnetic field, or when the strength of a current in a stationary conducting loop is made to vary. These experiments, in turn, led to the development of the electric motor.

Oersted, like so many other scientists, drove toward unification, simplification, and reduction. He believed that gravity, electricity, and magnetism were all different manifestations of a single force, which is why his discovery of a direct connection between two of these forces was so exciting. Ampère, too, looked for simplicity; he essentially tried to eliminate magnetism by considering it an aspect of electricity in motion, a field of study that would later become known as electrodynamics. The discoveries of Oersted and Ampère served as springboards for the work of Faraday, one of the most unlikely scientists and successful experimenters of all time.

X.

Michael Faraday

Born into poverty, Michael Faraday was unschooled but had a strong religious upbringing. Apprenticed to a bookbinder at the age of 14, he actually managed to read some of the books he bound. He thus educated himself while developing a manual dexterity that would serve him well as an experimenter. One day a client brought in a copy of the third edition of the Encyclopaedia Britannica to be rebound, including a volume with an article on electricity. Faraday read it and was hooked, and the world was never the same.

Over the next 50 years Faraday's discoveries literally electrified England and set in motion as radical a change in the way people live as has ever resulted from the inventions of one human being.

Faraday accomplished an amazing amount in the way of science and invention. Starting his professional life as a chemist at the age of 21, he discovered a number of organic compounds, including benzene. He made the transition to physics by thoroughly exploring the principles of electrochemistry. Faraday then went on to make major discoveries in the fields of electricity and magnetism. He was the first to produce an electric current from a magnetic field. He invented the electric motor and dynamo, demonstrated the relation between electricity and chemical bonding, and discovered the effect of magnetism on light. Faraday accomplished all this without a Ph.D., M.A., B.A., or high school equivalency degree. He was also mathematically illiterate. Faraday recorded his discoveries not in equations but in plain descriptive language, often accompanied by pictures based on his mental images, which helped him explain the data.

Faraday began his work in electrochemistry by systemizing the nomenclature. He called the metals immersed in the liquid electrodes. The negative electrode was a cathode, the positive an anode. When the electricity zipped through the water, it caused charged atoms to migrate through the liquid from cathode to anode. Normally, chemical atoms are neutral, having neither a positive nor a negative charge. But the electric current somehow charged the atoms. Faraday called these charged atoms ions. Scientists later learned that an ion is an atom that has become charged because it has lost or gained one or more electrons. Although the existence of electrons was unknown in Faraday’s time, some evidence suggests that he suspected their existence. In the 1830s he carried out a series of spectacular experiments that resulted in two simple summary statements known as Faraday’s laws of electrolysis:

What these laws mean is that electricity is not smooth and continuous but can be divided into “chunks.” Faraday’s laws tell us that atoms in the liquid (ions) migrate to the electrode, where each ion is presented with a particular quantity of electricity. The Faraday laws thus point to an unavoidable conclusion: There are particles of electricity. This conclusion, however, had to wait about 60 years to be dramatically confirmed by the discovery of the electron.

The route to the modern understanding of electricity is akin to a double play combination in baseball: in this case, Oersted to Ampere to Faraday. Oersted and Ampere 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.

Faraday struggled for a long time to unify electricity and magnetism. If electricity can make magnetic fields, he wondered, can magnets make electricity? Indeed, why not, he reasoned, since nature loves symmetry? It took Faraday more than ten years, from 1820 to1831, to prove that the process was indeed possible, and it was arguably his greatest achievement. Faraday's experimental discovery is called electromagnetic induction, and the symmetry he sought emerged in a surprising form.

Faraday wondered whether a magnet could move a current-carrying wire. Visualizing the forces, he rigged up a device in which one end of a wire was connected to a battery and the other end hung in a beaker of mercury, a liquid conductor that helped the current flow. The electric wire hung free so it could revolve around an iron magnet in the beaker. When he turned the current on, the wire moved in a circle around the magnet. Faraday had converted electricity to motion with this invention, which we know today as an electric motor.

In another experiment, Faraday wrapped a large number of turns of copper wire on one side of a soft iron doughnut, and 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.) Faraday now had two coils wound on opposite sides of a doughnut. One coil, call it coil A, is connected to a battery, while the other, coil B, is connected to a galvanometer. What happened when he turned 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, but only momentarily. After the sudden jump, the needle remained pointed maddeningly to zero. When Faraday disconnected the battery, the needle deflected briefly in the opposite direction, then again pointed at zero. Increasing the sensitivity of the galvanometer had no effect. Increasing the number of turns in each coil still had no effect. Even using a much stronger battery had no effect. And then what scientists call the “Eureka” moment came: Faraday figured out that a changing current in the first coil had induced a current in the second, but only when the first current was actively turning on or off—that is, in the process of changing. As soon as the current—and the surrounding magnetic field—became stable, the field stopped inducing a change in the second coil. As Faraday suspected, and as the next 30 years or so of research would demonstrate, a changing magnetic field generates an electric field.

The technology that eventually emerged from this discovery was the electric generator. By rotating a magnet mechanically, it is possible to 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 humankind had a potential way to generate electricity and turn night into day.

Faraday built the first hand-cranked electrical generator, which in those days was called a dynamo. But he was too involved in the process of experimenting and making new discoveries 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 had. 'I know not, but I wager that one day your government will tax it,' said Faraday. Sure enough, a tax on electrical generation was levied in England in 1880.

XI.

The Field Be with You

Faraday introduced the concept of field, which he defined as a space surrounding an object, such as an electron or magnet, in which other objects are subject to or affected by a force. The most common example of field is a magnet attracting iron nails. Faraday pictured the space around the magnet or coil as being 'strained' because of the magnetic force. The field concept emerged painfully over many years in many writings, and historians enjoy arguing about how and when it all came out. Faraday noted 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.' Thus the concept is that a 'disturbance'—for example a magnetic field—can travel through space and notify a grain of iron powder not only that it is there but also that it can exert a force.

Magnetic lines of force are revealed in an old experiment students do in school, in which they sprinkle iron powder on a sheet of paper placed over a magnet. The student gives the paper a tap to break the surface friction, and the iron powder clusters in a definite pattern of lines connecting the poles of the magnet. Faraday thought these lines were real manifestations of his field concept, and he provided detailed, if ambiguous, descriptions of this alternative to action-at-a-distance. Action-at-a-distance refers to the ability of one object to affect other objects without actually contacting them, and Faraday introduced the concept of the field as an explanation of how this can occur. The field concept was altered, used, and ultimately perfected by Maxwell.

XII.

At the Speed of Light: James Clerk Maxwell

Although Faraday the inventor changed the world, his science could not stand by itself and would have dead-ended if it were not for the synthesis performed by Scottish physicist James Clerk (pronounced 'klark') Maxwell. Maxwell played Kepler to Faraday's Brahe. Faraday's magnetic lines of force acted as a stepping-stone to the field concept. His extraordinary conclusion in 1832, that electromagnetic actions are not transmitted instantaneously but instead 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 claimed 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’s discoveries.

In the years from1860 to1868, Maxwell's papers—models of dense, difficult, complicated mathematics—emerged as the crowning glory of the electrical period of science that had begun in dim history with amber and lodestones. Maxwell not only set Faraday to mathematical music but, in so doing, also established the existence of electromagnetic waves moving through space at some finite velocity, as Faraday had predicted. This was an important point, as many of Faraday and Maxwell's contemporaries thought forces were transmitted instantaneously. Maxwell specified how Faraday's field would work. Faraday had found through experimentation that changing a 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 essential to Maxwell's major discovery, was the actual velocity of these electric magnetic waves. Maxwell pored over his equations, and after he plugged in the proper experimental numbers, out came 3 x 10⁸ meters per second. This number just happens also to be the speed of light, which had been measured for the first time a few years earlier. Maxwell knew that few real coincidences occur in science, and he therefore concluded that light is but one example of an electromagnetic wave. Electricity, it follows, 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 later 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, growing weaker with distance. The electric field 'points' toward the electron. To detect the field, place a positive charge anywhere, and it will feel a force pointing toward the negative charge of the electron. Now, force the electron to accelerate up a wire and 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. A moving charge is a current, so a magnetic field is created.

Now apply forces on the electron 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 the velocity of light. This is an electromagnetic wave. The wire is called an antenna, and the force driving the electron is a radio frequency signal. 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. It took more than a decade of further experimentation for his ideas to become accepted, a triumph that Maxwell, alas, did not live to experience.

XIII.

Hertz to the Rescue

The true hero of the unification of electromagnetism and light is Heinrich Hertz, who, in a series of experiments from 1873 to 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 6 to 9 m apart, while sound wavelengths range in centimeters. Electromagnetism also comes in waves. The difference between various electromagnetic waves—infrared, microwaves, 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 visible light waves and that these waves could be focused. It turned out that Maxwell was right. Hertz, in subjecting Maxwell's theory to rigorous experiment, clarified and simplified it into a system of four equations.

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 believed that he needed a medium to support his electric and magnetic fields, so he adapted the popular notion of an all-pervading ether, in which the electric and magnetic fields vibrated. This part of Maxwell’s theory would be discarded when the existence of the ether was disproved by experimentation in the late 1800s.

The Faraday-Maxwell-Hertz triumph spelled another success for reductionism (the idea that complex forces can be explained as aspects of a single force). No longer did universities have to hire a professor of electricity, a professor of magnetism, and a professor of light or optics. Since these subjects are all unified, only one staff position is now needed (more money for the football team). A vast set of phenomena was thus encompassed, including things created by science and technology and things belonging to the natural world—things like motors and generators, transformers, and an entire electrical power industry, and things like sunlight and starlight; radio, radar and microwaves; and infrared and ultraviolet light and X rays and gamma rays.

Maxwell’s four simple equations are famous in the world of physics, and physics and engineering students the world over wear T-shirts sporting them. For our purposes, it is not important to list them or explain their workings. The point is that they symbolize the scientific summons, “Let there be light!”

Maxwell's original equations were very long and bulky. Hertz rewrote them into much simpler versions that were easier to work with and understand. Hertz was a rare example of a scientist 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. Hertz's theoretical work consisted largely of reducing and popularizing Maxwell’s theory, an effort that made great strides in physicists’ continuing quest to unify all the forces of nature.

As the 19th century drew to a close, the powerful combination of Newton’s laws of motion, Newton’s law of gravity, and Maxwell’s equations provided the tools needed to explain seemingly all scientific phenomenon. Gravitational force explained the solar system and the motion of objects, matter was somehow made of electrically charged objects, and Newton’s law of motion enabled calculations that showed how these charged objects could attract to make atoms. The chemists had already proven the existence of atoms; only their detailed structure remained to be discovered. In 1897 British physicist Sir Joseph J. Thomson discovered the electron, further clarifying the basic structure of matter. The laws of thermodynamics, generated in part by Faraday’s discoveries, also helped round out the scientific picture by giving direction to chemical reactions and physical processes, and ushered in the beginning of the Industrial Revolution.

Optimism about the so-called end of science, the belief that all scientific mysteries could be understood, began to fade around 1900. With the end of the millennium, it became increasingly clear that some of the puzzles of physics could not be solved by the Newton/Maxwell set of intellectual armaments, however powerful they might be. The challenge inherent in this realization heralded a revolution, one that would prove to make the 20th century the most scientifically productive era in the history of humankind.

About the author: Physicist, professor, and author Leon M. Lederman is director emeritus of the Fermi National Accelerator Laboratory in Batavia, Illinois. Lederman won the Nobel Prize in physics in 1988 for his work with elementary particles. He has taught at Columbia University in New York City, the University of Chicago, and the Illinois Institute of Technology in Chicago.