Thematic Essay: Physics, from Leonardo to Hertz

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.”

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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.

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