Kepler's genius was often obscured in his books by massive amounts of spiritual clutter. He believed that comets were evil omens, that the universe was divided into three regions corresponding to the Holy Trinity, and that the tides were the breathing of the earth, which he likened to an enormous living animal. (This idea of earth-as-organism has been resurrected today in the form of the Gaia hypothesis.)
Even so, Kepler had a great mind. The stiff-upper-lipped Sir Arthur Eddington, one of the most eminent physicists of his time, in 1931 called Kepler "the forerunner of the modern theoretical physicist." Eddington lauded Kepler for demonstrating an outlook similar to that of the theorists of the quantum age. Kepler didn't look for a concrete mechanism to explain the solar system, according to Eddington, but "was guided by a sense of mathematical form, an aesthetic instinct for the fitness of things."
POPE TO GALILEO: DROP DEAD
In 1597, long before he had worked out the troublesome details, Kepler wrote to Galileo urging him to support the Copernican systern. With typical religious fervor, he told Galileo to "believe and step forth." Galileo refused to come out of the Ptolemaic closet. He needed proof. That proof came from an instrument, the telescope.
The nights of January 4 to 15, 1610, must be recorded as among the most important in the history of astronomy. On those dates, using a new and improved telescope that he had constructed, Galileo saw, measured, and tracked four tiny "stars" moving near the planet Jupiter. He was forced to conclude that these bodies were moving in circular orbits around Jupiter. This conclusion converted Galileo to the Copernican view. If bodies could orbit Jupiter, the notion that all planets and stars orbit the earth is wrong. Like most late converts, whether to a scientific notion or to a religious or political conviction, he became a fierce and unwavering advocate of Copernican astronomy. History credits Galileo, but we must here also honor the telescope, which in his capable hands opened the heavens.
The long and complex story of his conflict with the reigning authority has often been told. The Church sentenced him to life imprisonment for his astronomical beliefs. (The sentence was later commuted to permanent house arrest.) It wasn't until 1822 that a reigning pope officially declared that the sun could be at the center of the solar system. And it took until 1985 for the Vatican to acknowledge that Galileo was a great scientist and that he had been wronged by the Church.
THE SOLAR SPONGE
Galileo was guilty of a less celebrated heresy, one that is closer to the heart of our mystery than the orbits of Mars and Jupiter. In his first scientific expedition to Rome to report on his work with physical optics, he brought with him a little box containing rock fragments discovered by alchemists in Bologna. The rocks glowed in the dark. Today this luminescent mineral is known as barium sulfide. But in 1611 alchemists called it by the much more poetic name "solar sponge."
Galileo brought chunks of solar sponge to Rome to aid him in his favorite pastime: annoying the hell out of his Aristotelian colleagues. As the Aristotelians sat in the dark watching the glow from the barium sulfide, their rogue colleague's point did not escape them. Light was a thing. Galileo had held the rock in the sun, then brought the rock into the darkness and the light had been carried inside with it. This belied the Aristotelian notion that light was simply a quality of an illuminated medium, that it was incorporeal. Galileo had separated the light from its medium, had moved it around at will. To an Aristotelian Catholic, this was like saying you could take the sweetness of the Holy Virgin and place it in a mule or a stone. And what exactly did light consist of? Invisible corpuscles, Galileo reasoned. Particles! Light possessed a mechanical action. It could be transmitted, strike objects, reflect off them, penetrate them. Galileo's realization that light was corpuscular led him to accept the idea of indi visible atoms. He wasn't sure how the solar sponge worked, but perhaps a special rock could attract luminous corpuscles as a magnet attracts iron shavings, though he didn't subscribe to this theory literally. In any case, ideas such as these deepened Galileo's already precarious position with Catholic orthodoxy.
Galileo's historical legacy seems to be inextricably tied to the Church and religion, but he wouldn't have viewed himself as a professional heretic or, for that matter, a wrongly accused saint. For our purposes, he was a physicist, and a great one, far beyond his advocacy of Copernicanism. He broke new ground in many ñelds. He blended experiments and mathematical thinking. When an object moves, he said, it's important to quantify its motion with a mathematical equation. He always asked "How do things move? How? How?" He didn't ask "Why? Why is this sphere falling?" He was aware that he was just describing motion, a difficult enough task for his time. Democritus might have wisecracked that Galileo wanted to leave something for Newton to do.
THE MASTER OF THE MINT
Most Merciful Sir:
I am going to be murdered, although perhaps you may think not but 'tis true. I shall be murdered the worst of all murders. That is in the face of Justice unless I am rescued by your merciful hands.
Thus wrote the convicted counterfeiter William Chaloner—the most colorful and resourceful outlaw of his time—in 1698 to the official who had finally succeeded in capturing, prosecuting, and convicting him. Chaloner had threatened the integrity of English currency, then largely in the form of gold and silver coins.
The object of this desperate appeal was one Isaac Newton, warden (soon to become master) of the Mint. Newton was doing his job, which was to supervise the Mint, oversee a vast recoinage, and protect the currency against counterfeiters and clippers, those who shaved some of the precious metal off the coins and passed them as whole. This position, something like the Secretary of the Treasury, mixed the high politics of parliamentary infighting with the prosecution of thugs, crooks, thieves, launderers, and other riffraff who preyed on the currency of the realm. The crown awarded Newton, the preeminent scientist of his day, the job as a sinecure while he worked on more important things. But Newton took the job seriously. He invented the technique of fluting the edges of coins to defeat clippers. He personally attended the hangings of counterfeiters. The position was a far cry from the serene majesty of Newton's earlier life, when his obsession with science and mathematics generated the most profound advance in the history of natural philosophy, one that would not be clearly surpassed until, possibly, the theory of relativity in the 1900s.
In one of the quirks of chronology, Isaac Newton was born in England the same year (1642) that Galileo died. You can't talk about physics without talking about Newton. He was a scientist of transcendent importance. The influence of his achievements on human society rivals that of Jesus, Mohammed, Moses, and Gandhi, as well as Alexander the Great, Napoleon, and their ilk. Newton's universal law of gravitation and the methodology he created occupy the first half dozen chapters of every textbook on physics; understanding them is essential to anyone pursuing a scientific or engineering career. Newton has been called modest because of his famous statement "If I have seen further than most it is because I have stood on the shoulders of giants," which most assume refers to men such as Copernicus, Brahe, Kepler, and Galileo. Another interpretation, however, is that he was simply twitting his primary scientific rival and nemesis, the very short Robert Hooke, who claimed, not without some justice, to have discovered gravity first.
I have counted more than twenty serious biographies of Newton. And the literature that analyzes, interprets, extends, comments on Newton's life and science is enormous. Richard Westfall's 1980 biography includes ten dense pages of sources. Westfall's admiration for his subject is boundless:
It has been my privilege at various times to know a number of brilliant men, men whom I acknowledge without hesitation to be my intellectual superiors. I have never, however, met one against whom I was unwilling to measure myself, so that it seemed reasonable to say that I was half as able, or a third, or a fourth, but in every case, a finite fraction. The end result of my study of Newton has served to convince me that with him there is no measure. He has become for
me wholly other one of the tiny handful of supreme geniuses who have shaped the categories of the human intellect.
The history of atomism is one of reductionism—the effort to reduce all the operations of nature to a small number of laws governing a small number of primordial objects. The most successful reductionist of all was Isaac Newton. It would be another 250 years before his possible equal would emerge from the masses of Homo sapiens in the town of Ulm, Germany, in 1879.
THE FORCE BE WITH US
To have a sense of how science works, one must study Newton. Yet the Newtonian drill for the students in Physics 101 all too often obscures the power and sweep of his synthesis. Newton developed a quantitative and yet comprehensive description of the physical world that accorded with factual descriptions of how things behave. His legendary connection of the falling apple to the periodic moon captures the awesome power of mathematical reasoning. How the apple falls to the earth and precisely how the moon orbits the earth are included in one all-encompassing idea. Newton wrote: "I wish we could derive the rest of the phenomena of nature by the same level of reasoning from mechanical principles, for I am inclined by many reasons to suspect that they may all depend on certain forces."
By Newton's day how objects moved was known: the trajectory of the thrown stone, the regular swing of the pendulum, the motion down the inclined plane, the free fall of disparate objects, the stability of structures, the shape of a drop of water. What Newton did was organize these and many other phenomena in a single system. He concluded that any change of motion is caused by force and that the response of an object to the force is related to a property of the object he called "mass." Every schoolchild knows that Newton came up with three laws of motion. His first law is a restatement of Galileo's discovery that no force is required for steady, unchanging motion. What we're concerned with here is the second law. It centers around force but is inextricably entwined with one of the mysteries of our story: mass. And it prescribes how force changes motion.
Generations of textbooks have struggled with definitions and logical consistencies of Newton's second law, which is written like this: F = ma. Eff equals emm ay, or the force is equal to the mass multiplied by the acceleration. In this equation Newton defines neither the force nor the mass, and thus it is never clear whether this represents a definition or a law of physics. Nevertheless, one struggles through it somehow to arrive at the most useful physical law ever devised. This simple equation is awesome in its power and, despite its innocent appearance, can be a frightening thing to solve. Awrrk! Ma-a-a-ath! Don't worry, we'll just talk about it, not really do it. Besides, this handy prescription is the key to the mechanical universe, so there is motivation to stay with it. (We shall be dealing with two Newtonian formulas. For our purposes, let's call this formula I.)
What is a? This is the very same quantity, acceleration, that Galileo defined and measured in Pisa and Padua. It can be the acceleration of any object, be it a stone, a pendulum bob, a projectile of soaring beauty and menace, or the Apollo spacecraft. If we put no limit on the domain of our little equation, then a represents the motion of planets, stars, or electrons. Acceleration is the rate at which a speed changes. Your car's accelerator pedal is truly named. If you go from 10 mph to 40 mph in 5 minutes, you have achieved some value of a. If you go from 0 to 60 mph in 10 seconds, you have achieved a much greater acceleration.
What is m? Glibly, it is a property of matter. It is measured by the response of an object to a force. The larger the m, the smaller the response (a) to the imposed force. This property is often called inertia, and the full name given to m is "inertial mass." Galileo invoked inertia in understanding why a body in motion "tends to preserve that motion." We can certainly use the equation to distinguish among masses. Apply the same force—we'll get to what force is later—to a series of objects and use a stopwatch and ruler to measure the resulting motion, the quantity a. Objects having different m's will have different a's. Set up a long series of such experiments comparing the m's of a large number of objects. Once we do this successfully, we can arbitrarily fabricate a standard object, exquisitely wrought of some durable metal. Print on this object "1.000 kilogram" (that's our unit of mass) and place it in a vault at the Bureau of Standards in major capitals of the world (world peace helps). Now we have a way of attributing a value, a number m, to any object. It's simply a multiple or a fraction of our one-kilogram standard.
Okay, enough about mass, what is F? The force. What's that? Newton called it the "crowding of one body on another"—the causative agent for change of motion. Isn't our reasoning somewhat circular? Probably, but not to worry; we can use the law to compare forces acting on a standard body. Now comes the interesting part. Forces are provided to us by a bountiful nature. Newton supplies the equation. Nature supplies the force. Keep in mind that the equation works for any force. At the moment we know of four forces in nature. In Newton's day scientists were just beginning to learn about one of them, gravity. Gravity causes objects to fall, projectiles to soar, pendulums to swing. The entire earth, pulling on all objects on or near its surface, generates the force that accounts for the large variety of possible motions and even the lack of motion.
Among other things, we can use F = ma to explain the structure of stationary objects like the reader sitting in her chair or, a more instructive example, standing on her bathroom scale. The earth pulls down on the reader with a force. The chair or scale pushes up on the reader with an equal and opposite force. The sum of the two forces on the reader is zero, and there is no motion. (All of this happens after she goes out and buys this book.) The bathroom scale tells what it cost to cancel the pull of gravity—60 kilograms or, in the nations of low culture, not yet in the metric system, 132 pounds. "Ohmygod, the diet starts tomorrow." That's the force of gravity acting on the reader. This is what we call "weight," simply the pull of gravity. Newton knew that your weight would change, slightly if you were in a deep valley or on a high mountain, greatly if on the moon. But the mass, the stuff in you that resists a force, doesn't change.
Newton did not know that the pushes and pulls of floors, chairs, strings, springs, wind, and water are fundamentally electrical. It didn't matter. The origin of the force was irrelevant to the validity of his famous equation. He could analyze springs, cricket bats, mechanical structures, the shape of a drop of water or of the planet earth itself. Given the force, we can calculate the motion. If the force is zero, the change in speed is zero; that is, the body continues its motion at constant speed. If you throw a ball up, its speed decreases until, at the apex of its path, it stops and then descends with increasing speed. The force of gravity does this, being directed down. Throw a ball into the outfield. How do we understand the graceful arc? We decompose the motion into two parts, an up-and-down part and a horizontal part (indicated by the shadow of the ball on the ground). The horizontal part has no force (like Galileo, we must neglect the resistance of air, which is a small complicating factor). So the horizontal motion is at constant speed. Vertically, we have the ascent and the descent into the glove of the fielder. The composed motion? A parabola! Yeow! There She goes again, showing off her command of geometry.
Assuming we know the mass of the ball and can measure its acceleration, its precise motion can be calculated by F = ma. Its path is determined: it will describe a parabola. But there are many parabolas. A weakly batted ball barely reaches the pitcher; a powerful smash causes the center fielder to race backward. What is the difference? Newton called such variables the starting or initial conditions. What is the initial speed? What is the initial direction? It can range from straight up (in which case the batter gets bopped on his head) to almost horizontal, where the ball falls quickly to the ground. In all cases the trajectory is determined by the speed and direction at the start of the motion—that is, the initial conditions.
WAIT!!!
Now comes a deeply philosophical point. Given a set of initial conditions for a certain number of objects, and given a knowledge of the f
orces acting on these objects, their motions can be predicted ... forever. Newton's world view is predictable and determined. For example, suppose that everything in the world is made of atoms—a bizarre thought to raise on [>] of this book. Suppose we know the initial motion of each of the billions and billions of atoms, and suppose we know the force on each atom. Suppose some cosmic, mother-of-all-computers could grind out the future location of all these atoms. Where will they all be at some future time, for example on Coronation Day? The outcome would be predictable. Among these billions of atoms would be a small subset called "reader" or "Leon Lederman" or "the pope." Predicted, determined ... with free choice merely an illusion created by a mind with self-interest. Newtonian science was apparently deterministic. The role of the Creator was reduced by post-Newtonian philosophers to winding up the world spring and setting it into operation. Thereafter, the universe could run very well without Her. (Cooler heads dealing with these problems in the 1990s would demur.)
Newton's impact on philosophy and religion was as profound as his influence on physics. All out of that key equation . The arrows remind the student that forces and their consequent accelerations point in some direction. Lots of quantities—mass, temperature, volume, for example—don't point in any direction in space. But "vectors," quantities such as force, velocity, and acceleration, all get little arrows.
The God Particle Page 12
