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 forces 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.
Before we leave "Eff equals emm ay," lets dwell a bit on its power. It is the basis of our mechanical, civil, hydraulic, acoustic, and other types of engineering; it is used to understand surface tension, the flow of fluids in pipes, capillary action, the drift of continents, the propagation of sound in air and in steel, the stability of structures like the Sears Tower or one of the most wonderful of all bridges, the Bronx-Whitestone Bridge, arching gracefully over the waters of Pelham Bay. As a boy, I would ride my bike from my home on Manor Avenue to the shores of Pelham Bay, where I watched the construction of this lovely structure. The engineers who designed that bridge had an intimate understanding of Newton's equation; now, as our computers become faster and faster, our ability to solve problems using F = ma ever increases. Ya did good, Isaac Newton!
I promised three laws and have delivered only two. The third law is stated as "action equals reaction." More precisely it asserts that whenever an object A exerts a force on an object B, B exerts an equal and opposite force on A. The power of this law is that it is a requirement for all forces, no matter how generated—gravitational, electrical, magnetic, and so on.
ISAAC'S FAVORITE F
The next most profound discovery of Isaac N. had to do with the one specific force he found in nature, the Pof gravity. Remember that the F in Newton's second law merely means force, any force. When one chooses a force to plug into the equation, one must first define, quantify that force so the equation will work. That means, God help us, another equation.
Newton wrote down an expression for F (gravity)—that is, for when the relevant force is gravity—called the universal law of gravitation. The idea is that all objects exert gravitational forces on one another. These forces depend on how far apart the objects are and how much stuff each object has. Stuff? Wait a minute. Here Newton's partiality for the atomic nature of matter came in. He reasoned that the force of gravity acts on all atoms of the object, not only, for example, those on the surface. The force is exerted by the earth on the apple as a whole. Every atom of the earth pulls on every atom of the apple. And also, we must add, the force is exerted by the apple on the earth; there is a fearful symmetry here, as the earth must move up an infinitesimal amount to meet the falling apple. The "universal" attribute of the law is that this force is everywhere. It's also the force of the earth on the moon, of the sun on Mars, of the sun on Proxima Centauri, its nearest star neighbor at a distance of 25,000,000,000,000 miles. In short, Newton's law of gravity applies to all objects anywhere. The force reaches out, diminishing with the amount of separation between the objects. Students learn that it is an "inverse-square law," which means that the force weakens as the square of the distance. If the separation of two objects doubles, the force weakens to one fourth of what it was; if the distance triples, the force diminishes to one ninth, and so on.
WHAT'S PUSHING UP?
As I've mentioned, force also points—down for gravity on the surface of the earth, for example. What is the nature of the counterforce, the "up" force, the action of the chair on the backside of the sitter, the impact of wooden bat on baseball, or hammer on the nail, the push of helium gas that expands the balloon, the "pressure" of water that propels a piece of wood up if it is forced beneath the surface, the "boing" that holds you up when you lie on bedsprings, the depressing inability of most of us to walk through a wall? The surprising, almost shocking, answer is that all of these "up" forces are different manifestations of the electrical force.
This idea may seem alien at first. After all, we don't feel electric charges pushing us upward when we stand on the scale or sit on the sofa. The force is indirect. As we have learned from Democritus (and experiments in the twentieth century), most of matter is empty space and everything is made of atoms. What keeps the atoms together, and accounts for the rigidity of matter; is the electric force. (The resistance of solids to penetration has to do with the quantum theory, too.) This force is very powerful. There is enoug
h of it in a small metal bathroom scale to offset the pull of the entire earth's gravity. On the other hand, you wouldn't want to stand in the middle of a lake or step off your tenth-floor balcony. In water and especially in air, the atoms are too far apart to offer the kind of rigidity that will offset your weight.
Compared to the electrical force that holds matter together and gives it its rigidity, the gravitational force is extremely weak. How weak? I do the following experiment in a physics class I teach. I take a length of wood, say a one-foot-long piece of two-by-four, and draw a line around it at the six-inch mark. I hold up the two-by-four vertically and label the top half "top" and the bottom half "bot." Holding top, I ask, "Why does bot stay up when the entire earth is pulling down on it?" Answer: "It is firmly attached to top by the cohesive electrical forces of the atoms in the wood. Lederman is holding top." Right.
To estimate how much stronger the electrical force of top pulling up on bot is than the gravitational force (earth pulling down on bot), I use a saw to cut the wood in half along the dividing line. (I've always wanted to be a shop teacher.) At this point I've reduced the electrical forces of top on bot to essentially zero with my saw. Now, about to fall to the floor, two-by-four bot is conflicted. Two-by-four top, its electrical power thwarted by the saw, is still pulling up on bot with its gravity force. The earth is pulling down on bot with gravity. Guess which wins. The bottom half of the two-by-four drops to the floor.
Using the equation for the law of gravity, we can calculate the difference between the two gravitational forces. It turns out that the earth's gravity on bot wins out by being more than one billion times stronger than top's gravity on bot. (Trust me on this one.) Conclusion: The electrical force of top on bot before the saw cut was at least one billion times stronger than the gravitational force of top on bot. That's the best we can do in a lecture hall. The actual number is 1041, or a one followed by forty-one zeroes!! Let's write that out:
The God Particle: If the Universe Is the Answer, What Is the Question? Page 12