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CHAPTER ONE
Knowing
YOUR LIFE IS FILLED with routine—you set your alarm clock at night, take a shower in the morning, brush your teeth after breakfast, pay your bills on time, and fasten your seat belt. With each of these actions and a hundred others every day you acknowledge the power of predictability. If you don’t set the alarm you’ll probably be late for work or school. If you don’t take a shower you’ll probably smell. If you don’t fasten your seat belt and then get into a freeway accident you may die.
We all seek order to deal with life’s uncertainties. We look for patterns to help us cope. Scientists do the same thing. They constantly examine nature, guided by one overarching principle:
The universe is regular and predictable.
The universe is not random. The sun comes up every morning, the stars sweep across the sky at night. The universe moves in regular, predictable ways. Human beings can grasp the regularities of the universe and can even uncover the basic, simple laws that produce them. We call this activity “science.”
WAYS OF KNOWING
Science is one way of knowing about the world. The unspoken assumption behind the scientific endeavor is that general laws, discoverable by the human mind, exist and govern everything in the physical world. In its most advanced form, science is written in the language of mathematics, and therefore is not always easily accessible to the general public. But, like any other language, the language of science can be translated into simple English. When this is done, the beauty and simplicity of the great scientific laws can be shared by everyone.
Science is not the only way, nor always the best way, to gain an understanding of the world in which we find ourselves. Religion and philosophy help us come to grips with the meaning of life without the need for experimentation or mathematics, while art, music, and literature provide us with a kind of aesthetic, nonquantitative knowledge. You don’t need calculus to tell you whether a symphony or a poem has meaning for you. Science complements these other ways of knowing, providing us with insights about a different aspect of the universe.
The Regularity of Nature
Our ancestors perceived the universe in ways that sometimes seem very strange to us. For all but the past few hundred years of human existence the universe was viewed by most people as a place without deep order or rules, governed by the whims of the gods or even by chance. By noting the daily movements of objects in the sky, however, our ancestors got their first hints that some kind of order and regularity might exist in nature. The position of the sun, the phases of the moon, and the dominant constellations of stars cycled over the years, decades, and centuries with unerring regularity. Whatever governs its motion, the fact is that the sun does come up every morning.
Most historians of science point to the need for a reliable calendar to regulate agricultural activity as the impetus for learning about what we now call astronomy. Early astronomy provided information about when to plant crops and gave humans their first formal method of recording the passage of time. Stonehenge, the 4,000-year-old ring of stones in southern Britain, is perhaps the best-known monument to the discovery of regularity and predictability in the world we inhabit. The great markers of Stonehenge point to the spots on the horizon where the sun rises at the solstices and equinoxes—the dates we still use to mark the beginnings of the seasons. The stones may even have been used to predict eclipses. The existence of Stonehenge, built by people without writing, bears silent testimony both to the regularity of nature and to the ability of the human mind to see behind immediate appearances and discover deeper meanings in events.
The Invention of Science
Astronomy was the first science. Throughout history some of the best minds produced by the human race have pondered the meaning of the celestial display. Most of the resulting theories shared a common property—they all assumed that in some way Earth was special, and that what happened in the heavens had no relevance to phenomena on Earth. In one important version of the universe, for example, the stars and the planets turned eternally on crystal spheres, and their motion had nothing to do with mundane events like the fall of an apple in an orchard. People who believed that the universe was built this way produced a large body of accurate observations of the positions of heavenly bodies, but astronomers were divorced from craftsmen and artisans who were doing different things for the development of science.
While the astronomers were gazing into the heavens, other men and women, equally ingenious, were trying to understand the way things operated on Earth. Their motivation was practical: they studied the properties of heated metals because they wanted to develop stronger alloys, they studied the flow of fluids because they wanted to build canals, they experimented with different combinations of ingredients to make better-tasting food and more effective medicines, and so on. They never seemed to think that the prosaic tasks in which they were engaged had anything to do with the stars and planets.
The branch of science that finally broke out and forged a link between the cerebral astronomers and the practical artisans was “mechanics.” This is an old term for the study of motion. Every system, natural or man-made, contains matter in motion. Planets orbit, blood circulates, chemicals explode, people walk. Mechanics is the superbly pragmatic science of pocket billiards and car crashes, cannonballs and guided missiles. Today, the principles of mechanics point to such useful things as stronger buildings, faster cars, more exciting sports, and, as always, more sophisticated weapons. But more important from the point of view of the birth of modern science, the study of mechanics blazed the trail that subsequent scientists have followed. While studying mechanics, scientists developed and refined the scientific method, a technique that has given us so many new insights into the universe we inhabit.
THE CLOCKWORK UNIVERSE
Modern science can be said to have started with the work of Isaac Newton (1642–1727) in England. According to Newton, the universe is something like a clock. In a clock, the external appearance—the slow sweeping of the hands—is a result of the motion of internal gears. In the same way, all of the natural phenomena we see in the world around us are the result of a few natural laws working beneath the surface of things. Newton demonstrated that:
One set of laws describes all motion.
For Newton, the key fact about motion was that it occurs in response to the action of one or more forces. The “gears” that connect forces and motion are Newton’s three laws of motion, and they apply to everything that moves. Gases streaming out of an exploding star, a football thrown downfield, and blood cells in your arteries all move in compliance with these very simple, but very general, laws.
MOTION
Uniform Motion and Acceleration
If you’re going to study something like motion, the first thing you have to do is decide what sorts of motion are found in nature. Scientists recognize only two kinds: uniform and accelerated. Everything in the universe is either in uniform motion or accelerating.
Any object that stands still or moves in a straight line at constant speed is in uniform motion. A book sitting on your desk, a car driving along an interstate with the cruise control set at 65 mph, and a spaceship traveling at 1,000 miles per second in deep space are all in uniform motion.
Acceleration is any change in motion and occurs when something speeds up, slows down, or changes direction. This definition may seem a little strange, because when you drive a car “acceleration” means speeding up—not slowing down or turning a corner. Physicists use a more general meaning for acceleration—but whatever the definition, it’s something you feel in your gut. Flooring the gas pedal on your car, braking for a light, or rounding a bend all tend to move you around in your seat. And there’s nothing subtle about acceleration—people don’t ride roller coasters to experience uniform motion.
Newton’s Laws and the Idea of Force
Isaac Newton, building on results from centuries of experiments on moving objects, wrote down a compact set of laws that describes the nature of all motion. That these laws apply to such an immense assortment of situations illustrates the power behind thinking of nature as regular and predictable. Newton’s three laws of motion provide a cornerstone of physics and a model for what a science is supposed to be.
Newton’s laws tell us how to predict the motion of a system just by knowing the forces that act on it. The three laws are stated separately, but they work together like separate gears that run a clock. Like all the fundamental laws that govern science, Newton’s laws of motion may seem simple—almost simplistic. The deepest insights of the human mind often have this characteristic. Yet, as generations of physics students can testify, there is a subtlety and richness behind this apparent simplicity—how else could the laws describe everything from the orbits of Neptune’s moons to the movement of exploding gases in your car’s engine?
The First Law
Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it.
Newton has hidden two important concepts in this intuitively obvious statement. The first is inertia—the tendency of objects to continue doing what they’re doing. A rolling ball keeps on rolling, a rotating planet keeps on rotating, a stationary book keeps on sitting.
The second concept is force—the thing that compels objects to change their state of motion (i.e., accelerate). Rolling balls can slow down if acted upon by a force. A book will move if pushed.
The point of Newton’s first law is that changes in motion do not happen spontaneously—there is always a reason for the change. A pencil falls, wind blows, popcorn pops. You encounter hundreds of examples every day. If an object accelerates, some kind of force must be acting. Behind every action verb is a force.
The first law, by itself, says nothing about what forces are, what produces them, or how many different kinds there might be. Indeed, it took physicists more than two hundred years after Newton to discover the forces that hold atoms together, and we are still working to understand the force that cements the nucleus. Nevertheless, the first law tells us what a force does when it acts, and, perhaps more important, it tells us how we can recognize situations in nature in which a force is present.
The Second Law
Force equals mass times acceleration.
Newton’s second law defines the exact relationship between an object’s bulk, its acceleration, and the forces exerted on it. This is a commonsense sort of law that embodies two intuitively reasonable ideas. First, the second law says the greater the force, the greater the acceleration. The harder a pitcher throws, for example, the faster the ball travels. The more powerful your car engine, the better the pickup.
The second part of the law introduces the concept of mass, which is simply the amount of stuff being accelerated. Many of us use the words “mass” and “weight” interchangeably. That’s not quite correct, because an object’s weight depends on the local force of gravity (things weigh less on the moon), but the mass depends only on how much stuff there is (how many atoms there are). Again, common sense prevails. Objects with lots of mass (refrigerators, boulders, football linemen) are a lot harder to move than objects with less mass (ice cubes, pebbles, quarterbacks).
The second law is quantitative—it can be written down as an equation (F = ma, if you really want to know). Numbers can be plugged into the equation to find out exactly how fast a spear, cannonball, or spaceship of known mass will travel if it is acted upon by a known force.
In a typical mechanics problem, we know the mass of something (a billiard ball, for example, or a planet) and the force acting on it (the push of a cue stick or gravity). We then use Newton’s second law and the branch of mathematics known as calculus to predict how the thing will move.
Why Newton Would Tell You to Wear a Seat Belt
Imagine yourself driving at 60 miles per hour along the freeway when another car forces you off the road. What happens if you smash into a tree head-on? Newton’s laws of motion provide the answer.
You and the car have considerable inertia, which will be dealt with, one way or another, by the application of a force. The tree applies a force to the car, stopping it. In the absence of a seat belt, however, no force is applied to you, so you keep on moving. You are, in Newton’s words, “an object in a state of uniform motion,” and you will therefore “continue in a state of uniform motion unless acted on by a force.” The extent of your injuries will be determined by how that force is applied. Without a seat belt the driver and passengers will keep moving until they hit the steering wheel or the windshield.
Seat belts and air bags act to slow you down by applying a smaller force over a longer time, and that’s a much safer method of applying the stopping force than hitting the steering wheel or windshield. The total change of motion with or without seat belts and air bags is exactly the same, but with modern safety technology the injury-causing force is not nearly so great.
The Third Law
To every action force there is an equal and opposite reaction force.
Even though this law is probably the most often quoted of the three, it is the least intuitive. It is obvious that a pitcher exerts a force on the ball, but less obvious that the ball pushes back on the pitcher’s hand with an equal and opposite force. When you stand up, your shoes apply a force to Earth just as large as the force Earth’s gravity exerts on you. When you try to open a screw-top bottle that is stuck, your left hand twists one way while the right hand is twisted the opposite way. You cannot touch your lover without feeling his or her touch in return.
The third law says that forces always come in equal and opposite pairs, but that the forces in the pairs act on (and therefore accelerate) different objects. You are pushing down on the chair in which you are sitting. The third law says that the chair is exerting an equal upward force on you. You really can learn Newton’s laws by the seat of your pants.
