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Prologue: The Apple and the Moon
A falling apple tells us that the same laws govern heaven and earth.
I began to think of gravity extending to ye orb of the Moon & ... I deduced that the forces well keep the Planets in their Orbs must [be] reciprocally as the squares of their distances from the centers about well they revolve: & thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the earth, & found them answer pretty nearly. All this was in the two plague years of 1665-1666. For in those days I was in the prime of my age for invention and minded Mathematicks & Philosophy more than at any time since.
-NEWTON in his memoirs
THE PLAGUE
In the summer of 1665, England was visited by the plague. Cambridge University was closed, and the students were sent home. Among them was Isaac Newton, then twenty-three years old. He returned to his family farm at Woolsthorpe and spent the next two years there thinking and studying in rural isolation. One day an apple fell on his head. That fateful encounter between two solid objects inspired Newton to invent his theory of gravity.
Who will ever know if the story is true? It sounds as if it were fabricated by some scriptwriter. Actually, it was first told by Newton himself in his old age. In any case, it's a pretty good story, tinged with the Judeo-Christian imagery of the apple as the fruit of knowledge.
WHO WAS SIR ISAAC NEWTON?
Physicists revere Newton as the greatest of their profession who ever lived, and it is no exaggeration to say that his work laid the foundation of physical science as we know it. But who was Sir Isaac Newton?
This great genius was the first person on his father's side able to write his name. His father's brother saw no need to educate his sons, and they died illiterate. His mother was barely able to write and not particularly enthusiastic about sending Isaac to school. Newton was educated only at the urging of his mother's brother; that maternal uncle was in fact the only educated person in the entire clan.
Newton's paternal ancestors had risen within a century from obscure peasanthood to land ownership, a rise suggesting that they were above average in intelligence. Newton's father, said to be "a wild, extravagant, and weak man," died six months after his marriage. Newton was born fatherless some months later, on Christmas morning 1642. He was premature and so tiny that no one expected him to live.
When the fatherless boy turned three, his mother remarried, to a sixty-three-year-old clergyman. Bombastic and rather obnoxious, the reverend refused to let Newton live with his mother. Psychoanalysts have not hesitated to seize upon this traumatic loss of mother as an explanation for Newton's later behavior. As befitting the religious upbringing of the time, Newton kept note of his sins, and one of them was threatening to burn his stepfather and mother and their house.
When Newton was ten, his stepfather died. He was reunited with his mother but apparently felt intense jealousy, as his stepfather had in the meantime produced three children with Newton's mother. The reunion was brief as he was soon sent off to school in town. He lodged with an apothecary and apparently grew quite attached to the apothecary's stepdaughter. It was to be the first and last romantic attachment to a woman in his life.
When Newton turned seventeen, his mother decided that it was time for him to come home and help on the farm. Told to herd sheep, Newton would simply wander off and read. Court records showed that on several occasions he was fined for allowing his sheep to stray into the neighbor's fields. Newton's own list of sins for this period included "Punching my sister," "Peevishness with my mother," "Falling out with the servants," and "Striking many." The servants hated him and described him as a surly and lazy good-for-nothing.
Meanwhile, Newton's maternal uncle and the schoolmaster lobbied with his mother to let Newton go back to school. She relented only when the schoolmaster offered to waive the fee and to take Newton in at his own home. Newton's mother appeared to be quite a miser, as she was actually rather wealthy from the combined estates of her two husbands. When Newton went to Cambridge, he had to enroll as a subsizar, a poverty student who earned his way by performing menial tasks for the wealthier students. He fetched beer and emptied chamber pots, among other duties. The experience was mortifying for someone who grew up being surly to servants.
Richard S. Westfall, a leading Newton biographer, describes Newton as "a tortured man, an extremely neurotic personality who teetered always, at least through middle age, on the verge of breakdown." Small wonder, after that kind of boyhood. It doesn't take much psychoanalysis to see Newton's numerous bitter and nasty disputes with his scientific contemporaries as an expression of his infantile rage at his stepfather.
Newton was particularly ruthless in crushing his major scientific rival, Robert Hooke, seven years his senior and considered England's greatest scientist until Newton appeared on the scene. It is interesting to note in this connection that the often quoted line "If I have seen farther it is by standing upon the shoulders of Giants" is usually misinterpreted as evidence of Newton's modesty. In fact, the line was a sarcastic dig at Hooke, who was rather short and crooked in his posture. Some present-day physicists have been known to use the variant "If I have seen farther it is by looking over the shoulders of midgets" to put down their colleagues.
On the whole, Newton's years at Cambridge were the happiest of his life up till the plague years. Compared to the centers of learning on the Continent, Cambridge was an intellectual backwater at the time. The university had a prescribed curriculum based in part on Aristotelian studies, but fortunately by the 1660s the strict Aristotelian curriculum was not taken seriously, even at Cambridge. Newton, fortunately, was by and large left alone. He had time to reflect and to read what he wanted. By the time the plague came, he had already discovered the writings of Galileo and Descartes and invented the beginnings of calculus.
ANY TWO OBJECTS
By thinking on it continually.
-NEWTON (reply given when asked how he discovered the law of gravity)
Newton discovered that any two objects attract each other. The more massive the objects, the stronger is this universal force of gravitation. As the two objects move farther apart, the attraction between them weakens, but it never quite decreases to zero.
As is well known by now, the apple falls because the earth is pulling it down. In fact, since not only apples but also all objects fall, the force apparently does not depend on the precise nature of the object, only on its mass-that is, the amount of "substance" contained in the object. How does this force depend on the mass?
GALILEO'S CANNONBALLS
At that time, Newton had already figured out the laws of motion. One of these laws says that when a force of any kind is exerted on an object, it causes the object to accelerate. Furthermore, the mass of the object times the acceleration is equal to the force exerted. F = ma: Force equals mass times acceleration. In other words, the acceleration of an object subject to a force is just the force divided by the mass of the object:
a = F/m.
I should emphasize that Newton's law of motion F = ma is about the effect of forces in general. The force may be electric, magnetic, gravitational, or whatever. Until Newton, people were blinded by everpresent friction into believing that a force is necessary to keep an object moving at a constant velocity. Perhaps by watching a skater gliding gracefully across a pond of ice, Newton realized that if friction were minimal, an object. would maintain its velocity for a long time even without any force being exerted on the object. His law states that in the absence of friction a force exerted on an object changes the object's velocity-that is, it produces an acceleration.
Indeed, the gravitational force causes objects to accelerate as they fall. Already, Galileo had determined that falling objects accelerate at about thirty-two feet per second per second. That means that after falling for a second, a falling object is moving at a speed of thirty-two feet per second; after two seconds, sixty-four feet per second; and so on. Of course, air resistance would slow it down some.
Given all this, Newton deduced that the earth's gravitational pull on an object is proportional to its mass n in other words, F is equal to m times some constant. Call the constant g for gravity. Thus, F = mg. The proof is to show that this accords with Galileo's observations.
That's easy. The acceleration is a = F /m= mg/m = g. The mass m cancels out! The acceleration does not depend on the mass of the object!
But that's exactly right! Galileo said that the acceleration of a falling object is thirty-two feet per second per second. Period. He didn't have to specify what the object's mass is.
To underline this key point, let us suppose erroneously that the gravitational force is proportional to the mass squared, for example. Then the acceleration of a falling object would be a = F/m = constant xm z/m = constant xm. Thus an object twice as massive as another would accelerate twice as much as the other. That would contradict Galileo's observations.
Supposedly, Galileo demonstrated that all objects fall at the same rate by climbing up on the Leaning Tower of Pisa and dropping off two cannonballs of different sizes, showing that they hit the ground at the same time. Most people refused to believe Galileo, asking him how a rock and a feather could be said to fall at the same rate. These people didn't appreciate that air resistance on the feather far exceeds that on the rock. It is a dramatic and true fact that in a vacuum a rock and a feather would fall side by side.
As we will see, that falling objects fall at the same rate provides the clue to the true, nature of gravity and the cornerstone on which Einstein will construct his theory of gravity. From this fact flow the profound secrets of space and time...
