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The third book of Physics, called
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Thus the Second Law provides a reason for the seemingly random motion of a body. When a naturally lazy body speeds up or slows down, or swerves to the right or left or turns up or down, then it does so not on its own volition but because it was compelled to do so by a force. So when a coin is tossed up, turns over and falls to the ground, it does so because there is a force. And in this case, the force is gravity. Thus bodies that accelerate do so because of forces. And it is as though Nature mechanically compelled bodies to change behavior. Thus forces are the embodiments of natural commandments.
Motion without forces shall be free.
Chapter III: The Third Law
Now the Third Law shall say the following. When two bodies interact in isolation, the force that each exerts on one another shall be of the same strength, but opposite in direction. And this shall be the law of action and reaction.
Do unto others as you would have them do unto you.
When push comes to shove, neither push nor shove shall win.
Chapter IV: Gravity
Cupid shall forever fire arrows.
Now the law of gravity shall say the following. The force of gravity between two bodies shall be proportional to the product of their masses and weaken with the distance squared. And the force shall be attractive and directed along a straight line between the bodies. And this shall be Newton’s law of gravity.
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And what shall it mean for the force to weaken with the distance squared? It shall mean this: If the distance between the two objects is doubled, the force grows weaker by four times. And if the distance is tripled, the force grows weaker by nine times. And if the distance is quadrupled, the force grows weaker by sixteen. And so on. Thus only relatively nearby bodies feel the force of gravity. Thus the Moon is attracted to the Earth. And the Earth and Moon are attracted to the Sun. But the Earth and Moon feel a miniscule force from the nearest star, Alpha Centauri, because it is forty-trillion kilometers away.
The command from Heaven did in ancient times descend:
Now the weak equivalence principle shall be inherent in Newton’s law of gravity. It says that the mass in Newton’s Second Law shall be the selfsame mass in Newton’s law of gravity. Thus there really shall be one and only one type of mass.
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Chapter V: Planetary Motion
Now the movements of the planets around the Sun shall be explained by Newton’s laws of gravity and motion. These four laws shall integrate to yield three lesser rules called Kepler’s laws. Now the first rule says that a planet shall move in an ellipse around the Sun and that the Sun shall be at one of its two foci.181 And the second rule says that a straight line drawn between the Sun and a planet shall sweep out equal areas in equal times. And the third rule says that the period squared shall be proportional to the mean distance cubed. Now the period shall be the time it takes for a planet to go once around the Sun, while the mean distance shall be the average of the perihelion and the aphelion.182 And what shall it mean for the period squared to be proportional to distance cubed? If the distance is increased four-fold, then the period grows by eight. And if the distance is increased nine-fold, then the period increases twenty-seven times. And if the distance is increased sixteen-fold, then the period becomes sixty-four times bigger. And so on.
Chapter VI: Gravity on Earth
Now gravity shall govern the fall of objects at the surface of the Earth. And it shall make golf balls and basketballs come back to Earth. And what first goes up shall then come down. Now when air friction is insignificant, all bodies, independent of their mass, shall fall the selfsame way. And for example, a feather and an iron paper-weight fall in a vacuum chamber at precisely the same rate. And the distance that an object falls, when released from a tower or a cliff, increases with time squared. And in one second, five meters shall a body fall. So in two seconds, four times farther, or twenty meters, shall it fall. So in three seconds, nine times farther, or forty-five meters, shall it fall. And so on. Now projectile motion shall be the motion of any object, such as a spear, a ball or missile, through the air. The horizontal and vertical motions shall be independent. And for example, a projectile shall move horizontally with constant speed. But it shall move vertically with constant downward acceleration, falling five meters in the first second. And the acceleration shall be created by Earth’s gravity, which shall draw all objects toward the center of the Earth.
181 An ellipse, or "stretched circle," has two points called foci adjacent to its center.
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Chapter VII: Momentum
Now momentum shall be the amount of push a moving body can deliver on impact. More mass means more momentum. Given a truck and a leaf moving at the same speed, the truck has more momentum. Likewise, more speed means more momentum. A bullet from a gun has more momentum than a penny tossed into the air.
Chapter VIII: Energy
There shall be two kinds of energy: kinetic and potential. Now kinetic energy shall be the energy of motion. When any object moves, it has kinetic energy, and the faster it moves, the more it has. Now potential energy shall be energy stored by a body in an interaction. A ball on a table has a certain gravitational potential energy; a ball on the floor has less. And when a ball falls, it picks up speed, as potential energy is converted into energy of motion. Objects shall continually trade kinetic and potential energy, but total energy shall be conserved, which means it shall remain the same.
Chapter IX: Angular Momentum
Now angular momentum shall be rotational momentum. Spinning tops and skaters have angular momentum, but a sprinter running in a line has none. Now angular velocity shall be the rate at which a spinning body turns. More angular velocity shall mean more angular momentum.
Chapter X: Special Motions
A vibration shall be a movement back-and-forth. An example shall be the motion of a leaf on an autumn windy day. Harmonic motion shall be a repetitive and smooth vibration, like a guitar string that’s been plucked. Circular motion shall be motion in a circle, such as the turning of a Ferris wheel or the motion of the Earth around the Sun.
Chapter XI: The Electric Force
And Cupid shall forever fire arrows.
Now the electric force shall be like gravity except that charges shall play the role of masses. But unlike mass, of which there is only one type, there shall be two types of electric charge: positive and negative. And unlike mass, which may have any value, electric charge shall come in quantized bits. Thus there shall be a minimal and fundamental charge. And the proton’s charge shall be this fundamental unit one-sixth of one-billionth of one-billionth of a Coulomb, a very small amount of charge. And on an electron shall also be the fundamental unit, but negative shall be it.
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Now let the law of electric force be known: The force between two charged bodies shall be proportional to the product of their charges and weaken with the distance squared. And for example, if the distance between two charged objects is doubled, the electric force grows weaker by four times. And so on.183 Now if the charges are of opposite sign, the force shall be attractive. And if the charges are of the same sign, the force shall be repulsive. And the force shall be directed along a straight line between the charges. And this electrostatic law shall have a name Coulomb’s law shall be its name.
183 For more examples on the strength of the force versus distance, see the case of gravity in Chapter IV, which is the same.
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Chapter XII: The Magnetic Force
Now some materials such as iron shall be magnetizable. And when such a material is magnetized, it shall become a magnet. Now magnetization shall be a consequence of circulating charge. And when such currents flow in random ways, no magnetism shall be present. But when, like marching soldiers, the currents circulate in an ordered manner in the same direction, the material shall magnetize, and a magnet shall it be.
184 The effect of changing magnetic fields creating changing electric fields and of changing electric fields creating changing magnetic fields is the basis of electromagnetic waves.
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Chapter XIII: Electromagnetism
And the relation between electric and magnetic forces shall be a fundamental fact of Nature. The two shall be manifestations of one principle and four equations. And the principle shall be called electromagnetism. And the equations shall be Maxwell’s equations.
Chapter XIV: Determinism
Now at the end of the nineteenth century, it was thought that if Nature’s forces were all known, then Newton’s laws could be exploited to determine all. So if thou knew the classical macroscopic forces, then thou, like a prophet, could foresee the future thou would know all. And thou, like a prophet, could predict the motion of anything and everything.
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Now by the end the seventeenth century, Newton had determined and had understood the law of gravity. And in the eighteenth and nineteenth centuries, Coulomb, Ampère, Faraday, Biot, Savart, Lorentz and Maxwell had determined and had understood electromagnetism. And with the knowledge of these forces, the mystery of macroscopic motion seemed to disappear. And it was thought that all was known, that the golden age of omniscience had arrived. But Nature’s laws had been indelibly engraved in sacred stone. And they were more subtle than what nineteenth-century man had thought. And no one, neither scientists, nor philosophers, nor holy priests could alter Nature’s laws. And in the early twentieth century, new fundamental forces were uncovered which were microscopic and not understood. And special relativity was then discovered, rendering Newtonian gravity incompatible. Next quantum mechanics was discovered and was understood. And for man’s mind did it create new puzzles. And uncertainty and chaos so ensued. And hope for omniscience was consequently lost.
Predicting the future was no longer a question of information.
And in the quantum-revolution aftermath,
Chapter XV: Classical Physics
And after the Planck time when the wings of quantum gravity ceased to flap, and after the Big Bang aftermath when subatomic particles self-annihilated or combined, and after nucleosynthesis when subnuclear forces began to play a lesser role, and after Recombination when atoms formed, and after other quantum fluctuations began to wane, and after hundreds of thousands of years when matter had spread thinly, then did Nature’s classical laws and forces take control. And the Universe became somewhat predictable. And "F=ma" became the most important rule. And the three laws of Newton almost determined all. And macroscopic forces controlled the macroscopic motions. And gravitational collapse made giant structures in the Universe such as galactic clusters and great voids.