God and the Folly of Faith: The Incompatibility of Science and Religion (12 page)

NEWTON'S LAWS

Galileo, and to some extent Descartes, laid the foundation of mechanics. Isaac Newton carried the program to its conclusion. Although many improvements to Newton's methods and observations have since been elaborated, these basically decorate the Newtonian edifice.

Newton's greatest achievements are so simple that they can be easily understood by anyone with a high school education—and that is what makes them so great. They show just how comprehensible the universe really is. Science writers love to extol the “mysteries of the universe.” That sells books. But in today's physics and cosmology, there are no current mysteries that we require a new revolution in human thinking to solve—just unanswered questions on finer details.

Newton's masterwork, published in 1687, was titled
Philosophiae Naturalis Principia Mathematica
(
The Mathematical Principles of Natural Philosophy
), or referred to as just
Principia.
The book introduces the laws of motion, the law of universal gravitation, and a derivation of Kepler's laws of planetary motion. I will discuss each in turn, using my own words rather than Newton's for simplicity and to bring them up to date.

The Laws of Motion

1. A body at rest will remain at rest and a body in uniform motion will remain in uniform motion unless acted on by an external force.

We readily observe that bodies at rest do not start moving spontaneously. They require something to get them moving, an external agent we call a
force
.
I will precisely define force below. As we saw previously, Galileo had introduced the principle of relativity, which says that velocity is relative. There is no difference between being at rest and being in motion at constant velocity, that is, at both constant speed and constant direction, which we call
uniform motion
. It follows that a body moving at constant velocity will not change that velocity unless acted on by an eternal force. Thus, a force is needed to produce a change in velocity—an acceleration.

Now, Newton actually put it more generally. He introduced a “quantity of motion” we today call
momentum
. Also called
linear momentum
, it is defined as the product of the mass and velocity of a body. I will define
mass
below. The first law more fundamentally says that, in the absence of an external force, the momentum of a body does not change. That is, the mass and velocity could change, as in a rocket that expels mass as it accelerates, as long as the product remains the same.

2. Force is defined as the time rate of change of momentum.

I promised you I would precisely define force. The second law does that for us.

3. For every action there is an equal and opposite reaction.

More quantitatively, if you kick a brick wall, it kicks back at you with an equal and opposite force. You can feel that force, especially if you take off your shoe.

In another example, the force of gravity on your body is called your weight. It is pressing down on the floor where you are standing. The floor is pressing back up on you with an equal and opposite force, keeping you from crashing through to the room below.

Today we can derive the first and third laws from a single principle:
conservation of momentum
. The momentum of a body remains constant unless acted on by an external force, which I have already noted is another way to state the first law. To understand the third law, consider the example of firing a rifle while standing on ice wearing ice skates. You feel a recoil as the bullet goes flying off with high momentum in one direction, which must be balanced by your body recoiling in the opposite direction with the same momentum. Since
your mass is much greater than that of the bullet, you will recoil with a speed proportionally lower than that of the bullet.

An operational definition of mass, based on this observation, can be given as follows. Place two objects, such as wooden blocks, on a frictionless surface, with a compressed spring separating them. Release the spring and measure the recoil speeds of the objects. The ratio of the masses of the objects is then defined as inversely proportional to the ratio of their respective speeds. That is, the higher the mass, the lower the recoil.

The Law of Universal Gravity

Newton's great breakthrough here was to realize that the moon fell to Earth at the same rate as an apple. The only difference, other than their relative distances, is that the moon has an orbital velocity that keeps it from hitting Earth. Imagine firing a projectile from the top of a tall building with a velocity parallel to the ground. The projectile will follow a parabolic path and hit Earth some distance from the building. Now picture firing the projectile parallel to the ground at such a high speed that, before it lands, the ground falls away because of the curvature of Earth. This is the case with the moon and any other orbiting body, including the planets. The planets fall around the sun because of the same universal force by which the apple falls to Earth.

The universality of gravity was an enormous insight. Until it was discovered, everyone assumed a different set of laws for Earth and the heavens. This was the first example of the unification of forces, which continues to the present day.

Newton was able to infer from the relative accelerations of the apple and the moon, and their relative distances from the center of Earth, that this universal force fell off as the square of the distance between two bodies. He also was able to explain Galileo's observation that objects fell with the same acceleration, independent of their masses, by assuming that the force was proportional to the masses of the bodies.

More precisely, Newton's law of gravity gives the force between two particles as proportional to the product of their masses and inversely proportional to the square of the distance between them. The value of the proportionality
constant
G
, called Newton's constant, was not known until Henry Cavendish (died 1810) actually measured the gravitational force between two bodies in the laboratory. This is called the “experiment that weighed Earth,” since Newton's law of gravity could then be used to calculate the mass of Earth.

Now, since the law of gravity is defined for point particles, what right do we have to use it for calculating our own weight as we stand on the surface of a large planet? Newton put to use the mathematical tool called calculus, which he invented independently from the German philosopher Gottfried Leibniz (died 1646). Newton proved that the force between two extensive bodies is the same, as if the mass of each body is concentrated at a certain point in each, called the center of mass. Treating Earth as an approximate sphere, that point is the center of Earth.

Kepler's Laws of Planetary Motion

Newton's contemporary and less brilliant (but still very smart) rival, Robert Hooke (died 1703), had also inferred the inverse square law. One day Hooke, Edmond Halley, and Christopher Wren were sitting around trying to figure out what planetary orbits would be with an inverse square law of gravity. Halley said he would ask Newton. He did so and Newton said, “An ellipse.” Halley asked how he knew this and Newton replied, “I have proved it.”
³⁹

Again this turns out to be easy to understand, once someone tells you the principle. Let us look at the explanation found in today's elementary physics textbooks.

Linear momentum is accompanied by another quantity called
angular momentum.
Although this is not the general case, the angular momentum of a body moving in a circle is the linear momentum of the body multiplied by the radius of the circle.

Just as linear momentum is conserved when there are no external forces on a body, angular momentum is conserved when there are no external
torques
. A torque is the twisting force you apply when you use a screwdriver. Angular momentum conservation keeps a bicycle from falling over when it is moving and enables a figure skater to speed up her spin by pulling in her arms.

The planets conserve angular momentum to a good approximation since their attraction to bodies other than the sun is of second order. From conservation
of angular momentum one can show that a line from a planet to the sun will sweep out equal areas in equal times, defining an ellipse.

HALLEY'S COMET

Edmond Halley was a good friend of Newton's and an accomplished scientist in his own right with a lifetime of achievement. Today, however, he is best remembered for the comet bearing his name.

After learning that Newton had proved Kepler's laws, Halley saw to it that
Principia
was published, at his own expense. In 1705, Halley published his own
Synopsis of the Astronomy of Comets
, in which he used Newton's laws, along with historical tables, to determine that a comet that had appeared in 1682 and two comets seen in 1531 had the same orbits and were probably the same body. In the 1531 case, one sighting must have occurred when the comet was heading toward the sun; the second sighting must have happened when the comet came back after going around the sun. Halley then predicted that the same object would return in seventy-six years, in 1758. An amateur astronomer first observed the return of Halley's comet on December 25, 1758.

THE NEWTONIAN WORLD MACHINE

The wonder of Newtonian mechanics is that it enables scientists, and even high school physics students, to predict the future with precision—an ability that no prophet of any religion nor any modern-day psychic has ever demonstrated. Given the mass, initial position, initial velocity of a body, and the net force acting on it, the position and velocity of the body can be calculated at any future time with, in principle, unlimited accuracy that depends only on the accuracy of the initial measurements. And since, in the materialist worldview, the physical universe is composed of nothing more than bodies with mass, the initial conditions of the universe and the laws of physics determine everything that happens in the natural world. This is called the
clockwork universe
, or the
Newtonian world machine
.

As we will see in
chapter 6
, Heisenberg's uncertainty principle of quantum mechanics, introduced by the German physicist Werner Heisenberg in 1927, showed that the accuracy of such predictions is, in fact, limited in principle—not just by measurement errors. However, in the 240 years between the publication of
Principia
and the discovery of the uncertainty principle, it was assumed that everything that happens in the natural world has been predetermined since the creation.

Newton himself did not go so far as to reject God. In fact, he wrote extensively about the Bible, in particular the prophecies of an eventual paradise on Earth when Christ returns. He was not, however, an orthodox Christian. Although he held the chair in mathematics at Trinity College in Cambridge (the same chair held by Stephen Hawking today), Newton was an Arian and rejected the Trinity. He also spent a lifetime's effort on alchemy, which was motivated by his belief that mechanical action alone is not sufficient to account for living organisms and that God directs organisms' behavior through an animating force.
⁴⁰

Newton saw a need for God to determine the initial conditions and set the solar system in motion. He believed that the coplanar orbits of the planets and their unidirectional motion could not be explained naturally. He thought that these orbits would collapse together because of the mutual gravitational attraction of the planets, so it was necessary for God to step in continuously to adjust their orbits.
⁴¹

By including God as a part of scientific theories, Newton was applying what we now know as the “God of the gaps” argument, in which God is introduced to account for some observation that the science of the time, or sometimes just a science-challenged author (not Newton, of course), cannot explain. The God-of-the-gaps argument inevitably fails since we have no way of knowing that science will never find the missing explanation. In order to defeat the argument, the atheist merely has to produce a plausible explanation consistent with existing knowledge. No proof is needed; the theist has the burden of proving that no explanation will ever be found—an almost, but not quite, impossible task.

And, as it turned out, the scientists and mathematicians in the generations following Newton were able to fill in the gaps in Newton's understanding.
In 1734, the Swedish scientist and philosopher Emanuel Swedenborg (died 1772) proposed the
nebular hypothesis
that is still used today to describe the origin of the solar system. According to this picture, a massive ball of gas condenses down into smaller clumps by gravitational attraction.

The philosopher Immanuel Kant (died 1804) and the French mathematician and astronomer Pierre-Simon, Marquis de Laplace (died 1827) argued that the rotation of the gas will cause it to flatten into a disk, and the clumps that became planets and other smaller objects would all rotate in the same direction and on the same plane around the central clump that became the sun. While this model has many problems that are still not worked out in detail, most likely it is basically correct.

Laplace is remembered for his encounter with Napoleon, in which he presented the emperor with a copy of his work. Napoleon had heard the book contained no mention of God, and so said to Laplace, “M. Laplace, they tell me you have written this large book on the system of the universe, and have never mentioned its Creator.” Laplace answered, “
Je n'avais pas besoin de cette hypothèse-là.
” (“I had no need of that hypothesis.”)
⁴²
I mark this as the place in modern times where science and religion began to part company.