God and the Folly of Faith: The Incompatibility of Science and Religion (19 page)

Although treated by holists, paranormalists, and practitioners of complementary and alternative medicine as something mysterious,
⁷
the field is a very simple concept. It is a mathematical object that has a value at every point in space. The gravitational, electric, and magnetic fields are what are called
vector fields
, since they have both a magnitude and direction at each point. Another way to say this is that you need three numbers to represent a vector field at each point: one number to specify the magnitude and two numbers to specify the direction in three-dimensional space.

We can define other fields in physics. On the everyday scale, matter looks continuous. In that approximation, a material medium is described by measurable quantities such as density, pressure, and temperature that are each specified by a single number at every point within the medium. These are examples of
scalar fields
that are used in thermodynamics and fluid mechanics.

Notice, however, that these scalar fields describe matter as a continuous medium. We now know that familiar matter is composed of individual chemical atoms and molecules that move around according to the laws of particle mechanics. We can neglect the gravitational forces between these particles, and, if they are electrically neutral, they will also experience no electric or magnetic forces. They will then interact simply by colliding locally with one another, with no holistic processes involved. The whole is the sum of its parts and the scalar fields are reduced to particles the way a smooth, sandy beach can be reduced to tiny pebbles.

Even before the atomic nature of matter was empirically verified, nineteenth-century physicists were able to derive all the principles of thermodynamics and fluid mechanics from particle mechanics alone. For example, the pressure of a gas was derived as the statistical result of the impacts provided by the molecules colliding with the walls of the container. The internal energy of a gas is just the sum of the kinetic energies and other energies (vibrational, rotational, chemical) of the molecules within. A new science called
statistical mechanics
was developed that combined probability theory with particle mechanics.

The theological significance of statistical mechanics will be discussed in
chapter 8
.

In the twentieth century, it was found that all the fields of physics exist in one-to-one correspondence with particles called
quanta
. For example, the
photon
is identified as the quantum of the electromagnetic field. We still await a definitive identification of a quantum for gravity, although a quantum of the gravitational field has been postulated called the
graviton
. Once a quantum theory of gravity is established, the triumph of atomism will be complete.

THE ARROW OF TIME

These developments in nineteenth-century physics produced an important advance on the question of the nature of time, which also plays a major role in theology. Nowhere in classical mechanics can you find a fundamental mechanical principle that defines a direction for time. All physics equations work equally well in either time direction. They allow us to postdict the past as well as we can predict the future. For example, astronomers have postdicted that a full eclipse of the sun occurred over Asia Minor on May 28, 585 BCE (current calendar). This may have been the one that Herodotus said was predicted by Thales (see
chapter 2
). We will see later that time is also reversible in quantum mechanics.

Nevertheless, the fact that time has a direction is one that seems as commonsense obvious to us as the commonsense fact that Earth is flat. Near the end of the nineteenth century, Ludwig Boltzmann proposed that our conventional definition of the direction of time is a statistical one.

Boltzmann proved a theorem, the
H-theorem
, showing that if a closed system contains a large number of randomly moving particles, it will evolve with time toward a state of equilibrium that has maximum entropy. Once it reaches that state, it will remain there on average, although there will be statistical fluctuations away from equilibrium. These fluctuations will become smaller as the number of particles becomes larger. This was a proof of the second law of thermodynamics. The entropy of an isolated system tends to increase with time. There seems to be a natural trend from order to disorder, at least for a closed system.

In effect, Boltzmann showed that the direction, or arrow, of time is in fact simply
defined
as the direction of increase in the entropy of a closed system. Now, it would seem that the arrow of time could be different for different closed systems, but no realistic system of particles can be completely isolated from the rest of our universe; therefore these imperfectly closed systems of particles all have the same arrow of time. Different universes, independent and isolated from one another, could have opposite arrows of time.
⁸
In
chapter 7
, we will consider a scenario in which our universe appeared by
quantum tunneling
from an earlier universe. That earlier universe would have an arrow of time opposite to ours!

Make note that the definition of the direction of time is statistical. This implies that what are called “irreversible” processes in thermodynamics are actually still, in principle, reversible. For example, suppose you have a chamber in which most of the air has been pumped out. If you open an aperture in the chamber wall, air will rush through it from the outside. The reverse is never observed to happen. Once outside air has filled the chamber, in our experience it will not rush out the aperture at some later time, leaving behind a vacuum. This is an example of an “irreversible” process.

However, looking at it from the particulate viewpoint, it is not impossible for the air in the chamber to rush back out through the aperture. What has to happen is that all the molecules inside are moving in the direction of the opening the instant the aperture is opened. For example, suppose you are sitting in an auditorium with a thousand other people listening to me lecture. The doors are closed. Then a latecomer opens the door and all the air leaves the room, killing us all as our bodies explode from the lack of external pressure. This is highly unlikely, but technically not impossible.

Now, suppose we have two chambers with an opening between them. They contain just three or four molecules that bounce back and forth. Observing this we would be unable to specify a direction of time. Such is the case for the fundamental processes of physics and chemistry. For example, the chemical reactions C + O
₂
→ CO
₂
+
Q
, where
Q
is a certain amount of energy, and its reverse, CO
₂
+
Q
→ C + O
₂
are both observed. All fundamental processes are reversible, although not necessarily with equal probabilities. The probabilities in both directions just have to be high enough so the processes can occur
either way in a reasonably short time. At the everyday level of experience, the probabilities are far from equal for those processes we classify as irreversible.

The theological implications of the fundamental reversibility of time are never discussed. Most theologians (and most scientists) assume that an intrinsic arrow of time exists “in reality.” The central theological doctrines of creation, causation, and ultimate purpose are meaningless without a fundamental arrow of time. However, as we will see in
chapter 7
, there may be many different universes besides ours, some with the same arrow of time as ours and some with an opposite arrow. How can that be reconciled with the doctrine of creation?

SPECIAL RELATIVITY

As the twentieth century approached, most physicists pictured the electromagnetic field as a vibration of a continuous, invisible, frictionless medium called the
ether
(or
aether
) that pervaded all of space. Maxwell himself was cautious, suggesting that this might be just a mathematical model and not reality.

There was a problem. Maxwell's equations predicted that light traveled at the speed
c
in a vacuum independent of the motion of source or observer. This was true in all reference frames, seemingly violating the principle of Galilean relativity, discussed in
chapter 3
, which said that all speeds are relative. Certainly the speed of sound depends on relative motion. When you move toward a source of sound, your speed is added to the speed of the sound wave approaching you. When you move away from a source of sound, your speed is subtracted. This all follows from the theory of sound. It does not follow from the theory of light.

In 1887, physicists Albert Michelson and Edward Morley performed an experiment to measure Earth's motion through the hypothesized ether. They attempted to do this by measuring the speed of light along two perpendicular paths using an interferometer invented by Michelson. If light is a vibration of an all-pervading ether, the way sound is a vibration in air, then its speed should be different for different directions of the Earth's motion through the ether.
The expected change was a hundredth of the speed of light, well within the measuring accuracy of the instrument. But they found no difference in speeds between the two directions. This result is expected from Maxwell's equations but seems to violate Galilean relativity. Michelson and Morley failed to find any empirical evidence for the ether.

However, think about it another way. The principle of Galilean relativity says our physics models must be the same in all reference frames. If they were not, then they would be distinguishable from one another. Since Maxwell's model of electromagnetic waves has them traveling at the speed of light, then relativity
requires
that the speed of light be the same in all frames.

In 1905, Albert Einstein published a world-shaking paper titled “On the Electrodynamics of Moving Bodies.”
⁹
He did not mention Michelson and Morley, although he must have known of the result. Einstein argued purely theoretically and perhaps saw no reason to sully his results with grubby data. He asked what the logical consequences would be if both the principle of relativity were correct and the speed of light were absolute. While Lorentz, Henri Poincaré, and others had pondered the problem and had made some headway, Einstein derived the daring conclusion that we must reconsider our notions of space, time, mass, energy, and other fundamental concepts of physics.

Einstein showed that time intervals measured on a clock and space intervals (distances) measured with a meter stick depend on your frame of reference. Observers moving at a constant velocity (constant speed and direction) relative to one another will measure different time intervals and different distances between the same two events. If you watch a moving clock go by, that clock will appear to you to run slower. This is called
time dilation.
An observer sitting on the clock will not notice anything different about her clock but will see yours moving more slowly.

The same is true for the measured distance between events. A meter stick is, by definition, a meter long as measured in a reference frame at rest with respect to the stick. If that meter stick is moving across your line-of-sight, you will observe it to shrink in the direction of its motion. This is called
Fitzgerald-Lorentz contraction
. An observer sitting on the meter stick will not notice anything different about his meter stick, but he will see one at rest in your reference frame shrink in the direction of its motion.

Unless you are using an atomic clock that can measure time with an accuracy of one nanosecond (a billionth of a second) or better, you will not notice the effect at the typical speeds of everyday experience. In his 1905 paper, Einstein only considered constant relative velocities, and the theory presented there is called
special relativity
. Many experiments have verified special relativity in the century following Einstein, including those done with atomic clocks at jetliner speeds.
¹⁰
In my own field of particle physics, special relativity is as much an everyday tool as a drill is to a dentist.

CAUSE AND EFFECT

In special relativity, two events in space and time are “local” if you can find a reference frame where they occur at the same position in space. Here's an example: You and your girlfriend go for a ride on a train. You kiss her when the train leaves the station and again when you arrive at your destination. Although these are two different spatial locations in Earth's reference frame, the kisses are still local because they occurred at the same location in space in the train's reference frame and on the same pairs of lips.

Two events are nonlocal if they cannot be put in the same reference frame without exceeding the speed of light. For example, suppose you are a Houston mission control scientist for a manned Mars mission and you discover a bug in a program that will cause the spaceship on Mars to explode in ten minutes. Any message you send to the astronauts on the planet will take eleven minutes. There is no way you can warn them since the event of which you are sending a message is nonlocal with the event of the explosion.

According to special relativity, two nonlocal events cannot be in causal contact. That is, one event cannot be the cause of the other. This has a profound implication for science and theology that is not always fully appreciated in either school. Most of science and virtually all of theology are deeply based on the notion of cause and effect. In Newtonian physics, a force is needed to cause a change in momentum. In medicine, smoking causes lung cancer. In theology, God causes everything.

But now we find that events can happen in the universe that cannot be
connected by cause and effect. This is not a big problem for physics or the rest of science, because it just means that there could be multiple causes of events. But it presents a big problem for theology, which reduces everything to a single cause. Furthermore, as we will see in
chapter 7
, quantum events happen without an evident cause, that is, they happen spontaneously. So it is hard to see how the theological principle of a single being as the cause of all phenomena can be maintained in the light of relativity and quantum mechanics.