Outer Limits of Reason (35 page)

The End of Well Defined: Superposition

The first experiment is called the double-slit experiment. Richard Feynman (1918–1988), in discussing this experiment, waxed lyrical: “We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery. We cannot make the mystery go away by ‘explaining' how it works. We will just tell you how it works.”
¹²
The experiment was first performed by Thomas Young (1773–1829) in the early nineteenth century. Imagine a barrier with two slits in it that we can view from above, as in figures
7.6
and
7.7
. In the first figure we close one of the slits and shine a light at the barrier. As expected, the light will pass through the slit and radiate out to the screen on the right. The light will be intense directly across from the open slit and will be less intense farther away from the slit. This is depicted by the curve on the right of
figure 7.6
.

If the second slit is opened, something very interesting happens. The light passes through both slits, but rather than having the expected pattern, there will be an alternating pattern where some regions have intense light and some have no light, as in
figure 7.7
. The reason for this strange light pattern is that light is acting like a wave with crests and troughs. When the crests of the light wave from one slit meet the crests of the other light wave, they add up and the light is intense. In contrast, when the crests meet the troughs, the waves cancel each other out and there is no light at all. When such canceling occurs, we say the light has “an interference effect.” This is similar to waves in a pond after dropping in pebbles. So far so good.

Now, for the amazing aspect of this experiment and probably the most mind-blowing result in all of science. Physicists have a way of performing this experiment by releasing one piece of light at a time. A piece of light, or a light atom is called a
photon
, and physicists have become adept enough to be able to fire one photon at a time through the slits. After releasing a photon, it passes the barrier, hits the right-hand wall, and makes a little light. They can perform this experiment millions of times and see the pattern that the photons make on the right-hand side. The remarkable aspect is that an interference pattern is still found. That is, many individual photons will land in the area where there was high intensity, few will land in areas where there was low intensity, and none will land where there was total interference. How can this be? When we have many photons, we can say that the photons are interfering with each other like waves in a pond. But when each photon is released one at a time, what can a single photon interfere with to create such a pattern? The answer is that the single photon interferes with
itself
. The individual photon does not pass through the top or bottom slit. Rather, the photon passes through both slits simultaneously and when it (singular) emerges through both slits, it interferes with itself.

How can one object pass through both slits simultaneously? That is the major mystery of quantum mechanics. Usually an object has a
position
—that is, a single place where the object is found. But here, an object can be found in more than one position. The phenomenon of being in more than one place at one time is called
superposition
.

Whenever I open my eyes, I see objects in exactly one place, not in many places. It seems as though we live in a world with position, not superposition. The computer screen I am looking at is only in one place. And yet there is superposition. We might not see it, but we see the consequences of superposition. After all, we do not see wind, but we see the trees bend.

Researchers are not in total agreement as to why we do not see things in superposition. All that is known is that when we examine the results of a quantum experiment, or to use the right lingo, when the system is
measured
, we no longer see a superposition. We say the system
collapses
from a superposition of many positions to one particular position. The
measurement problem
asks why this collapse occurs and is one of the major discussion points in the philosophy of quantum mechanics.

We need a simple example of such a superposition and a collapse. In high school we learned that an electron orbits the nucleus of an atom in one of its shells. This is a little false. Actually the electron orbits the nucleus in a superposition of
all
of its shells. Such a superposition is called a “probability cloud.” Like a cloud, it is a bit amorphous. It is only when we measure the position of the electron that it collapses to one particular level, as depicted in
figure 7.8
.

This concept of superposition is the main idea in quantum mechanics. It will be our central concern throughout the rest of this section. The position of an object is not the only property that is subject to such craziness. Many other properties in the quantum world like energy, momentum, and velocity will also have many values simultaneously and then collapse to one value when we measure them. For all these different properties of quantum systems, superposition will be the norm until the system is measured.

Before we leave the double-slit experiment, let us rephrase the experiment in a slightly different way. The photon leaves the light source, and then depending on whether the barrier has one or two slits open, the photon will have a position or a superposition. If only one slit is open, it will remain as a single photon. If, on the other hand, both slits are open, the photon will go into a superposition. How does the photon “know” what to do when it leaves its source? Should it remain as one photon or should it go into a superposition? The answer can be seen from the point of view of the Wholeness Postulate, namely, that the outcome (whether there will be interference) depends on the setup of the whole experiment. The outcome of the experiment depends on whether the second slit is open. This does detract from the mystery. After all, how can the photon “know” the setup of the entire experiment when it leaves the source? There might be some real distance between the source of the photons and the slits. There is no real answer to that mystery.

The End of Determinism: Collapsing of a Superposition

We have seen that objects are in a superposition until they are measured, and when they are measured they collapse to a single position. The obvious question is which of the possible positions a measured superposition collapses to. Physicists tell us that it is random. There is no deterministic law that states exactly which position each object will collapse to. The laws that tell us how the particle will collapse are probabilistic laws. That is, the laws say that there is a probability that it will collapse this way and a probability that it will collapse that way. For example, in terms of 
figure 7.8
, a law in quantum mechanics might say that there is an 11.83 percent chance that the electron will collapse to the outside shell, a 47.929 percent chance that it will collapse to the middle shell, and a 40.241 percent chance that it will collapse to the inner shell. However, what the electron will actually do cannot be determined.

In slightly more detail, a superposition is described as many possible positions of the system. The different positions are indexed by complex numbers—that is, every position has a complex number associated with it. When a superposition collapses, the chances that it collapses to a particular position are determined by that complex number.

The fact that the laws are given by probabilities should not lead one to think that quantum mechanics is somehow an approximation of a real theory. On the contrary, quantum mechanics is the most exact physical theory that we have. Experimental evidence shows that our predictions are correct to many, many decimal places. One must realize that the predictions of quantum mechanics are made about subatomic particles. Experiments are done on a very large number of such subatomic objects. The outcomes show that the many particles follow the probabilities given. So we do not know what each particle will do, but we do know what a large ensemble of them will do.

A distinction must be made between the laws of quantum mechanics and the laws of chaotic systems that we met in the last section. With chaos theory we learned about some processes that are deterministic but not predictable. Here we have processes that are not even deterministic and of course not predictable. If there are no exact laws that describe the actions of all the parts of the system, then we definitely cannot predict where the system will end. It is one thing not to be able to predict the long-term future of a system, but it is far worse not even to be able to tell what will happen in the short term. We cannot determine what a single object in a quantum system will do in the short term. This takes us one more step outside the bounds of reason.

At this point, you might be skeptical about this lack of determinism. After all, all the other laws of physics are deterministic. There must be something that physicists are missing that would explain the seeming randomness of it all. You would not be alone with such skepticism. Albert Einstein, one of the forefathers of quantum mechanics, also did not believe it. He expressed his skepticism with the rather colorful phrase “God does not play dice with the universe.” Einstein did not believe that the fundamental laws of physics are random. Supposedly, Niels Bohr responded to Einstein by saying, “Don't tell God what to do.” The universe works the way it does and it does not have to satisfy our wishes. Although we might want Einstein to be correct, most contemporary physicists assure us that Einstein was wrong and the universe at its very core is not deterministic and hence random.

There are those who have taken up Einstein's challenge and are looking for laws of quantum mechanics that are somewhat deterministic. They believe these laws are governed by
hidden variables
. That is, there are extra variables in the system that cannot be seen but when they are taken into account, the laws of quantum mechanics are deterministic. This is similar to a chaotic system in the classical world. Consider the lottery machines that work by mixing up balls in a giant jar. Such machines are used because there is no way to predict which balls they will choose. Nevertheless, despite the machine being unpredictable, the laws describing what goes on in the machine are totally deterministic. Every ball bounces around following fixed deterministic laws, but there are too many individual parts of the system for there to be predictability. The exact positions of every ball and every air molecule are the hidden variables in this system. Some physicists posit that quantum mechanics also has variables that cannot be seen. Such hidden variables are a possibility, and if they are true then all of the laws of the universe are deterministic. I return to the possibility of hidden variables at the end of this section.