Outer Limits of Reason (36 page)

 

Let us come back to the collapse from a superposition to a position. There is an easy experiment that can be seen as a demonstration of this collapse. First a little background about light and polarization filters. Light can be thought of as a wave, which can come in many different forms. Consider three typical waves in
figure 7.9
. The first wave moves up and down and is called a
vertical wave
. The second wave moves left and right and is called a
horizontal wave
. The final wave moves in a
diagonal
direction. I have highlighted three directions, but obviously light can come in any direction. Only the light from a laser has all of its waves uniformly lined up. The usual light that we see has many different waves coming in many different directions.

Sheets of flexible plastic called
polarization filters
, which block light coming in certain directions, are used in fancy sunglasses. They can be oriented in different directions and block light in those directions. One can think of the filter as a measuring instrument that collapses a superposition of different directional light waves into one direction. We will draw the filters as discs with a slit to indicate its direction, as in figures
7.10
through
7.12
. A filter in the horizontal direction will permit all horizontal waves to pass through it but it will block all vertical waves. What about the intermediate waves? The closer a light wave is to being horizontal, the more of a chance there is for the wave to pass through the horizontal filter. The diagonal waves, which are halfway horizontal and halfway vertical, will allow have about 50 percent of their light go through and about 50 percent of their light will be blocked.

Let us combine these filters for a fascinating result. Take a horizontal polarization filter and place all different types of light through it as in
figure 7.10
. About half the light will pass through it and that light will be a horizontal wave.

Now take a vertical polarization filter and place it to the right of the first one as in 
figure 7.11
. Since the right filter is in the position that blocks all the light that passes through the left filter, nothing will come through the right filter. So with the two filters arranged as in
figure 7.11
, no light will permeate both.

Now for the magic. Take a third diagonal polarization filter and add it to the filters already there. Don't put the filter to the left or the right of the previous filters. Rather, place the diagonal filter between the other two filters as in
figure 7.12
.

Something amazing happens: whereas two filters can block all the light from going through, three filters permit light through. In fact, there is really no magic here. Whatever light passes through the left horizontal filter comes out in the horizontal direction. When that horizontal light hits the diagonal filter, approximately half of it will be blocked while the other half will pass through in the diagonal direction. In a sense, the horizontal light is in a superposition with respect to the diagonal filter. The middle filter measures this diagonal light and collapses it. Now that diagonal wave will meet the vertical filter on the right. On average, half of the diagonal wave will be blocked while the other half will pass through the vertical filter and come out as a vertical wave. Since the light in 
figure 7.12
must pass through three filters and on average half the light is blocked by each filter, only one-eighth of the light will pass all three of the filters. Nevertheless, some light will pass. So even though two filters can prevent all the light from passing through, three filters permit some of the light to pass.

The End of Certainty: Heisenberg's Uncertainty Principle

Watch a car speeding down a highway. It is easy to determine both the color and speed of the car as it moves. One can effortlessly figure out a person's weight and height simultaneously. Similarly, with ease one can determine the exact position and momentum of a flying baseball. The point is that it is not hard to determine two different properties of an object. This obvious fact is true for the world we live in but simply fails in the quantum world. There are situations in the subatomic world where one cannot determine two properties at the same time.

Heisenberg's uncertainty principle
is one of the central features of quantum mechanics. It says that there are certain pairs of properties of subatomic systems such that it is impossible to know both of these properties at one time. For example, it is impossible to know both the position and the momentum of a moving subatomic particle. The doctrine that states this limit on human knowledge is called
complementarity
.

In detail, given two such properties, X and Y, we will get one pair of answers if we measure X first and then measure Y, and other answers if we measure Y first and then measure X. For example, first measuring the momentum and then the position of a subatomic particle will yield different answers than first measuring the position and then the momentum of that particle. This leads to the obvious question: What exactly are the momentum and the position of the object? Why are we getting two different answers here? Aren't there objective values of these properties that are independent of our observations?

We must stress that our inability to know both values simultaneously is not some problem with our present-day technology. It is not the case that as our microscopes and measuring instruments improve, the uncertainty principle will be less bothersome. These are not technological limitations. Rather, complementarity is an inherent limitation of our ability to know about our universe.

Notice that a radical new element comes into play here. The outcome of measurement Y depends on whether or not the person doing the experiment decided to perform measurement X first. The experimenter is not separate from the experiment. Rather, the experimenter has become part of the experiment and influences the outcomes of the experiment. The person who does the experiment influences the world that he or she is investigating. This is a revolutionary idea. No longer is there a closed system and an experimenter examining that closed system. Now the human experimenter is also part of the system. This can be seen in terms of the Wholeness Postulate: the experimenter is part of the
whole
experiment.

Researchers going back to Bohr take this one step further. They proclaim that it is wrong to say that humans learn the properties when they measure them. Rather, they say that the very act of measurement causes the properties to become well defined.
¹³
Before the measurement, it is not that we do not know what the property is, rather there is no property to know. Before any measurements, the properties are in a superposition. When X is measured, the X property collapses to a single value while the Y value remains in a superposition. If the Y property is then measured, then it too collapses. The point is that if the measurements were done in a different order, then the values could collapse into different values.

Philosophers discuss a philosophical position called
naive realism
. This is the belief that physical objects have a real existence outside of our minds and these objects have well-defined properties that can be determined when they are observed. This is obvious and every child knows this to be true. However, Heisenberg's uncertainty principle and the concept of complementarity destroy naive realism. Properties of an object do not exist before they are measured, and even when they are measured, the property depends on how it is measured. The realism that you feel is true in the regular world of cars and baseballs. It is not true in the subatomic world. Such realism is naive.

Do you believe all of this? A sane person would be justifiably skeptical. Read on!

The End of Ontology: The Kochen-Specker Theorem

At this point, you are legitimately allowed to feel disbelief and yell in a loud voice, “Balderdash!” You might say that all this talk of superposition is foolish and that when a subatomic object is measured, a property is determined that was there before we measured it. The measurement did not cause the property to come into existence; it was always in existence. Alas, this seemingly sane and bold stance that you are taking is wrong and I will prove it.

We need some preliminary notions. One of the central ideas of quantum mechanics is the notion of
spin.
Certain subatomic particles have spin. This is not the same as the usual notion of a basketball spinning on a finger. It is a little more complicated than that. Nevertheless, given a direction, a particle can spin one way, the other way, or not at all.
Figure 7.13
shows the direction with the arrow, and we find it spinning one way or the other. We might call the directions
positive spin
and
negative spin
, or
spinning up
and
spinning down
. As with most properties of quantum mechanics, before a particle is measured or observed, the particle will be in a superposition of both positive spin and negative spin.