Outer Limits of Reason (37 page)

We can “see” the particle spinning by performing a
Stern-Gerlach experiment
, as depicted in
figure 7.14
. A ray of particles is shot out of a source. North and south magnets are set up to test for spin in a certain direction. The ray will then split up with the particles spinning in one direction going to one part of the screen and particles spinning in the other direction going to the other part of the screen. A particle can also not have spin and will simply go forward. One can think of the particles as spinning magnets (or charges) that are attracted by the magnets in the experiment. Measuring spins in different directions can be accomplished by moving the north and south magnets around the ray. It is important to reiterate that the particles in the ray are in a superposition of states where they are spinning positively and negatively in all directions before they are measured by the magnets.

It is the magnets that are performing the observation and causing this superposition to collapse to one particular spin direction. Once a ray is split up, we can measure the spin in other directions and get different spins, as shown in
figure 7.15
.

There is a form of the Heisenberg uncertainty principle for spin. It says that there are certain directions such that if you measure the spin in one direction and then measure the spin in another direction, you are going to get different answers than if you measure them in the other order. In general, if the two directions are orthogonal to each other, then we can measure both of them and get both values. As long as they are orthogonal, Heisenberg's uncertainty principle will not play a role. If, however, the angles are not orthogonal to each other, then we will not be able to measure those two directions simultaneously.

Now that we have the ideas and language of spin in hand, let us move on to the
Kochen-Specker experiment
. In 1967, Simon Kochen and Ernst Specker described an experiment to show that objects do not have properties until they are measured. They worked with a certain subatomic particle called a “spin-1 particle” that has the following property: if you choose any three orthogonal directions for measuring spin, two of the directions will have spin and the third will not have spin. Since these three directions are going to be orthogonal, Heisenberg's uncertainty will not play a role. However, there are many different triplets of orthogonal directions (see
figure 7.16
). For any triplet you choose, two directions will have spin and a third will not.

Now suppose you did not believe Mr. Bohr and you felt that objects have properties even before they are measured. You think this whole business with measurement causing a property to come into effect is nonsense. Then you would believe that whether or not the particle had spin
in any direction
was a fact that was true even before measurement. In other words, you feel that before any measurement in any direction takes place, there is spin or there is no spin. And when we measure it, we determine what already existed before.

Unfortunately you would be wrong! It is simply impossible to attribute spin or lack of spin before measurements to
all
the possible directions. If you think of a subatomic particle as a sphere, then each point on the sphere corresponds to a direction from the center of the sphere to that point. Saying that the directions have or do not have spin is like assigning 1s or 0s to the points of the sphere. We have the following conditions on assigning the 1s and 0s:

1. If a particle is spinning in one direction then it must also be spinning in the opposite (antipodal) direction. So if a 1 is assigned to a point on the sphere, then a 1 must be assigned to the opposite point because it is the same direction. Similarly, if a 0 is assigned to one point, it must be assigned to its opposite point.

2. Also, for any three orthogonal directions chosen, two of them will be spinning and one will not. That is, two points will get a 1 and one point will get a 0.

There is simply not enough room for the particle to be assigned such properties. This is a mathematical fact!

It would take us too far afield to provide a rigorous proof of this fact. It suffices to provide an intuition of why it is true. Consider for a moment that the North Pole direction does not have any spin. We can depict this as a 0 at the North Pole of the spheres in
figure 7.17
(a). From the first proviso the South Pole direction also lacks spin. Now look at the directions orthogonal to the north-south direction. These directions are along the equator of the sphere. By proviso 2, all of those directions must have spin. We depict the spins as a thick line around the equator. In part (b), we further imagine that the direction slightly to the east of the North Pole also does not have spin. This is depicted by another 0. By proviso 1, the direction slightly to the west of the South Pole also does not have spin. The directions orthogonal to this are slightly off the equator and must have spin. Those directions are also depicted as a thick black line. Yet a third direction off the North Pole is depicted in (c). We can further say what does and does not have spin as in (d). In (d), half of the sphere has thick dark lines, and there are two thin lines of directions from the poles to the equators that do not have any spin. We are not done. If you believe that every direction has or does not have spin, you should be able to continue this process and assign to every point either a 0 or a thick black point. It should be obvious that such an assignment cannot be made. There simply is not enough room! The black line is too extensive for every 0 point. There is no way we can give every point of the sphere a determination of whether there is spin.

What we have shown is that one cannot take it as fact that every direction has or does not have a spin before measurement. Only after choosing three orthogonal directions and performing an experiment can we determine if there is spin. There was no spin beforehand. The measurement does not tell you what was there before. Rather, the measurement
produces
the outcome.

This is crazy! We have just proved that objects cannot have certain properties until we measure them. We showed geometrically that there is not enough room for there to be such properties. An object only acquires properties after we measure it. Einstein (who died before Kochen and Specker described their experiment, but was nevertheless told of Bohr's ideas that objects don't have properties until they are measured) ridiculed this by asking whether one was really to believe “that the moon exists only when I look at it.”
¹⁴
But again, the vast majority of contemporary physicists would tell Einstein that, as crazy as it sounds, the moon is only there when it is measured. Heisenberg wrote: “The idea of an objective real world whose smallest parts exist objectively in the same sense as stones or trees exist, independently of whether or not we observe them . . . is impossible.”
¹⁵

The End of the Microscopic-Macroscopic Distinction: Schrödinger's Cat

One might try to be flippant about all these problems. After all, what does the “real” world have to do with all this quantum stuff? You have never seen a subatomic particle in one position, let alone in a superposition. How does this idea of superposition in the subatomic world affect the larger world? One of the founding fathers of quantum theory, Erwin Schrödinger (1887–1961), described an interesting experiment that has come to be known as
Schrödinger's cat
. Imagine a sealed box with a piece of radioactive material in it. This material is subject to the laws of quantum mechanics and is in a superposition of “ready to decay” and “not ready to decay.” Place a Geiger counter that can detect any decay in the box with the radioactive material. Connect the Geiger counter to a hammer that will break a vial of poisonous gas when the Geiger counter beeps, as in 
figure 7.18
. Now place a living cat inside the box and close the box.

As with all quantum mechanical processes, we cannot determine whether the radioactive material will actually decay. Hence, there is no method of determining whether the Geiger counter will beep. If the radioactive material decays, the Geiger counter will beep, the poison will be released, and the cat will die.
¹⁶
On the other hand, if the radioactive material does not decay, then the cat will be alive. Since there is a 50-50 chance for the decay to occur in the time given, there is a 50-50 chance that the cat is dead. That is, before we open the box, the cat will be in a superposition of both being alive and dead. It is only after the box is opened and a measurement is made that one of these possibilities really happens. The experiment has successfully transformed the weirdness of the subatomic world into the everyday world of cats and human beings.