8    Hidden Variables

Figure 5.1 is precisely what we might imagine my Great Predictor sees as he peers beyond the veil of appearances to see the underlying reality—that reality of which he so adamantly refuses to speak. Vividly obvious in that figure is something that quantum theory fails to give us: an actual situation. We see in this figure a full specification of the direction to which the spin points. We can even measure that direction, and come up with a definite number: so-and-so many degrees off to the right.

That number is the hidden variable describing the electron’s spin. We call it a “variable” because it could have one value or another—fourteen degrees, for instance, or maybe one hundred and ten. And it is “hidden” because it is tucked away, hidden from the theory’s gaze. Quantum mechanics cannot give us the value of a hidden variable. Indeed, it seems to have no place for them within its way of doing things.

The problem goes beyond spin. It infects everything that quantum theory addresses. Consider as another example the matter of radioactive decay, in which an atomic nucleus spontaneously breaks apart into pieces. Such nuclei are found to possess a certain half-life—the length of time during which half of them decay. There is an isotope of radium, for instance, that has a half-life of a bit more than eleven days. Start out with a chunk of pure radium: if you come back eleven days later, half the atoms will have decayed. If you wait yet another eleven days, half the remaining ones will be gone.

Quantum theory can make predictions about this half-life. But what the theory cannot tell us is when any given radium nucleus will decay. Imagine that two such nuclei lie before you. They are identical: nevertheless, if you come back a couple of weeks later, you might find that one of them has decayed while the other is still intact. But why? What is the difference between the two, which allowed one to survive longer than the other? The theory has nothing to say on the matter.

In speaking of radioactive decay I have already used the analogy of leaves falling from a tree (chapter 2). Here is another analogy. Suppose that the weather bureau has predicted a 50 percent chance of rain on Monday—but that when Monday rolls around, you find that it fails to rain. Suppose further that again on Tuesday the prediction is for a 50 percent chance of rain, and that again Tuesday remains sunny. So it might go for several days until, on Saturday (for which the prediction is still a 50 percent chance of rain), the rain finally comes.

What was different about Saturday? We do not know, but we have some suspicions. Maybe it was a sudden incursion of cooler air from Canada, which the weather bureau had not foreseen. Or maybe it was a lower-than-usual air pressure coming up from the south. Weather is complicated, after all, so we forgive the weather bureau.

We may not know the reason for Saturday’s rain, but we are positive that this reason exists. That reason is a hidden variable. If we ever managed to figure out why it rained on Saturday, it would no longer be hidden. It would be a “seen variable”—a known variable.

In terms of radioactive decay, if there is a reason, quantum theory does not give it to us. Just as the theory has no way within its language to give a precise specification of the direction of spin, it has no way to predict when any given nucleus will decay. If you are looking for such a reason, you are looking for a hidden variable. And if you are looking for a hidden variable, you are looking for a more complete theory than quantum mechanics. A better theory. A loquacious Predictor, one willing to speak more openly.

John Bell’s Theorem dealt with the question of hidden variables. Do they exist? Is there a reality that my Great Predictor sees, but refuses to speak of? Is quantum mechanics a mere half-theory, destined to be replaced by a clearer view of reality? Or are hidden variables and the reality they represent a naive fantasy, a leftover from an earlier and outmoded picture of the world?

We are ready to turn to Bell’s Theorem.