Quantum Foundations Detail

Quantum theory was developed during the first part of the last century by studying the behaviour of small things like atoms and photons (particles of light). The word "quantum" refers to the fact that light is apparently released and absorbed in lumps or quanta. But this is not the main point of quantum theory. There are other features of the theory that mark it out as representing a radical point of departure from classical theories (theories predating quantum theory are often collectively referred to as "classical") and force us to reconsider our picture of reality. In classical theories the mathematical symbols in the theory relate in a simple way to a picture of the world that is not far removed from our everyday experience. For example, a ball flying through the air might be described in Newtonian mechanics by mathematical symbols representing its speed, its position, the direction in which it is moving, and the speed and direction in which it is spinning. These quantities relate directly to the picture (which we can quite easily visualize in our minds) of a spinning ball moving through the air. Before quantum theory came along, it was taken for granted that the quantities we use in physics relate in a simple way to some such picture of the world and it came as something of a shock that quantum theory is not obviously like that. What quantum theory provides us with is a neat and simple mathematical formalism for calculating probabilities relating to measurements we might make on quantum systems.

In fact, once stripped of all its inessential structure, quantum theory can be regarded as a generalization of classical probability theory—that theory we use to calculate the odds when rolling dice. The quantum formalism consists of various mathematical symbols. The great thing about quantum theory is that it works! So far no one has seen a deviation from the rules of quantum theory. However, unlike in the classical case (for example with the spinning ball), the symbols in the theory do not relate in any obvious way to any simple intuitive picture of reality. Knowing how to use quantum theory is a little like knowing how to perform magic but without understanding why the magic works. This leads us to ask three types of question:

• Exactly what is it that is odd about quantum theory—where does it contradict our usual intuitions about reality?
• How should we interpret quantum theory—what kind of picture of reality, if any, does it give us?
• Why is nature described by quantum theory (rather than some other possibly more sensible theory)?

Attempts to answer these questions represent the main research efforts in the foundations of quantum theory.

What Is Odd About Quantum Theory?

Let us start by considering a ball (a baseball for example) which can be in one of two boxes—box A or box B. Imagine we do not know which box it is in. In this case we are still inclined to believe it is actually in one of the two boxes while nothing is in the other box. The fact that we do not know which one is interpreted as ignorance on our part, having nothing to do with the real world. However, now imagine that rather than a ball, we have a quantum object like an atom. In this case it would be wrong, in general, to suppose that the atom was actually in one box and not the other. In quantum theory the atom can behave like it is, in some sense, in both boxes at once. Of course, if we look into the boxes to find out where the atom is (we could do this by shining bright laser light into the boxes and look for the light scattered by the atom) then we will only find it in one of the two boxes, not both, since there is only one atom. Why, then, say it can behave like it is in both boxes at once? Well, physics is ultimately a discipline which relates to experiments, so to answer this question let us consider an experiment which, as we will see, leads us to the strange conclusion that something can be in two places at the same time.

Consider a quantum particle (it could be an electron, an atom, a photon, or any other type of quantum particle). Let the particle impinge on a beam splitter. This is a device which may either transmit the particle or reflect it as shown on the next page.