The main positivist/instrumentalist interpretation is the Copenhagen interpretation which was developed by Niels Bohr and colleagues working in Copenhagen. Bohr emphasizes that all experiments must be described in classical language. Thus, we have to make statements like "the pointer is pointing at the number 5" or "the ball was found in box A". Any laboratory notebook consists of many statements just like this. Bohr then argues that quantum theory is simply a consistent way of dealing with such statements. Often one can tell a story about what happened in an experiment such as "the photon was reflected at the beam splitter and travelled along path A, finally being detected at detector A". In fact, we did not see the particle being reflected nor travelling along path A. All we know is that the detector in path A fired. In an interference experiment we would not be so keen to tell a story about which path the particle travelled along. In this case we might tell a different type of story in which a wave travelled along both paths, these two waves being brought back together at the second beam splitter. The type of story we are likely to tell depends on the experimental context. Bohr describes such descriptions as complementary and he describes his interpretation of quantum theory as complementarity. It is not clear whether these "stories" should be regarded as anything more than just stories, or whether we should think of them as corresponding to what is actually happening in the world. The advantage of the Copenhagen interpretation is that it provides a consistent way of talking about quantum experiments. However, since it requires all physical statements to be related to concrete classically described apparatuses, it is difficult to arrive at a picture of what is happening in the world independent of any measurements that may be made.

Why Quantum Theory?

We know from experimental evidence that quantum theory works very well. But we also know that it is a very strange physical theory. This motivates the obvious question: why is nature described by quantum theory? How do we begin to answer a question like this? Usually explanation in physics is by means of appealing to some set of deep, simple and intuitive principles. The principles of quantum theory, whilst mathematically simple, are rather abstract and cannot be described as intuitive. It is instructive to compare this with the situation in Einstein's theory of special relativity which follows from two principles: the laws of physics are the same in all frames of reference and the speed of light is a constant for all observers. Is it possible to find a similar set of simple and intuitively reasonable principles for quantum theory? This question has been around for a while. One approach has been to reconsider logic. It can be argued that quantum theory forces us to modify the rules of logic. In this case, we could attempt to derive quantum theory from a modified set of logic rules. There has been a tremendous amount of work on quantum logic (which is, by now, a field in its own right). However, it is fair to say that, so far, no simple approach has emerged. Another approach stems from the observation that quantum theory is, when stripped of inessential structure, simply a new type of probability theory. Hence, we can consider what a reasonable theory of probability might look like. One of our researchers, Lucien Hardy, has shown that we can obtain quantum theory from five principles in this probability context. Four of the five principles are true in classical probability theory and hence it is the remaining principle that gives rise to quantum theory. To understand this remaining principle, consider a system which can be in the state 0 or the state 1 (a bit). In classical physics the only way to go from the 0 state to the 1 state is to jump—one moment the state is 0, the next it is 1. But in physics we prefer things to change in a gradual fashion. The remaining principle (which gives rise to quantum theory) demands that there exist a way of gradually transforming the state. This implies that there exist an infinity of states between 0 and 1. These "in between" states are just the usual quantum superpositions.

The future of quantum theory?

Quantum theory remains a deeply mysterious subject. Progress in understanding it will come from theoretical, philosophical and experimental developments. On the experimental side we might, one day, expect to see some deviation from the laws of quantum theory in the laboratory. Perhaps we will observe collapse for macroscopic objects. Perhaps we will see a violation of quantum theory at a much more fundamental level. At the theoretical end we need new tools for gaining insight into the theory. By understanding more deeply the reasons why nature is described by quantum theory we might be able to go beyond the theory. At a philosophical level, we might come to a better understanding of the world and our place in it if we can decode what the equations of quantum theory are trying to tell us.

Lucien Hardy.