How Should We Interpret Quantum Theory?

There are many interpretations of quantum theory. At the risk of committing a gross over-simplification, we can say that they fall into two basic categories. There are realist/ontological interpretations and positivist/instrumentalist interpretations. Realism is the idea that the real world exists independently of us. To provide an ontology is to provide a picture of the world. So, in realist/ontological interpretations, an attempt is made to come up with a picture of an independently existing world which goes beyond what we actually see (that is to say it goes beyond the detector clicks and meter readings we record in our laboratory notebooks). Positivism is the doctrine that there is nothing beyond what we directly observe. An instrumentalist emphasizes the role of instruments (in our case, the laboratory equipment) in the description of any phenomena. Positivist/instrumentalist interpretations are not so concerned with developing a picture of an independently existing world. Rather, an attempt is made to develop a consistent way of thinking about the various detector clicks, meter readings, and other effects.

The realist/ontological interpretations can best be summarized by where they fall on the following table:

In collapse models the evolution of the state is chosen such that the state will collapse whenever a superposition of a sufficiently large object occurs. This means that the macroscopic world does consist of objects with definite properties and explains why, when we look, we do not have the experience of seeing a baseball in two places at once. The quantum state can be regarded as a real existing object which, in the limit of the macroscopic world, accords with our usual experience. There have been various attempts to build explicit collapse models with some degree of success, though without guidance from some overriding principle, such models are ad hoc. It has been suggested by Penrose and others that gravitational mechanisms should induce collapse, but this idea has yet to lead to a fully worked out model. If collapse really happens then this should be detectable in experiments and there is currently some effort being made to do this. Unfortunately, it may be a long time before experimental techniques are sufficiently refined to detect collapse—if it happens.

In the pilot wave model, the usual quantum description of the state (as a state vector or wavefunction) is supplemented by an additional variable actually specifying the positions of the particles. In the interferometer we can say that there is a wave that goes along both paths whilst the particle only goes along one path. The wave collects information about both paths and the particle uses this information to decide which way to go at the second interferometer (hence the "pilot-wave"). This interpretation of quantum theory has various advantages. For example, it explains why the particle is only detected in one place at once and it provides an almost classical picture of what is happening at the microscopic level. However, to do this it is necessary to introduce variables which go beyond quantum theory and detract from much of its simplicity and elegance.

The third option on the table is when we have no collapses and no hidden variables. In this case, we really do get superpositions of macroscopic objects. We need a way to explain why we do not actually see this. The solution proposed by what is variously called the many worlds interpretation, the Everett interpretation (after Hugh Everett who invented it), and the relative state interpretation (this was Everett's name for it and, despite being less popular is a more accurate description of Everett's idea) is that we can regard the world as splitting when a macroscopic superposition occurs. In each branch one of the macroscopic possibilities happens. In an individual world, macroscopic objects have well defined locations but when all the worlds are taken together, it is still the case that there are superpositions of macroscopic objects. One way of thinking about the splitting is that it is merely an artefact introduced to help us understand the whole picture. Consider the analogy of drawing a grid on a map so we can describe features on the map relative to the grid. The grid does not actually exist. Likewise we can argue that there is, in Everett's interpretation, only one universe but by introducing a splitting we can explain the appearance of the world relative to a particular observer. There are many problems with this interpretation. The most obvious is that it represents an extremely radical new view of the universe that many of us feel uncomfortable with. But, even if we can swallow this, there remain technical problems. One is that there are many ways to introduce the splitting into many worlds and yet we need to pick out some preferred way of doing this. Another more serious problem is probability. Each world in the splitting has a weighting attached to it which is supposed to represent the probability of that world. A probability is usually regarded as a probability of some particular possible outcome actually happening. However, in the Everett picture all outcomes are realized and so it is not clear what this probability is a probability of.