"Surely, after 62 years, we should have an exact formulation of some serious part of quantum mechanics?" wrote the eminent Northern Irish physicist John Bell in the opening salvo of his Physics World article, "Against 'measurement' ". Published in August 1990 just two months before his untimely death at the age of 62, Bell's article outlined his concerns. As he further explained, "By 'exact' I do not of course mean 'exactly true'. I mean only that the theory should be fully formulated in mathematical terms, with nothing left to the discretion of the theoretical physicist...until workable approximations are needed in applications."

Although Bell spent the majority of his career as a theoretical particle physicist and worked on accelerator design at the CERN lab in Geneva, today he is best known for his contributions to deep, foundational questions that probe the meaning of quantum mechanics. Nearly a century after it was first formulated, there is still no consensus among physicists on how the theory should be interpreted. "I think I can safely say that nobody understands quantum mechanics," Richard Feynman famously declared - a rather extraordinary admission for a foundational theory that underpins much of our understanding of modern physics.

Indeed, the debate about the interpretation of quantum mechanics, which began in 1927, continues to this day. It became polarized around the views of its two leading protagonists - Niels Bohr and Albert Einstein. In essence, this was a debate about the meaning of the theory's central concept, the quantum wavefunction - a mathematical description of the quantum state of a system, which contains all its measurable information.

According to Bohr the wavefunction shouldn't be taken as a literal representation of the real physical state of a real physical system. While he acknowledged its importance and significance in solving quantum problems, he insisted that "it must be recognized, however, that we are here dealing with a purely symbolic procedure, the unambiguous physical interpretation of which in the last resort requires a reference to a complete experimental arrangement" (Essays 1958-1962 on Atomic Physics and Human Knowledge, Wiley Interscience). Indeed, he is famously quoted as saying "There is no quantum world. There is only an abstract quantum physical description."

For Bohr, the quantum formalism is a "purely symbolic procedure" that lets us use our experiences of past measurements to predict the results of future ones. On this understanding all measurements are classical, as this is the only kind of physics we can experience directly. But the quantum nature of the objects under study means that the apparatus and the way it is set up determines what we can expect to observe. With one kind of apparatus we can choose to observe the wave-like nature of a "beam" of electrons. With another kind of apparatus, we can choose to observe the particle-like nature of individual electrons. These are mutually exclusive, not because we lack the ingenuity to conceive of an apparatus to expose both types of behaviour simultaneously, but because such an apparatus is simply inconceivable.

According to Bohr what we cannot do is go beyond these complementary descriptions and say what an electron actually is when it is not being observed. This became known as the "Copenhagen interpretation", named after the location of Bohr's Institute for Theoretical Physics. This and other variants on the general theme of the Copenhagen interpretation are essentially "anti-realist". This doesn't mean that such interpretations deny the existence of an objective reality, or the reality of "invisible" entities such as electrons. It means that the theoretical representation of these entities shouldn't be taken too literally.