COMPLEMENTARITY > Implications According to Bohr's ‘principle of complementarity’, wavelike and corpuscular pictures, though mutually exclusive, are both necessary to give an exhaustive account of the behavior of a quantum system. This does not give rise to inconsistency, since the system behaves differently in different situations, and, within the ‘Copenhagen view’, we should not expect from the quantum formalism anything more than a method to establish correlations between meansurement results obtained in well-defined situations.

Since the Thirties, this approach was rejected as ‘positivistic’ by some influent physicists (the issue was at stake in some famous debates between Einstein and Bohr). According to the critics of the Copenhagen view, meansurement results reflect properties that must exist independently of the kind of meansurement one chooses to perform upon a given system. The fact that quantum mechanics says nothing definite about these putative properties should be ascribed to a lack of completeness of that theory. Furthermore, for some scientists, the indeterminism of quantum phenomena might be taken to imply that a deeper, deterministic description of reality existed. They suggestested that quantum theory could be derived from a more fundamental theory, in the same way as thermodynamics had been derived from statistical mechanics.

Following this line of thought, a number of attempts were made to develop a theoretical framework based on the so called hidden variables, i.e. variables which were supposed to escape the formalism of quantum mechanics and to govern phenomena at a deeper, perhaps deterministic level. David Bohm elaborated for example a model in which particles follow a precise (thought not entirely knowable) trajectory, determined not only by conventional physical forces, but also by a quantum potential that is supposed to supply ‘active information’ about the whole environment in which the motion takes place.

However, hidden variables models suffer severe limitations. Some fundamental works, and in particular a couple of famous theorems by John Bell, have proved that, in order to be compatible with the (successfully tested) predictions of quantum mechanics, ‘hidden reality’ must exhibit quite exotic features (for example, in order to reproduce the correlations predicted by entangled states, ‘hidden reality’ must be ‘non-local’, allowing for instantaneous influence between spatially separated systems). Aside from fundamental implications, interference phenomena are responsible for crucial quantum effects and have wide applications. Just to mention an example, Pauli's exclusion principle can be understood as an interference effect, as well as many other situations in which a particle is never found in a place or configuration which - on grounds of classical considerations - one would expect to be accessible.

The quantum theory of radiation led to the invention of devices, like the laser for example, whose applications in contemporary technology are virtually unlimited. The corpuscular aspect of radiation has recently become available to direct experimental investigation and individual photons can now be manipulated or used to manipulate atoms. Conversely, atomic physics has become more and more familiar with the ‘wavelike nature’ of atoms. Many techniques inherited from quantum optics, have been successfully applied both to individual atoms and to ensembles of atoms. For example, one can build-up gratings of standing waves to implement an atom interferometer, or use light momentum to trap the atoms or to stop their thermal motion, cooling them down to temperatures of the order of nanokelvin. The field of ‘atom optics’ is improving rapidly, and devices like atom lasers and atom interferometers are being currently operated in the laboratory. The wavelike nature of quantum particles is particularly apparent in collective phenomena, in which massive particles no longer behave as independent material bodies, but display collective patterns governed by a global wave function.

Among the most impressive collective phenomena, we can mention superconductivity (i.e. the ability of some materials to conduct electric charges without dissipation; extremely strong magnetic fields can thus be generated and highly reflecting surfaces manufactured), superfluidity (i.e. the ability of liquid Helium to flow without dissipation when cooled down to very low temperatures), and Bose-Einstein condensates of atoms.

The later examples, which refer to macroscopic effects, are quite exceptional, since, as a rule, wave-particle duality is a characteristic feature of microscopic phenomena. Indeed, to provide a satisfactory quantum account of everyday ‘macroscopic’ experience, which does not exhibit wave-particle duality, is a challenging problem. As discussed in the section about the Schrödinger's cat, this can perhaps be achieved by taking into account the bad isolation of macroscopic systems and their entanglement with the environment (see also origins).