COMPLEMENTARITY One of the most astonishing characteristics of the quantum world is the so called ‘wave-particle duality’, i.e. the fact that microscopic physical systems appear to behave either like massive bodies or like a wave depending on the experimental context in which they are observed. Thus, for example, the tracks observed in a bubble chamber are naturally ascribed to material particles that occupy at any instant a small portion of space and scatter each other when they come into contact. On the other hand, the same sistems display wavelike features when sent through an interferometer (see experimental evidence). In this case they appear as if they were completely delocalized (which allows one to use the notions of wavelength and frequency in this context ).

This state of affairs was expressed in the following terms by Niels Bohr, the patriarch of the Copenhagen School: ‘As a description of microentities and microprocesses, neither a particle description nor a wave description is fully adequate. Between them, however, they form a complete, complementary description ’. The ‘corpuscular nature’ of light was not a new hypothesis in physics (it had been popular in the Middle Ages and had been later advocated by Newton). However, it was Max Planck who, in 1900, demonstrated its essential role in the analysis of the interaction between matter and radiation. Following Planck's work (which can be considered the act of birth of quantum physics), Einstein suggested that electromagnetic energy is carried by corpuscular massless entities: the photons.

Given an electromagnetic plane wave of frequency ν and wavelength λ, the associated photons have energy E=hν (h being the Planck constant) and momentum p=h/λ (parallel to the wave's propagation vector, see origins). Influenced by Einstein's ideas and by his work on the equivalence of energy and mass, Louis de Broglie postulated similar relations for material particles as well. If light had a corpuscular aspect, material particles had a wavelike one.

The subsequent step was the recognition (due in particular to Max Born) of the statistical nature of ‘matter waves’. According to the probabilistic interpretation of the wave function, wavelike patterns refer to the probability of detecting a particle within a given region of space. Therefore, it is necessary to process an ensemble of particles in order to see interference fringes. These interference fringes reflect a general behaviour of the probability distributions associated with the possible outcomes of quantum observables. They are the empirical manifestation in ordinary space of the superposition of quantum states occurring in the abstract Hilbert space.

The necessity of employing ‘complementary’ pictures in the description of quantum phenomena is linked to the existence of incompatible observables and to the impossibility of deriving the empirical data from a deterministic model conceived in terms of classical objects and properties. Concepts like the one of material body are so deeply rooted in our common language that their use can hardly be avoided when describing the phenomena and the conditions under which they occur. However, there is no a priori guarantee that the ensemble of the observed results can be taken to reflect a world conceived in terms of such concepts. Indeed, quantum theory does not seem to provide a pictorial model of the world, but rather an effective formal tool for predicting the results of measurements performed in any specific experimental context. According to Bohr, an unambiguous, objective description of quantum phenomena can only be provided by using complementary ‘classical’ pictures for the same system observed under different conditions. (See implications for further discussion.)