SUPERPOSITIONS > Implications The principle of superposition is closely connected to the indeterminism of quantum phenomena. If the principle did not hold (i.e. if the set of quantum states required to account for the empirical data included some state vector, but not their superpositions), one could possibly find a deterministic model of quantum phenomena. Yet, a careful examination of the correlations existing between entangled systems shows that such models (or at least a large class of them) are not rich enough to account for all the situations covered by the quantum formalism (see wave-particle duality).

The exotic empirical implications of the principle of superposition raise concerns about the possibility of extending quantum mechanics beyond the domain of atomic phenomena.

The Schrödinger's cat paradox, for example, emphasizes the fact that the principle of superposition does not seem to apply to the ‘macroscopic’ world, although there is nothing in quantum mechanics that forbids the entanglement between atomic systems and macroscopic bodies. As pointed out by John von Neumann, this situation presents itself each time that a measurement is performed, since, according to quantum mechanics, the observed system becomes entangled with the measuring device. This is one aspect of the so called ‘measurement problem’ (see Schrödinger's cat).

A second aspect is illustrated by the following situation. Consider an atom in a box and suppose that, based on its wave function, we predict that the atom is anywhere inside the box. Now suppose that at time t₀ we measure the exact position of the atom and find it in a small region around point . The immediate repetition of the measurement will of course confirm this information. This means that the probability of detecting the atom - a uniform distribution at t < t₀– has become a peak that differs from zero only in a small region centered in . In other words, it appears as an abrupt change in the mathematical form of the wave function occurred as an effect of observation. One says in this case that the wave function underwent a reduction (or collapse). If the wave function is taken to mirror some objective properties of the atom, its collapse seems to entail a real physical process which remains entirely unexplained. However, if - following the Copenhagen view the wave function is regarded as merely an abstract symbol for predicting results, the only thing that demands to be explained is why, once the measurement has been performed any further possible observation will agree with the predictions of the reduced wave function.

The far-reaching implications of the superposition principle have also been analyzed in the framework of logic. At the price of modifying the axioms of classical logic, one can trace quantum phenomena back to an underlying world of objects and properties. Since such objects obey the rules of quantum logic, however, they exhibit behaviors that differ substantially from those of their classical counterparts.

The study of the formal structure of the state space, and in particular of entangled states, has proved very stimulating in the fields of information and computer science. Recent experiments have demonstrated the possibility of ‘teleporting’ a quantum state, broadcasting encrypted quantum information and entangling a few quantum logic gates in order to implement elementary quantum algorithms (see also Schrödinger’s cat).