Individualistic Versus Statistical Interpretation of Quantum Mechanics

Abstract

The quantum mechanical formalism which was discovered by Heisenberg [1] and Schrödinger [2] in 1925 was first interpreted by Born [3] in a statistical sense. The formal expressions p(φ, a _i ) = |(φ, φ ^ai )|² , i ∈ ℕ are interpreted as the probabilities to find the value a _i after the measurement of the observable A of the system S with preparation φ. In this improved version the statistical or ‘Born interpretation’ is used in the present day literature. Usually the statistical (Born) interpretation of quantum mechanics is taken for granted and the formalism of quantum mechanics is considered as a theory which provides statistical predictions. On the other hand, the meaning of the same formal terms p(φ, a _i ) for an individual system is highly problematic. Heisenberg [4] tried to understand the meaning of the terms p(φ, a _i ) for a single system by means of the Aristotelian concept of ‘potentia’. Popper introduced for the same reason the new concept of ‘propensity’. However, since both attempts to understand probability on the individual level don’t give rise to any observable prediction, in the current literature the individualistic interpretation of quantum mechanics is not considered as an alternative which should be taken seriously.