Individualistic and Statistical Interpretation of Quantum Mechanics

The quantum mechanical formalism which was discovered by Heisenberg¹ and Schrödinger² in 1925 was first interpreted by Born³ in a statistical sense. The formal expressions p(φ,a _i )=|(φ,φa _i |², i∈N were interpreted as the probabilities that a quantum system S with preparation φ possesses the value a _i which belongs to the state φa _i . This original Born-interpretation which was formulated for scattering processes was, however, not tenable in the general case. The probabilities must not be related to the system S in state φ since in the preparation φ the value a _i of an observable A is in general not subjectively unknown but objectively undecided. Instead, one has to interpret the formal terms p(φ, a _i ) as the probabilities for finding 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 present day literature.