Position and quantum theory (Q1114986)

It is customarily maintained that the concept of unmeasured (i.e., unobserved) position is without meaning in quantum theory. However, the vast literature on the subject, as shown here through the typical example of the double-slit experiment, really does not provide an iron-clad proof that this is indeed so. The question of the possible meaning of unobserved position is thus open. The problem is then resolved by showing quite rigorously that, after all, unobserved position is meaningless in quantum theory. The criterion for unobserved position to be meaningful in any theory (probabilistic or not) is taken to be that the probability density for position must satisfy the Einstein-Chapman-Kolmogorov equation with a positive-semidefinite kernel which is also properly normalized.