According to quantum mechanics, the measurement of a property A necessarily disturbs the system, so that the value of a different property B obtained after the measurement of A is different from the value of B before the measurement of A. However, it is possible to decrease the measurement interaction to the point where the disturbance of B is negligible. In this weak measurement limit, it is possible to determine the value of A conditioned by the final measurement outcome of B, without disturbing B in the process. The weak values obtained in such measurements have attracted a lot of attention because they can exceed the limits set by the extremal eigenvalues of A [1]. Recently, it has been shown that weak values can be described as averages of complex valued probability distributions, where the possibility of negative real parts not only explains the observation of averages outside the range of eigenvalues, but also resolves a number of quantum paradoxes, which are usually based on the assumption of positive joint probabilities [2].
In this presentation, I show that complex conditional probabilities provide a consistent explanation of all quantum effects. In particular, it is pointed out that complex conditional probabilities describe universal relations between three physical properties that represent the correct quantum limit of classical determinism. In these relations, the complex phase corresponds to the action of transformations between two physical properties along the third. Importantly, a simultaneous assignment of realities to the three different properties is impossible, because measurement interactions change the effective reality of the system according to the laws of dynamics. This relation between complex probabilities and measurement dynamics can be summarized by a quantitative relation which I call the law of quantum ergodicity. As I recently showed, this law can be used to derive the complete Hilbert space formalism, providing a physical explanation of quantum mechanics in terms of the fundamental relation between the reality of physical properties and the dynamics by which they are observed [3]. The results recently obtained from weak measurements of quantum systems might thus be the key that unlocks the mysteries of quantum mechanics.
[1] Aharonov et al., PRL 60, 1351 (1988)
[2] Hofmann, NJP 14, 043031 (2012)
[3] Hofmann, arXiv:1306.2993