The noninvariance of deterministic causal models (Q1568381)

The author defends the use of deterministic causal models in explaining certain ergodic mechanical systems by using an important theorem in ergodic theory on \(\alpha\)-congruency due to \textit{D. S. Ornstein} and \textit{B. Weiss} [Bull. Am. Math. Soc. 24, No. 1, 11-116 (1991; Zbl 0718.58038)]. This theorem leads to the conclusion that if one has only finite accuracy of measurement, then one cannot observationally distinguish between a deterministic and an ergodic stochastic model that are \(\alpha\)-congruent. However, the property of being deterministic is not invariant under \(\alpha\)-congruency. The author argues that since we cannot discard with finite accuracy, in fact in quantum mechanics errors in measurement are essential part of the theory, the choice between deterministic and ergodic stochastic models remains with us and we are free to choose which we prefer for historical, metaphysical or perhaps computational reasons.