Essay review

Classical versus quantum ontology

It is assumed that in the physical phenomenon under investigation a one-dimensional signal is chosen as a measurement subject and the estimation of the numerical value of a certain parameter of such a signal is the main goal of all undertaken activities. In the paper, the formal framework and also the methodology are presented by which all the available knowledge about the investigated signal may be taken into account.

First, the signal is modeled as a point in the multidimensional number space. Next, the entire available signal knowledge is broken down into a set of individual information items and each of them is modeled as a specific constraint introduced into such signal space, which leads to a geometrical interpretation. Consequently, the measurement of any parameter of the signal may be considered as acquiring the additional information item and may be modeled consistently with other items of the prior knowledge.

Then measurability conditions of an interesting signal parameter with an acceptable value of the final uncertainty, have been formulated in the form of the following demands: (1) precise enough definition of the estimated parameter, guaranteeing parameter repeatability for the available knowledge; (2) sufficient stationarity of the investigated signal; and (3) appropriate manner and accuracy of the signal investigation for the available knowledge. The last demand has been discussed in detail: appropriate notions are introduced, necessary for the description and analysis of the information gathering process and for the information usability evaluation.

Finally, an example of the signal mean-square value uncertainty analysis was presented for four cases of progressive signal knowledge.

In the Bayesian approach to quantum mechanics, probabilities—and thus quantum states—represent an agent's degrees of belief, rather than corresponding to objective properties of physical systems. In this paper we investigate the concept of certainty in quantum mechanics. Particularly, we show how the probability-1 predictions derived from pure quantum states highlight a fundamental difference between our Bayesian approach, on the one hand, and Copenhagen and similar interpretations on the other. We first review the main arguments for the general claim that probabilities always represent degrees of belief. We then argue that a quantum state prepared by some physical device always depends on an agent's prior beliefs, implying that the probability-1 predictions derived from that state also depend on the agent's prior beliefs. Quantum certainty is therefore always some agent's certainty. Conversely, if facts about an experimental setup could imply agent-independent certainty for a measurement outcome, as in many Copenhagen-like interpretations, that outcome would effectively correspond to a preexisting system property. The idea that measurement outcomes occurring with certainty correspond to preexisting system properties is, however, in conflict with locality. We emphasize this by giving a version of an argument of Stairs [(1983). Quantum logic, realism, and value-definiteness. Philosophy of Science, 50, 578], which applies the Kochen–Specker theorem to an entangled bipartite system.