An Approach to Quantum Mechanics via Conditional Probabilities

Gianni Cassinelli, Nino Zanghı̀

Wawrzyniec Guz

John Halpin

The nature of quantum mechanical probability has often seemed mysterious. To shed some light on this topic, the present paper analyzes the logical form of probability assignment in quantum mechanics. To begin the paper, I set out and criticize several attempts to analyze the form. I go on to propose a new form which utilizes a novel, probabilistic conditional and argue that this proposal is, overall, the best rendering of the quantum mechanical probability assignments. Finally, quantum mechanics aside, the discussion here has consequences for counterfactual logic, conditional probability, and epistemic probability.

Gábor Hofer‐Szabó

The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical representation of classical conditional probabilities is situated within the broader frame of noncommutative representations. To this goal, we adopt some parts of the quantum formalism and ask whether empirical data can constrain the rest of the representation to conform to quantum mechanics. We will show that as the set of empirical data grows, conventional elements in the representation gradually shrink and the noncommutative representations narrow down to the unique quantum mechanical representation.

C. T. K. Chari

Peter Mittelstaedt