We develop an algebraic frame for the simultaneous treatment of actual and possible properties of quantum systems. We show that, in spite of the fact that the language is enriched with the addition of a modal operator to the orthomodular structure, contextuality remains a central feature of quantum systems.
Modality, Potentiality and Contradiction in Quantum Mechanics
在[11]中，Newton da Costa与本文作者一起论证了用次协调方法考虑量子叠加的可能性。我们声称，尽管对量子力学（QM）的大多数解释都试图逃避矛盾，但有许多迹象表明，从事这类研究可能是值得的。最近，Arenhart和Krause [1，2，3]提出了几个反对这种方法的论点，并声称，考虑到反对的平方，量子叠加更好地理解为矛盾命题而不是矛盾命题。在[17]中，我们捍卫了量子叠加的次协调方法（PAQS），并提供了支持其发展的论据。本文分析了量子力学中模态、势和矛盾的含义，并进一步论证了为什么PAQS比Arenhart-Krause提出的量子叠加的多样性方法（CAQS）更适合于面对量子技术迫使我们考虑的解释性问题。
I argue that Bohmian mechanics (or any similar pilot-wave theory) cannot reasonably be claimed to be a deterministic theory. If one assumes the "quantum equilibrium distribution" provided by the wave function of the universe, Bohmian mechanics requires an external random oracle in order to describe the (Kolmogorov-Levin-Chaitin) algorithmic randomness properties of typical outcome sequences of long runs of repeated identical experiments (which provably follow from the Born rule). This oracle lies beyond the scope of Bohmian mechanics (or any deterministic extension thereof), including the impo…
A recent series of experiments have demonstrated that a classical fluid mechanical system, constituted by an oil droplet bouncing on a vibrating fluid surface, can be induced to display a number of behaviours previously considered to be distinctly quantum. To explain this correspondence it has been suggested that the fluid mechanical system provides a single-particle classical model of de Broglie's idiosyncratic 'double solution' pilot wave theory of quantum mechanics. In this paper we assess the epistemic function of the bouncing oil droplet experiments in relation to quantum mechanics. We fi…
In this brief review, we comment on the concept of shape invariant potentials, which is an essential feature in many settings of $N=2$ supersymmetric quantum mechanics. To motivate its application within supersymmetric quantum cosmology, we present a case study to illustrate the value of this promising tool. Concretely, we take a spatially flat FRW model in the presence of a single scalar field, minimally coupled to gravity. Then, we extract the associated Schrödinger-Wheeler-DeWitt equation, allowing for a particular scope of factor ordering. Subsequently, we compute the corresponding supersy…
Gleason's theorem [A. Gleason, J. Math. Mech., \textbf{6}, 885 (1957)] is an important result in the foundations of quantum mechanics, where it justifies the Born rule as a mathematical consequence of the quantum formalism. Formally, it presents a key insight into the projective geometry of Hilbert spaces, showing that finitely additive measures on the projection lattice $\PH$ extend to positive linear functionals on the algebra of bounded operators $\BH$. Over many years, and by the effort of various authors, the theorem has been broadened in its scope from type I to arbitrary von Neumann alg…
