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The structure of a complete lattice formed by closed linear subspaces of a Hilbert space (i.e., a Hilbert lattice) entails some unreasonable consequences from the physical point of view. Specifically, this structure seems to contradict to…
In recent work, Benjamin Schumacher and Michael~D. Westmoreland investigate a version of quantum mechanics which they call "modal quantum theory" but which we prefer to call "discrete quantum theory". This theory is obtained by…
Experiments in cognitive science and decision theory show that the ways in which people combine concepts and make decisions cannot be described by classical logic and probability theory. This has serious implications for applied disciplines…
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
Linearity allows several versions of reality to simultaneously exist in the state vector. But it implies that there is no interaction between versions, and that there will never be perception of more than one version. It also implies, in…
The convenience of coherent state representation is discussed from the viewpoint of what is in a broad sense called the measurement problem in quantum mechanics. Standard quantum theory in coherent state representation is intrinsically…
Quantum game theory, whatever opinions may be held due to its abstract physical formalism, have already found various applications even outside the orthodox physics domain. In this paper we introduce the concept of a quantum auction, its…
Since its inception, many physicists have seen in quantum mechanics the possibility, if not the necessity, of bringing cognitive aspects into the play, which were instead absent, or unnoticed, in the previous classical theories. In this…
Studying the extent to which realism is compatible with quantum mechanics teaches us something about the quantum mechanical universe, regardless of the validity of such realistic assumptions. It has also recently been appreciated that these…
Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of…
While complex numbers are essential in mathematics, they are not needed to describe physical experiments, expressed in terms of probabilities, hence real numbers. Physics however aims to explain, rather than describe, experiments through…
The purpose of this article is threefold. Firstly, it aims to present, in an educational and non-technical fashion, the main ideas at the basis of Aerts' creation-discovery view and hidden measurement approach: a fundamental explanatory…
It is sometimes stated that Gleason's theorem prevents the construction of hidden-variable models for quantum entities described in a more than two-dimensional Hilbert space. In this paper however we explicitly construct a classical…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
An hidden variable (hv) theory is a theory that allows globally dispersion free ensembles. We demonstrate that the Phase Space formulation of Quantum Mechanics (QM) is an hv theory with the position q, and momentum p as the hv. Comparing…
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several…
Recently, it has been argued that quantum mechanics is a complete theory, and that different quantum states do necessarily correspond to different elements of reality, under the assumptions that quantum mechanics is correct and that…
It has been experimentally demonstrated that quantum coherence can persist in macroscopic phenomena [J.R. Friedman et al.,Nature, 406 (2000) 43]. To face the challenge of this new fact, in this article QM in its standard form is assumed to…
We survey some of the main conceptual developments in the study of PT-symmetric and pseudo-Hermitian Hamiltonian operators that have taken place during the past ten years or so. We offer a precise mathematical description of a quantum…
In the tradition of toy models of quantum mechanics in vector spaces over finite fields (e.g., Schumacher and Westmoreland's "modal quantum theory"), one finite field stands out, 2, since vectors over 2 have an interpretation as natural…