Related papers: The logic of quantum mechanics

I present the background of the Bohm approach that led John Bell to a study of quantum non-locality from which his famous inequalities emerged. I recall the early experiments done at Birkbeck with an aim to explore the possibility of…

The tensor product postulate of quantum mechanics states that the Hilbert space of a composite system is the tensor product of the components' Hilbert spaces. All current formalizations of quantum mechanics that do not contain this…

Quantum mechanics provides a statistical description about nature, and thus would be incomplete if its statistical predictions could not be accounted for some realistic models with hidden variables. There are, however, two powerful theorems…

Lorentz covariance imposed upon a quantum logic of local propositions for which all observers can consistently maintain state collapse descriptions, implies a condition on space-like separated propositions that if imposed on generally…

Quantum theory is usually formulated in terms of abstract mathematical postulates, involving Hilbert spaces, state vectors, and unitary operators. In this work, we show that the full formalism of quantum theory can instead be derived from…

In the area of the foundations of quantum mechanics a true industry appears to have developed in the last decades, with the aim of proving as many results as possible concerning what there cannot be in the quantum realm. In principle, the…

In spite of the very common opinion we show that QM is not complete and that it is possible to create prequantum models providing finer description of physical reality than QM. There exists (at least in theoretical models) dispersion free…

Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…

We derive the Hilbert space formalism of quantum mechanics from epistemic principles. A key assumption is that a physical theory that relies on entities or distinctions that are unknowable in principle gives rise to wrong predictions. An…

"Ever since the advent of modern quantum mechanics in the late 1920's, the idea has been prevalent that the classical laws of probability cease, in some sense, to be valid in the new theory. [...] The primary object of this presentation is…

The apparent nonlocality of quantum theory has been a persistent concern. Einstein et. al. (1935) and Bell (1964) emphasized the apparent nonlocality arising from entanglement correlations. While some interpretations embrace this…

This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…

The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…

A foundation of quantum mechanics based on the concepts of focusing and symmetry is proposed. Focusing is connected to c-variables - inaccessible conceptually derived variables; several examples of such variables are given. The focus is…

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…

We argue that quantum nonlocality of entangled states is not an actual phenomenon. It appears in quantum mechanics as a consequence of the inconsistency of its superposition principle with the corpuscular properties of a quantum particle.…

We explore a simple approach to quantum logic based on hybrid and dynamic modal logic, where the set of states is given by some Hilbert space. In this setting, a notion of quantum clause is proposed in a similar way the notion of Horn…

Quantum theory and functional analysis were created and put into essentially their final form during similar periods ending around 1930. Each was also a key outcome of the major revolutions that both physics and mathematics as a whole…

A modern computer system, based on the von Neumann architecture, is a complicated system with several interactive modular parts. Quantum computing, as the most generic usage of quantum information, follows a hybrid architecture so far,…

Any quantum-mechanical system possesses a U(1) gerbe naturally defined on configuration space. Acting on Feynman's kernel exp(iS/h), this U(1) symmetry allows one to arbitrarily pick the origin for the classical action S, on a…