Related papers: Quantum points/patterns, Part 2. From quantum poin…
Aiming at providing an objective motion picture for the microscopic object described by the wave function, new analysis about motion is presented by use of the point set theory in mathematics, through which we show that a new kind of motion…
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…
The possibility of a quantum system to exhibit properties that are akin to both the classically held notions of being a particle and a wave, is one of the most intriguing aspects of the quantum description of nature. These aspects have been…
Supmech, which is noncommutative Hamiltonian mechanics \linebreak (NHM) (developed in paper I) with two extra ingredients : positive observable valued measures (PObVMs) [which serve to connect state-induced expectation values and classical…
In resisting attempts to explain the unity of a whole in terms of a multiplicity of interacting parts, quantum mechanics calls for an explanatory concept that proceeds in the opposite direction: from unity to multiplicity. It concerns the…
The quantum theory of a harmonic oscillator with a time dependent frequency arises in several important physical problems, especially in the study of quantum field theory in an external background. While the mathematics of this system is…
An interpretation and re-formulation of modern physics which removes the presumption of the space-time continuum, and bases physical theory on a small number of rational and empirical principles. After briefly describing the philosophical…
One of the most difficult problems in quantum mechanics is the analysis of the measurement processes. In this paper, we point out that many of these difficulties originate from the different roles of measurement outcomes and observable…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
Quantum Shannon theory is loosely defined as a collection of coding theorems, such as classical and quantum source compression, noisy channel coding theorems, entanglement distillation, etc., which characterize asymptotic properties of…
Quantum mechanics is derived from the principle that the universe contain as much variety as possible, in the sense of maximizing the distinctiveness of each subsystem. The quantum state of a microscopic system is defined to correspond to…
The modes of the electromagnetic field are solutions of Maxwell's equations taking into account the material boundary conditions. The field modes of classical optics - properly normalized - are also the mode functions of quantum optics.…
This paper is a review of our recent work on three notorious problems of non-relativistic quantum mechanics: realist interpretation, quantum theory of classical properties and the problem of quantum measurement. A considerable progress has…
We investigate whether quantum theory can be understood as the continuum limit of a mechanical theory, in which there is a huge, but finite, number of classical 'worlds', and quantum effects arise solely from a universal interaction between…
The quantum measurement problems are revisited from a new perspective. One of the main ideas of this work is that the basic entities of our world are various types of particles, elementary or composite. It follows that each elementary…
Interest in combinatorial interpretations of mathematical entities stems from the convenience of the concrete models they provide. Finding a bijective proof of a seemingly obscure identity can reveal unsuspected significance to it. Finding…
This introductory text on the basics of quantum mechanics is intended to serve as a kind of travel guide through the quantum world. It starts by asking whether quantum physics is important, or weird, or incomprehensible. It explains why…
We derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The basic setting is a set $\mathcal{A}$ of incompatible experiments, and a transformation group $G$ on the…
The second quantum revolution is all about exploiting the quantum nature of atoms and molecules to execute quantum information processing tasks. To support this growing endeavor and by anticipating the key role of quantum chemistry therein,…
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…