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An understanding of quantum theory in terms of new, underlying descriptions capable of explaining the existence of non-classical correlations, non-commutativity of measurements and other unique and counter-intuitive phenomena remains still…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
A rigorous mathematical theory of dimensional analysis, systematically accounting for the use of physical quantities in science and engineering, perhaps surprisingly, was not developed until relatively recently. We claim that this has…
We discuss the problem of hidden variables and the motivation for introducting them in quantum mechanics. These include determinism, and the problem of meassurement and incompleteness. We first discuss Von-Neumann's imposisbility proof and…
Multiplying a likelihood function with a positive number makes no difference in Bayesian statistical inference, therefore after normalization the likelihood function in many cases can be considered as probability distribution. This idea led…
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…
We present a derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. Combined to Gleason's theorem, this approach naturally leads to the usual…
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…
A non-geometrical (but with curved space) theory of gravitation characterized by a vector field representing gravitational matter and a metric tensor presenting space is presented. It is derived from a more general theory of matter and…
We present a simple dynamical systems model for the effect of invisible space dimensions on the visible ones. There are three premises. A: Orbits consist of flows of probabilities [P].which is the case in the setting of quantum mechanics.…
It is argued that the so-called holographic principle will obstruct attempts to produce physically realistic models for the unification of general relativity with quantum mechanics, unless determinism in the latter is restored. The notion…
The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an…
As a laboratory for loop quantum gravity, we consider the canonical quantization of the three-dimensional Chern-Simons theory on a noncompact space with the topology of a cylinder. Working within the loop quantization formalism, we define…
Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this…
The quantum description of the microscopic world is incompatible with the classical description of the macroscopic world, both mathematically and conceptually. Nevertheless, it is generally accepted that classical mechanics emerges from…
The formalism of abstracted quantum mechanics is applied in a model of the generalized Liar Paradox. Here, the Liar Paradox, a consistently testable configuration of logical truth properties, is considered a dynamic conceptual entity in the…
We relate three-dimensional loop quantum gravity to the combinatorial quantisation formalism based on the Chern-Simons formulation for three-dimensional Lorentzian and Euclidean gravity with vanishing cosmological constant. We compare the…
We consider the coupling between massive and spinning particles and three dimensional gravity. This allows us to construct geometric operators (distances between particles) as Dirac observables. We quantize the system a la loop quantum…
The quantum theory of ur objects postulates that all existing physical objects and their properties are constructed from fundamental objects called ur objects being described by an element of a two dimensional complex Hilbert space. This…
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…