Related papers: Fundamental length from algebra
Our title challenges the reader to venture beyond linear algebra in designing models and in thinking about numerical algorithms for identifying solutions. This article accompanies the author's lecture at the International Congress of…
Natural philosophy integrates scientific observation with abstract frameworks, often using a mathematical Ansatz to hypothesise about physical phenomena. Exploring the possibility of other universes, however, challenges assumptions that…
The aim of "A glance beyond the quantum model" [arXiv:0907.0372] to modernize the Correspondence Principle is compromised by an assumption that a classical model must start with the idea of particles, whereas in empirical terms particles…
I consider a thought experiment measuring the decoherence for quasiclassical superpositions of gravitational field. A version of the hole argument allows to prove that a covariant (background-free) theory is completely unable to define the…
The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical…
We give an overview of the applications of noncommutative geometry to physics. Our focus is entirely on the conceptual ideas, rather than on the underlying technicalities. Starting historically from the Heisenberg relations, we will explain…
The progress of noncommutative geometry has been crucially influenced, from the beginning, by quantum physics: we review this development in recent years. The Standard Model, with its central role for the Dirac operator, led to several…
Consider a proposed model of the universe with $\hbar$ much greater than its well-known value of $10^{-34} Js$. In this model universe, very large objects can show quantum behaviors. In a scenario with large extra dimensions, $\hbar$ can…
Effect algebras were introduced in order to describe the structure of effects, i.e. events in quantum mechanics. They are partial algebras describing the logic behind the corresponding events. It is natural to ask how to introduce the…
Over the past 25 years, I have been involved in some intriguing developments in the foundations of physics, exploring the quantum reality problem, the relationship between quantum theory and gravity and the interplay between consciousness…
We study the role of context, complex of physical conditions, in quantum as well as classical experiments. It is shown that by taking into account contextual dependence of experimental probabilities we can derive the quantum rule for the…
Most approaches towards a quantum theory of gravitation indicate the existence of a minimal length scale of the order of the Planck length. Quantum mechanical models incorporating such an intrinsic length scale call for a deformation of…
By consireding representation theory for non-associative algebras we construct the fundamental and adjoint representations of the octonion algebra. We then show how these representations by associative matrices allow a consistent octonionic…
The concept of emergence is critically analyzed in particular with respect to the assumed emergence of mental properties from a neuronal basis. We argue that so-called contextual emergence is needed to avoid an eliminatory reductionism.…
We study measures, finitely additive measures, regular measures, and $\sigma$-additive measures that can attain even infinite values on the quantum logic of a Hilbert space. We show when particular classes of non-negative measures can be…
The rules of quantum mechanics require a time coordinate for their formulation. However, a notion of time is in general possible only when a classical spacetime geometry exists. Such a geometry is itself produced by classical matter…
This paper presents an alternative proof of the Fundamental Theorem of Algebra that has several distinct advantages. The proof is based on simple ideas involving continuity and differentiation. Visual software demonstrations can be used to…
The main objective consists in endowing the elementary particles with an algebraic space-time structure in the perspective of unifying quantum field theory and general relativity: this is realized in the frame of the Langlands global…
A new version of the delta expansion is presented, which, unlike the conventional delta expansion, can be used to do nonperturbative calculations in a self-interacting scalar quantum field theory having broken symmetry. We calculate the…
Quantum field theory (QFT) in classical spacetime has revealed interesting and puzzling aspects about gravitational systems, in particular black hole thermodynamics and its information processing. Although quantum gravitational effects may…