Related papers: Pregeometry, Formal Language and Constructivist Fo…

In this article I deal with the notion of observation in the most fundamental sense and its representation by means of formal languages serving as expressional tools of formal-axiomatical theories. In doing so, I have taken this notion in…

The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship…

This essay is a tour around many of the lesser known pregeometric models of physics, as well as the mainstream approaches to quantum gravity, in search of common themes which may provide a glimpse of the final theory which must lie behind…

The unsatisfactory status of the search for a consistent and predictive quantization of gravity is taken as motivation to study the question whether geometrical laws could be more fundamental than quantization procedures. In such an…

Starting from a recently-introduced algebraic structure on spin foam models, we define a Hopf algebra by dividing with an appropriate quotient. The structure, thus defined, naturally allows for a mirror analysis of spin foam models with…

This is a foundation for algebraic geometry, developed internal to the Zariski topos, building on the work of Kock and Blechschmidt. The Zariski topos consists of sheaves on the site opposite to the category of finitely presented algebras…

This text aims to give a pedagogical introduction into the main concepts of the theory of structure formation in the universe. The text is suited for graduate students of astronomy with a moderate background in general relativity. A special…

We develop a system that formally represents spatial semantics concepts within natural language descriptions of spatial arrangements. The system builds on a model of spatial semantics representation according to which words in a sentence…

In a previous effort [arXiv:1708.05492] we have created a framework that explains why topological structures naturally arise within a scientific theory; namely, they capture the requirements of experimental verification. This is…

General relativity is a covariant theory of two transverse, traceless graviton degrees of freedom. According to a theorem of Hojman, Kuchar, and Teitelboim, modifications of general relativity must either introduce new degrees of freedom or…

In this paper we start from a basic notion of process, which we structure into two groupoids, one orthogonal and one symplectic. By introducing additional structure, we convert these groupoids into orthogonal and symplectic Clifford…

We describe the elements of a novel structural approach to classical field theory, inspired by recent developments in perturbative algebraic quantum field theory. This approach is local and focuses mainly on the observables over field…

Constructor theory seeks to express all fundamental scientific theories in terms of a dichotomy between possible and impossible physical transformations - those that can be caused to happen and those that cannot. This is a departure from…

Approaching limitations of digital computing technologies have spurred research in neuromorphic and other unconventional approaches to computing. Here we argue that if we want to systematically engineer computing systems that are based on…

The problem of constructing a quantum theory of gravity is considered from a novel viewpoint. It is argued that any consistent theory of gravity should incorporate a relational character between the matter constituents of the theory. In…

The quantum mechanical formalism doesn't support our intuition, nor does it elucidate the key concepts that govern the behaviour of the entities that are subject to the laws of quantum physics. The arrays of complex numbers are kin to the…

The aim of this article is to represent the general description of an entity by means of its states, contexts and properties. The entity that we want to describe does not necessarily have to be a physical entity, but can also be an entity…

The physical models of a successful unified theory about the Universe must operate in different phase of matter evolution and different fields of physics. The attempts to build such wide range theory as a bunch of theories developed for…

This paper introduces the Quantum Contextual Topos (QCT), a novel framework that extends traditional quantum logic by embedding contextual elements within a topos-theoretic structure. This framework seeks to provide a classically-obedient…

This review paper is concerned with the generalizations to field theory of the tangent and cotangent structures and bundles that play fundamental roles in the Lagrangian and Hamiltonian formulations of classical mechanics. The paper…