Related papers: Topos-theoretic Model of the Deutsch multiverse
The theory of quantum mechanics is examined using non-standard real numbers, called quantum real numbers (qr-numbers), that are constructed from standard Hilbert space entities. Our goal is to resolve some of the paradoxical features of the…
It is shown that properties of a discrete space-time geometry distinguish from properties of the Riemannian space-time geometry. The discrete geometry is a physical geometry, which is described completely by the world function. The discrete…
We introduce a Geometry of Interaction model for higher-order quantum computation, and prove its adequacy for a full quantum programming language in which entanglement, duplication, and recursion are all available. Our model comes with a…
The models of cyclic universes and cyclic multiverses based on the alternative gravity theories of varying constants are considered.
We construct the teleparallel dynamics for extended geometry where the structure algebra is (an extension of) an untwisted affine Kac-Moody algebra. This provides a geometrisation of the Geroch symmetry appearing on dimensional reduction of…
The many-worlds interpretation (MWI) of quantum mechanics is studied from an unprecedented ontological perspective based on the reality of (semi-) deterministic parallel worlds in the interpretation. It is demonstrated that with thanks to…
Speculations and theories about the existence of other worlds have a long history. In recent times, the arguments have shifted away from their typical philosophical and theological character to supposedly become more objective thanks to…
An idealised experiment estimating the spacetime topology is considered in both classical and quantum frameworks. The latter is described in terms of histories approach to quantum theory. A procedure creating combinatorial models of…
We describe a class of topological field theories called ``balanced topological field theories.'' These theories are associated to moduli problems with vanishing virtual dimension and calculate the Euler character of various moduli spaces.…
Using geodesic length functions, we define a natural family of real codimension 1 subvarieties of Teichm\"uller space, namely the subsets where the lengths of two distinct simple closed geodesics are of equal length. We investigate the…
This paper evaluates some important aspects of the multiverse concept. Firstly, the most realistic opportunity for it which is the spacetime variability of the physical constants and may deliver worlds with different physics, hopefully…
The possibility of obtaining an open set of regular cosmological models is discussed. Cylindrical stiff perfect fluid cosmologies are studied in detail. The condition for geodesic completeness is easy to check. A large family of…
A new cosmological theory is proposed in the theoretical framework of modified gravity theories which is based on a tachyonic field non-minimally coupled with a specific topological invariant constructed with third order contractions of the…
Is the universe finite or infinite, and what shape does it have? These fundamental questions, of which relatively little is known, are typically studied within the context of the standard model of cosmology where the universe is assumed to…
The cosmic web structure is studied with the concepts and methods of fractal geometry, employing the adhesion model of cosmological dynamics as a basic reference. The structures of matter clusters and cosmic voids in cosmological N-body…
Grothendieck Duality -- the theory of the twisted inverse image pseudofunctor (-)^! over a suitable category of scheme-maps -- can be developed concretely, with emphasis on explicit constructions, or abstractly, with emphasis on…
The evolution of a class of inhomogeneous spherically symmetric universe models possessing a varying cosmological term and a material fluid, with an adiabatic index either constant or not, is studied.
We develop the theory of arrangements of spheres. Consider a finite collection of codimension-$1$ subspheres in a positive-dimensional sphere. There are two posets associated with this collection: the poset of faces and the poset of…
To each quantum system, described by a von Neumann algebra of physical quantities, we associate a complete bi-Heyting algebra. The elements of this algebra represent contextualised propositions about the values of the physical quantities of…
In this paper we pursue a new technique to search for evidence of a finite Universe, making use of a spherical mexican-hat wavelet decomposition of the microwave background fluctuations. Using the information provided by the wavelet…