Related papers: An Ultimate Hyperfinite Ultralogic Unification for…
The principle which allows to construct new physical theories on the basis of classical mechanics by reduction of the number of its axiom without engaging new postulates is formulated. The arising incompleteness of theory manifests itself…
The linear superposition principle in quantum mechanics is essential for several no-go theorems such as the no-cloning theorem, the no-deleting theorem and the no-superposing theorem. It remains an open problem of finding general forbidden…
The no-supervenience theorem limits the capacity of physicalist theories to provide a comprehensive account of human consciousness. The proof of the theorem is difficult to formalize because it relies on both alethic and epistemic notions…
This paper gives a summary of a body of work at the intersection of control theory and smooth nonlinear dynamics. The main idea is to transfer the concept of uniform hyperbolicity, central to the theory of smooth dynamical systems, to…
The process of cognition is analysed to adjust the set theory to physical description. Postulates and basic definitions are revised. The specific sets of predicates, called presets, corresponding to the physical objects identified by an…
I summarize here the logic that leads us to a program for the Theory of the Total Field in Einstein's sense. The purpose is to show that this theory is a logical culmination of the developments of (fundamental) physical concepts and, hence,…
The stipulation that no measurable quantity could have an infinite value is indispensable in physics. At the same time, in mathematics, the possibility of considering an infinite procedure as a whole is usually taken for granted. However,…
I review some aspects of supersymmetric grand unification and emphasize a recent development in the area of gauge coupling unification.
We provide an example of an ultraviolet finite supersymmetric grand unified theory of safe rather than free nature endowed with a supersymmetric dynamical breaking mechanism. Our results simultaneously enlarge the number of ultraviolet…
We are emerging from a period of consolidation in particle physics. Its great, historic achievement was to establish the Theory of Matter. This Theory will serve as our description of ordinary matter under ordinary conditions -- allowing…
A recollection of some theoretical developments that preceded and followed the first formulation of supergravity theory is presented. Special emphasis is placed on the impact of supergravity on the search for a unified theory of fundamental…
No theory of physics has been collectively scientifically verified in an experiment so far. It is pointed out that probabilistic structure of quantum theory can be collectively scientifically verified in an experiment. It is also argued…
Manifestly invariant renormalization scheme for supersymmetric gauge theories is proposed. This scheme is applied to supersymmetric quantum electrodynamics.
A global picture is drawn tying together most exact cosmological solutions of gravitational theories in four or more spacetime dimensions.
The present paper shows how one might model Everettian quantum mechanics using hyperfinitely many worlds. A hyperfinite model allows one to consider idealized measurements of observables with continuous-valued spectra where different…
The renormalization-group improved effective potential ---to leading-log and in the linear curvature approximation--- is constructed for ``finite'' theories in curved spacetime. It is not trivial and displays a quite interesting,…
In this note, we shall overview some results related to ultraparacompactness and ultranormality in the general topological and point-free contexts. This note contains some standard results and counterexamples along with some results which…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…
The need for revolution in modern physics is a well known and often broached subject, however, the precision and success of current models narrows the possible changes to such a great degree that there appears to be no major change…
This short note contains the proofs of two small but somewhat surprising results about ultrafilters on $\mathbb{N}$: 1. strongly summable ultrafilters are rapid, 2. every rapid ultrafilter induces a closed left ideal of rapid ultrafilters.…