Related papers: Mathematical genesis ? Big Bang and Cantor set
In this note I present the main ideas of my proposal about the theoretical framework that could underlie, and therefore "unify", Quantum Mechanics and Relativity, and I briefly summarize the implications and predictions.
The `Little Bangs' made in particle collider experiments reproduce the conditions in the Big Bang when the age of the Universe was a fraction of a second. It is thought that matter was generated, the structures in the Universe were formed…
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
The origins of matter and radiation in the universe lie in a Hot Big Bang. We present a number of well-motivated cosmologies in which the Big Bang occurs through a strong first order phase transition -- either at the end of inflation, after…
A model is presented for the origin of the large scale structure of the universe and their Mass-Radius scaling law; a fractal power law, $M \propto R^D$, with dimension $D=2$, most significantly. The physics is conventional, orthodox, but…
Topos theory, a branch of category theory, has been proposed as mathematical basis for the formulation of physical theories. In this article, we give a brief introduction to this approach, emphasising the logical aspects. Each topos serves…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
Quantum and classical mechanics are derived using four natural physical principles: (1) the laws of nature are invariant under time evolution, (2) the laws of nature are invariant under tensor composition, (3) the laws of nature are…
Classical geometric fractals - Cantor set and Sierpinski continua - are presented in the manual as set-theoretic objects.
The human mind is endowed with innate primordial perceptions such as space, distance, motion, change, flow of time, matter. The field of cognitive science argues that the abstract concepts of mathematics are not Platonic, but are built in…
This paper provides a thorough introduction to the causal set hypothesis aimed at students, and other interested persons, with some knowledge of general relativity and nonrelativistic quantum mechanics. I elucidate the arguments for why the…
In the context of earlier work, we investigate the emergence of a "distance" in the physical world. For this we consider a Cantor ternary like process, but much more general: properties like perfectness and disconnectedness are not invoked,…
We review physical motivations, phenomenological consequences, and open problems of the so-called pre-big bang scenario in superstring cosmology.
The standard model of cosmology posits that some time in the remote past, labelled as t=0, a Big-Bang occurred. However, it does not tell what caused the Big-Bang and subsequently the Inflation. In the present work the cause of the Big-Bang…
A conceptual framework for variational formulations of physical theories is proposed. Such a framework is displayed here just for statics, but it is designed to be subsequently adapted to variational formulations of static field theories…
These notes are intended as an introductory course for experimental particle physicists interested in the recent developments in astrophysics and cosmology. I will describe the standard Big Bang theory of the evolution of the universe, with…
Numerical relativity is finally approaching a state where the evolution of rather general (3+1)-dimensional data sets can be computed in order to solve the Einstein equations. After a general introduction, three topics of current interest…
The pre-big bang scenario describes the evolution of the Universe from an initial state approaching the flat, cold, empty, string perturbative vacuum. The choice of such an initial state is suggested by the present state of our Universe if…
Lattice regularization of the theory of gravity provides a new possibility for study of the Big Bang problem. In the 4D lattice theories of gravity, the existence of a high-temperature phase is proved, which is characterized by the folding…
Classical mathematics (involving such notions as infinitely small/large and continuity) is usually treated as fundamental while finite mathematics is treated as inferior which is used only in special applications. We first argue that the…