Related papers: Mathematical genesis ? Big Bang and Cantor set
Discussions surrounding the nature of the infinite in mathematics have been underway for two millennia. Mathematicians, philosophers, and theologians have all taken part. The basic question has been whether the infinite exists only in…
The exactly solvable quantum model of the homogeneous, isotropic and closed universe in the matter-energy production epoch is considered. It is assumed that the universe is originally filled with a uniform scalar field and a perfect fluid…
The it Global Time Theory (GTT) is the further development of the General Relativity (GR). GTT significantly differs from GR in the general physical concepts, but retains 90% of the mathematical structure and main results. The dynamics…
This study describes such a situation that a Cantor set emerges as a result of the exploration of sufficient conditions for the property which is generalized from fundamental chaotic maps, and the Cantor set even guarantees infinitely many…
Over the past century, rooted in the theory of general relativity, cosmology has developed a very successful physical model of the universe: the {\em big-bang model}. Its construction followed different stages to incorporate nuclear…
This short review is addressed to cosmologists. General relativity predicts that space-time comes to an end and physics comes to a halt at the big-bang. Recent developments in loop quantum cosmology have shown that these predictions cannot…
The mathematical formulation of Quantum Mechanics is derived from purely operational axioms based on a general definition of "experiment" as a set of transformations. The main ingredient of the mathematical construction is the postulated…
We propose a picture, within the pre-big-bang approach, in which the universe emerges from a bath of plane gravitational and dilatonic waves. The waves interact gravitationally breaking the exact plane symmetry and lead generically to…
A unified framework for different formulations of quantum theoery is introduced specifying what is meant by a quantum mechanical theory in general.
We study a five-dimensional cosmological model, which suggests that the universe bagan as a discontinuity in a (Higgs-type) scalar field, or alternatively as a conventional four-dimensional phase transition.
Recent data suggest that the Universe could be positively curved. Combined with an inflationary stage, this might lead to a curvature bounce instead of the Big Bang. The background evolution is presented, as a function of the parameters…
Fractals such as the Cantor set can be equipped with intrinsic arithmetic operations (addition, subtraction, multiplication, division) that map the fractal into itself. The arithmetics allows one to define calculus and algebra intrinsic to…
A two boundary quantum mechanics incorporating a big bang / big crunch universe is carefully considered. After a short motivation of the concept we address the central question how a proposed a-causal quantum universe can be consistent with…
The expansion of our universe, when followed backward in time, implies that it emerged from a phase of huge density, the big bang. These stages are so extreme that classical general relativity combined with matter theories is not able to…
Our conventional understanding of space-time, as well as our notion of geometry, break down once we attempt to describe the very early stages of the evolution of our universe. The extreme physical conditions near the Big Bang necessitate an…
We present a consistent framework that enables us to understand the big bang singularity of our universe.
An overview of baryogenesis in the early Universe is presented. The standard big bang model including big bang nucleosynthesis and inflation is breifly reviewed. Three basic models for baryogenesis will be developed: The ``standard"…
A short phenomenological account of the genesis and evolution of the universe is presented with emphasis on the primordial phases as well as its physical composition, i.e. dark matter and dark energy. We discuss Einstein's theory of General…
The gravitational collapse and the birth of a new universe are considered in terms of quantum mechanics. Transitions from annihilation of matter to deflation in the collapse and from inflation to creation of matter in the birth of a…
Quantum computation has suggested, among others, the consideration of "non-quantum" systems which in certain respects may behave "quantum-like". Here, what algebraically appears to be the most general possible known setup, namely, of {\it…