Related papers: \"Uber Nichts
We present several philosophical ideas emerging from the studies of complex systems. We make a brief introduction to the basic concepts of complex systems, for then defining "abstraction levels". These are useful for representing…
Nothing---the absence of spacetime---can be either an endpoint of tunneling, as in the bubble of nothing, or a starting point for tunneling, as in the quantum creation of a universe. We argue that these two tunnelings can be treated within…
Based on the model of a "soft" cellular space and deterministic quantum mechanics developed previously, the scattering of a free moving particle by structural units of the space -- superparticles -- is studied herein. The process of energy…
The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…
We discuss the existence of asymptotically Euclidean initial data sets to the vacuum Einstein field equations which would give rise (modulo an existence result for the evolution equations near spatial infinity) to developments with a past…
We uncover a universal sector of relativistic fluid dynamics by taking a novel ultrarelativistic limit in which the temperature tends to zero while the flow simultaneously approaches the speed of light. In this regime, hydrodynamics becomes…
We study some claims in Krauss' recent book, \emph{A Universe from Nothing: Why there is something rather than nothing}, that are employed to show that a universe can come from "nothing". In this brief paper, we show that many of the claims…
This work explores a possible course of evolution of mathematics in ancient times in India when there was no script, no place-value system, and no zero. Reviewing examples of time-reckoning, large numbers, sacrificial altar-making, and…
Complete residue systems play an integral role in abstract algebra and number theory, and a description is typically found in any number theory textbook. This note provides a concise overview of complete residue systems, including a robust…
For more seventy years physicists have appreciated that Nature's vacuum is far from empty. The discovery of the Lamb shift in Hydrogen provided dramatic verification of the reality of the quantum vacuum. The advent of gauge theories has led…
A crucial goal of quantum information is to find new ways to exploit the properties of quantum devices as resources. One of the prominent properties of quantum devices of particular interest is their negativity in quasi-probability…
Hilbert's Nullstellensatz characterizes polynomials that vanish on the vanishing set of an ideal in C[x]. In the free algebra C<X> the vanishing set of a two-sided ideal I is defined in a dimension-free way using images in…
It is proven that, contrarily to the common belief, the notion of zero is not necessary for having positional representations of numbers. Namely, for any positive integer $k$, a positional representation with the symbols for $1, 2, \ldots,…
Some models of set theory are given which contain sets that have some of the important characteristics of being geometric, or spatial, yet do not have any points, in various ways. What's geometrical is that there are functions to these…
There exists a dispute in philosophy, going back at least to Leibniz, whether is it possible to view the world as a network of relations and relations between relations with the role of objects, between which these relations hold, entirely…
Non-static, spherically symmetric clusters of counter-rotating particles, of the type first introduced by Einstein, are analysed here. The initial data space can be parameterized in terms of three arbitrary functions, namely; initial…
This essay traces the history of three interconnected strands. Firstly, changes in the concept of number, secondly, the study of the qualities of number, which evolved into number theory, and thirdly, the nature of mathematics itself, from…
We suggest that the question of why is there something rather than nothing can be answered by the existence of two types of nothing. We propose that matter occurs at the boundaries of intersection of both nothings. This accords with the…
In our previous arXiv papers (more systematically the informational conception is presented in the paper "The Information as Absolute", 2010) it was rigorously shown that Matter in our Universe - and Universe as a whole - are some…
This article introduces Universal Quantum Relativity which is a simple Theory of Everything. It relies on an ultimate doctrine that is the absence of absolute existence. This generalizes relativity principles up to a mother quantum theory.…