Related papers: Complex Numbers and Physical Reality
At this point in time there is a need for a new representation of different information, to identify and organize descending its characteristics. Today, science is a powerful tool for the description of reality - the numbers. Why the most…
Complex-valued data is ubiquitous in signal and image processing applications, and complex-valued representations in deep learning have appealing theoretical properties. While these aspects have long been recognized, complex-valued deep…
In standard quantum mechanics, complex numbers are used to describe the wavefunction. Although complex numbers have proven sufficient to predict the results of existing experiments, there is no apparent theoretical reason to choose them…
A long-standing tradition, largely present in both the physical and the philosophical literature, regards the advent of (special) relativity -- with its block-universe picture -- as the failure of any indeterministic program in physics. On…
There has been always an ambiguity in division when zero is present in the denominator. So far this ambiguity has been neglected by assuming that division by zero as a non-allowed operation. In this paper, I have derived the new set of…
We investigate complex self-testing, a generalization of standard self-testing that accounts for quantum strategies whose statistics is indistinguishable from their complex conjugate's. We show that many structural results from standard…
We have discovered that two significant quantities within hard particle systems: the probability of successfully inserting an additional particle at random and the scale distribution function, can be connected by a concise relation. We…
Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of…
In this paper we provide a complete approach to the real numbers via decimal representations. Construction of the real numbers by Dedekind cuts, Cauchy sequences of rational numbers, and the algebraic characterization of the real number…
The goal of this paper consists of developing a new (more physical and numerical in comparison with standard and non-standard analysis approaches) point of view on Calculus with functions assuming infinite and infinitesimal values. It uses…
The main purpose of this paper is to prove that the positive real numbers can be decomposed into finitely many disjoint pieces which are also closed under addition and multiplication. As a byproduct of the argument we determine all the…
It is argued that a realistic interpretation of quantum mechanics is possible and useful. Current interpretations, from Copenhagen to many worlds are critically revisited. The difficulties for intuitive models of quantum physics are pointed…
We offer a fresh perspective on the relational interpretation of quantum mechanics as a way of thinking about the world described by quantum theory based on quantifiable notions of information. This allows us to provide a definition of a…
We introduce complex intersection bodies and show that their properties and applications are similar to those of their real counterparts. In particular, we generalize Busemann's theorem to the complex case by proving that complex…
We investigate the possible structures of numbers (as physical quantities) over which accelerated observers can be modeled in special relativity. We present a general axiomatic theory of accelerated observers which has a model over every…
Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not…
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…
In resisting attempts to explain the unity of a whole in terms of a multiplicity of interacting parts, quantum mechanics calls for an explanatory concept that proceeds in the opposite direction: from unity to multiplicity. It concerns the…
Both metamathematics and physics are posited to emerge from samplings by observers of the unique ruliad structure that corresponds to the entangled limit of all possible computations. The possibility of higher-level mathematics accessible…
We study weighted simultaneous rational approximation to points of the form $(1,\xi,\xi^2)$, for a class of extremal real numbers $\xi$, within the framework of multi-parametric geometry of numbers.