Analyticity and the Global Information Field

Evgeni Solov'Ev

doi:10.3390/math3010040

Abstract

The relation between analyticity in mathematics and the concept of a global information field in physics is reviewed. Mathematics is complete in the complex plane only. In the complex plane, a very powerful tool appears—analyticity. According to this property, if an analytic function is known on the countable set of points having an accumulation point, then it is known everywhere. This mysterious property has profound consequences in quantum physics. Analyticity allows one to obtain asymptotic (approximate) results in terms of some singular points in the complex plane which accumulate all necessary data on a given process. As an example, slow atomic collisions are presented, where the cross-sections of inelastic transitions are determined by branch-points of the adiabatic energy surface at a complex internuclear distance. Common aspects of the non-local nature of analyticity and a recently introduced interpretation of classical electrodynamics and quantum physics as theories of a global information field are discussed.

Highlights

The scientific approach to the study of inorganic nature was formulated by Galileo Galilei.He discovered the fundamental role of experiment in inorganic nature—physical events are reproduced at any place and any moment under the same external conditions, i.e., they obey the laws of nature.In the most famous experiment, Galileo dropped different balls from the Leaning Tower of Pisa to demonstrate that their time of descent was independent of their mass, and the distance, starting from rest, is proportional to the square of the elapsed time
In the е переходы через скрытые квазипересечения Slm, а мнимая section an adiabatic asymptotic expansion is presented to demonstrate the global nature of analyticity in Комплексная величина имеет важное прикладное значе венная часть определяет область прицельных параметров, пр quantum physics
Mathematics does not produce new information; it just transforms the laws of nature into a form more transparent for our consciousness

Summary

Introduction

The scientific approach to the study of inorganic nature was formulated by Galileo Galilei.He discovered the fundamental role of experiment in inorganic nature—physical events are reproduced at any place and any moment under the same external conditions, i.e., they obey the laws of nature.In the most famous experiment, Galileo dropped different balls from the Leaning Tower of Pisa to demonstrate that their time of descent was independent of their mass, and the distance, starting from rest, is proportional to the square of the elapsed time. This method is based on the theorem that the deformation of the contour of integration in the complex z-plane does not change the value of I( ), if the integrand is an analytic function. In the е переходы через скрытые квазипересечения Slm, а мнимая section an adiabatic asymptotic expansion is presented to demonstrate the global nature of analyticity in Комплексная величина имеет важное прикладное значе венная часть определяет область прицельных параметров, пр quantum physics.

Results

Conclusion