Entropy of A Scalar Field In (3 + 1)-dimensional Taub-NUT Space-Time

TL;DR

This paper explores various fundamental aspects of space-time, fields, and particles, including entropy of scalar fields in Taub-NUT space, and discusses coordinate systems, causal structure, and quantum theories.

Contribution

It provides a detailed analysis of the entropy of scalar fields in (3+1)-dimensional Taub-NUT space and compares quantum field theory with quantum mechanics.

Findings

Entropy of scalar fields in Taub-NUT space calculated.

Discussions on coordinate systems and causal structures.

Contradictions in quantum theories and space-time analysis.

Abstract

In this article we discuss a few aspects of the space-time description of fields and particles. In sectionn II and III we demonstrate that fields are as fundamental as particles. In section IV we discuss non-equivalence of the Schwarzschild coordinates and the Kruskal-Szekeres coordinates. In section V we discuss that it is not possible to define causal structure in discrete space-time manifolds. In App.B we show that a line is not just a collection of points and we will have to introduce one-dimensional line-intervals as fundamental geometric elements. Similar discussions are valid for area and volume-elements. In App.C and App.D we make a comparative study of Quantum Field Theory and Quantum Mechanics and contradictions associated with probabilistics interpretation of these theories with space-time dimensional analysis. In App.E and App.F we discuss the geometry of Robertson-Walker model and electrostatic behavior of dielectrics respectively. In Sup.I we discuss the regularity of Spin-Spherical harmonics and also derive an energy-spectrum which is free of back-reaction problem. In Sup.II we discuss that in general the integral version of Gauss's divergence law in Electrodynamics is not valid and rederive Gauss's law and Ampere's law. We also show that under duality transformation magnetic charge conservation law do not remain time reversal symmetric. In Sup.III we derive the complete equation for viscous compressible fluids and make a few comments regarding some cotradictions associated with boundary conditions for fluid dynamics. In Sup.IV we discuss a few aspects on double slit interference experiments. We conclude this article with a few questions in Sup.V.