Quantum Mechanics Formal Logic and Material Basis Exploration - Philosophical and Mathematical Reflections on the Foundation of Modern Natural Sciences (Three Volumes)

Author: Yang Benlao
Publisher:
Publish Date: 2006-09-01
Features: The book is divided into three volumes, consisting of four parts. The first volume includes and the second part. As the foundational basis for the entire discussion, the part reveals the "circular definition" nature of the "inertial system" and reassigns its "material connotation," pointing out that natural sciences must universally adhere to the two fundamental principles of "materiality" and "logical self-consistency." In the second part, it first clarifies that the classical "quantum mechanics" has never mathematically solved the Schr?dinger wave equation for the "uncertainty principle," the equivalence proof of the Schr?dinger formulation and the Heisenberg formulation is merely a "null factor" with an "empty statement," and the "uncertainty principle" in the continuous domain must be replaced by discrete "quantum constraints" as fundamental facts. Subsequently, it reveals and formally defines the material objects studied by quantum mechanics through examples. Finally, it reconstructs the fundamental equations of quantum mechanics that are strictly logically compatible with "quantum jumps" and all "classical theories." The second volume only includes the third part, which falls under the discussion of "electrodynamics." It first points out that, unlike quantum mechanics, the classical electromagnetic field theory, which aims to "directly express related empirical facts," is philosophically reasonable. However, due to improper understanding of numerous elementary concepts, several mathematical derivations, and unresolved mathematical foundations, the erroneous identification of Maxwell's displacement current, Lorentz gauge, or Coulomb gauge still belongs to the "dogmatism" of errors. This not only leads to the logical inadequacy and unsolvability of Maxwell's fundamental equations but also fails to distinguish between the two distinct physics concepts of "electromagnetic field" and "electromagnetic wave" to this day, and it also leads to a completely paradoxical "relativity." Moreover, the unreasonable state of quantum mechanics based on "dogmatism" is still the inevitable logical chaos of classical electrodynamics. Based on the above recognition, it systematically discusses the proper construction of related "determination and solution problems," re-establishes the fundamental equations of electromagnetic fields and electromagnetic waves, and thus provides a reliable approach for solving physical phenomena such as "light bending." The third volume is the fourth part of the entire book, which involves a re-examination of the foundation of natural sciences across three different fields. First, still within the scope of quantum mechanics, it points out that a series of concepts derived from the "dogmatism—uncertainty principle" based on a violation of logic are necessarily logically improper. Second, it focuses on discussing modern mathematics, pointing out that the self-deception of concealing and tolerating the existence of numerous logical paradoxes in the mathematical foundation through "dogmatism" makes the entire modern mathematics, including "modern differential geometry," truly in a "self-negation" crisis, and it is necessary to honestly confront and resolve actual mathematical propositions such as "set theory paradoxes" and "electromagnetic field determination and solution problems." Finally, it roughly explores Western philosophy, pointing out that the fundamental reason why a series of "epistemological" basic propositions remain unresolved to this day still lies in the logical chaos of cognition. This book can be used as a reference for basic science researchers engaged in physics, mathematics, and philosophy, as well as related engineering technical personnel.