TITLE:
First Principles in Fundamental Physics
AUTHORS:
Yingqiu Gu
KEYWORDS:
First Principle, Clifford Algebras, Hypercomplex Numbers, Nonlinear Spinors, Unified Field Theory
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.4,
April
25,
2025
ABSTRACT: “All is Number”—the universe follows a few profound mathematical rules, and pure thought can grasp reality. This paper explores the first principles of fundamental physics, focusing on the principle of relativity, the principle of least action, and the principle of regularity. By illustrating the principle of relativity with an example of coordinate transformation, the paper clarifies the nature of spacetime: spacetime exists objectively, whereas coordinate systems are merely mathematical constructs. It also discusses the uniqueness of natural coordinate systems and their roles in both quantum and classical mechanics. Clifford geometric algebra is introduced as a mathematical framework for physical theories, and the principle of least action is analyzed, emphasizing the Lagrangian as an intrinsic characteristic of physical systems, which can be expressed as a linear combination of the system’s energy terms. Through examples from complicated systems, the paper demonstrates the structural characteristics, applications, and limitations of this principle. Furthermore, it examines the fundamental distinction between the finite and the infinite, noting that infinity is merely an analytical variable rather than a number. If a physical equation yields a solution with infinite energy density, the theory must be revised to maintain consistency. These first principles not only constitute the foundation of physics but also unveil profound symmetries and universal patterns in mathematical structures.