Mathematics
Mathematics, as the key tool of natural science, is emerging as the abstract science of structure, order and relationship. As applied mathematics, mathematical physics has to generate a complete and consistent representation of nature as the system of natural entities, forces and changes, the total sum of material existences and forces in the universe, all in terms of mathematical systems of definitions and axioms, rules, as the function rule, principles, as duality, and theorems, deduced laws.
Natural Ontology
Natural ontology is the study of the universe as such, the basic features of all the universe, as the nature of force, matter and energy, space and time, natural entities and cause-effect relationships. As an example, mathematical and theoretical physics is to combine physics, mathematics and theoretical ontology of nature. Or, the unity of the all forces of nature is an ontological axiom.
Therefore, despite seeming differences, all the physical sciences are interrelated by the basic principles underlying all natural processes, phenomena and interactions, provided by the principal natural science of physics.
Modern Physics: Its Key Subjects and Principles
“Physics has evolved and continues to evolve without any single strategy”, while its ultimate goal to find a unified set of principles and laws governing force and energy, matter and change, at micro-, meso– and macro-world (Physical Sciences, the New Encyclopedia Britannica, 25, Knowledge in Depth, Chicago-Toronto, Encyclopedia Britannica, Inc., 1994 ).
Generally, the key achievements in physical science lie in the serendipitous and intuitive and ingenious discovering of empirical physical laws and effects, subatomic entities, symmetry principles, conservation laws, or unified force fields (See Supplement 1. All Nobel Prizes in Physics. Available: https://www.nobelprize.org/nobel_prizes/physics/laureates/).
Modern physics was founded as an empirical synthesis of separate sciences: mechanics, optics, acoustics, electricity, magnetism, heat and studies of matter and its properties.
Meantime, the whole idea of physics consisted in the intuitive understanding that different forces of nature and forms of energy are INTERRELATED and INTERCONVERTIBLE, but these universal phenomena have never been expressly formulated as the basic laws of nature. The Faraday’s intuitive belief in the unity of the forces of nature, or that all the forces of nature are but manifestations of a single universal force and must be convertible one into another made possible the classical electromagnetic field theory, the foundation of modern physics.
Modern physics includes the subjects of gravitation, mechanics and sound, particles and atoms, thermodynamics and heat, electricity and magnetism, light and electromagnetic radiation. Its main task is the nature, origin, actions and interactions of force-fields, gravitational, electromagnetic and nuclear, the strong color force between quarks and the weak nuclear interactions, all mediated by the quanta exchange, as vector gauge symmetry bosons.
In all, modern physics viewed as natural science doing the general analysis of nature to understand how the universe behaves, while being in the space of force fields and relying on a few simple laws and principles of nature and the universe.
