The Nature of the Higgs Mechanism in the Optic-String Field, the Origin of Planck's Formula, and the Unified Derivation of Mass-Energy Relations

In modern physics, the Higgs mechanism, as the core of the Standard Model, is used to explain the origin of particle mass. However, it is only a phenomenological theoretical assumption that does not reveal the underlying physical mechanism of mass generation. As the foundation of quantum mechanics, Planck’s formula only quantifies the relationship between quantum energy and frequency, while the physical origin of Planck’s constant h has never been clarified. The mass-energy equation E=mc² only states the equivalence of mass and energy, without explaining the underlying logic of this equivalence or the true physical nature of mass. Based on the Optic-String First-Principle Unified Theory and the universal continuous optic-string field, this paper derives from first principles, without logical jumps or additional assumptions, the origin of Planck’s formula and the physical meaning of Planck’s constant h. It clarifies that the instantaneous quantum energy described by Planck’s formula and the total bound energy described by the mass-energy equation are identical in physical essence. Then it rigorously combines the two equations to derive the core mass-frequency relation M=KF and explains the mathematical and physical connotation of the proportional coefficient K=h/c². It further reveals the optic-string field nature of the Higgs mechanism and defines the true physical meaning of mass, realizing the universal unification of quantum energy, mass-energy relation, and the origin of mass. This work completely fills the mathematical and physical gaps in existing physical theories.