Abstract In stochastic mechanics, one of the interpretations of realistic quantum mechanics, the Schrödinger equation can be derived by assuming the Brownian motion (BM) of minute particles. In this study, we theoretically derive Planck’s constant (h), a fundamental constant of quantum physics, by assuming same BM. Einstein investigated the BM of a resonator caused by photons in a black body; meanwhile, in this study, BM is considered to be caused by the particle and wave natures of light. As a result, as the functional form of h, hN=cε04πe2β1 h N = 4 π e 2 c ε 0 1 β (e: elementary charge, ε0 ε 0 : permittivity, c: speed of light) was derived, where the undetermined coefficient 2β β 2 represents the probability that the interaction between electrons and electromagnetic waves becomes particle-like absorption in one cycle of oscillation. The theoretical value of h was calculated to be cε04πe2π3 4 π e 2 c ε 0 π 3 by obtaining β from the transition conditions of the BM model and uncertainty relation. This theoretical value is within 0.3% of the most recent value of h. Besides, Nelson’s assumed diffusion coefficient in the stochastic mechanics, which is essential in obtaining Schrödinger’s equation, was proved to be obtained from the BM model and the uncertainty relation. This finding and the conclusion that the Planck’s constant can be mathematically derived, provide support for Nelson’s stochastic mechanics.
This work offers an original view of the internal structure of Planck's constant h through the prism of classical Maxwellian electrodynamics and the complex geometry of phase space. This presents a development of the chronal field interpretation of quantum phenomena proposed earlier by the author. Based on the concept of the photon as a dynamic phase node of field switching (h=π+1), a revision of classical paradoxes of quantum mechanics is carried out. A generalized energy equation E=ℏ/(τ0+τtransition) is formulated, eliminating the duality of rest mass and photon momentum. Bohr's postulates and the structure of electronic orbits are explicated as topological invariants of phase resonance (ei2πn=1). A geometric model of the Zeeman effect is proposed as a dynamic asymmetry of counter-propagating complex rotations of the field under the influence of an external magnetic potential. This work lays the foundation for causal chronodynamics of the microcosm without the use of probabilistic Copenhagen description. This presents an alternative deterministic interpretation of quantum mechanics, eliminating the probabilistic Copenhagen postulate. The author introduces the concept of the chronal field τ(r,t) as the local time of one radian of phase. The wave function Ψ is explicated as a real physical deformation of this field.