驻波量子化公设(粒子性) The Standing Wave Quantization Postulate (Particle Nature)

Hidemi Munakata

Abstract In quantum mechanics, quantization conditions have traditionally been introduced as postulates, such as the Bohr condition, without a clear physical necessity. In this study, we reinterpret the quantization condition using a dimensionless phase criticality index defined as α = rω/c. Within this framework, the stability of the electron in the hydrogen atom is determined by the simultaneous satisfaction of phase self-consistency and the balance of Coulomb interaction. Without invoking the de Broglie standing-wave assumption, we show that the ground-state radius naturally emerges as r = ℏ/(mcα), corresponding to the Bohr radius. This result suggests that the quantized structure of the hydrogen atom can be understood as a numerical consequence of electromagnetic interaction and phase criticality, rather than an independent quantization postulate.

Todor S. Todorov

V.A.Induchoodan Menon

The author introduces the concept of a primary gas which is an abstract gas where the microstates are occupied successively in time unlike in the case of a real gas where the microstates are occupied simultaneously. He shows that a single plane wave associated with a standing wave formed by the confinement of a luminal wave could be treated as the microstate of the primary gas that represents a particle. This approach makes it possible to understand the dynamics of a particle in terms of the thermodynamics of the primary gas. In this approach, time and space turn out to be the intrinsic properties of the primary gas that represents a particle and the quantized nature of time and space emerges from it in a natural manner. It is shown that the action (with a negative sign) of a particle could be identified with the entropy of the primary gas and the principle of least action is nothing but the second law of thermodynamics. The author shows that the uncertainty relation of quantum mechanics can be derived directly from the equation for fluctuations and he explains the statistical basis of the virtual interactions.

Mahn‐Soo Choi

Nilsson, Henrik

This preprint proposes a physical mechanism for several foundational quantum phenomena—spin, wave–particle duality, and nonlocal correlations—by modeling the electron as a stable standing-wave resonance node in a 4D extended field domain (x,y,z,w,t). The internal coordinate w represents field-depth, a compact resonance dimension of the underlying medium. Within this framework, spin-½ arises from SU(2) holonomy in the (r,w) subspace; charge quantization from mixed curvature KrwK_{rw}Krw; the electron’s magnetic moment (g≈2) from internal rotational symmetry; and Pauli exclusion from the two-dimensional spinor fiber structure. These results appear naturally, without postulating intrinsic point particles or abstract quantum axioms. Wave–particle duality emerges as a projection effect: a localized 4D resonance is observed as a delocalized probability wave in 3D space, while self-interference and quantum correlations follow from the geometric coupling between the lateral and depth components of the node. The model connects directly to atomic and molecular structure, describing shells, pairing, and bond geometry as standing interference patterns of the projected field density. This preprint builds on the author’s Field-Depth framework and provides a unified resonance-based interpretation of the electron and its quantum behavior.

Luigi E. Picasso