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.
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.
This work 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 (), a revision of classical paradoxes of quantum mechanics is carried out. A generalized energy equation 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 (). 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.
Schrödinger's equation is the foundation of quantum mechanics. But it doesn't explain where phase comes from, why it can be synchronized, or what "time" is in a quantum system. The paper shows that the Schrödinger equation is a special case of chronal dynamics, where τ = ħ/E — the duration of 1 radian of phase — is considered constant. If we abandon this assumption and introduce the scalar field τ(x, t), we get a generalized equation from which we follow: Attractor E_χ = 1.41983487 MeV is the first eigenvalue of the chronal operator ("God's number") Fine-structure constant α = 1/137.036 as the ratio E_el/E_χ Electron mass m_e = (E_χ – 0.42)/2 Hierarchy of leptons through scaling χ = φ·τ Synchronization condition cos φ = 1, K = 0.316, Δω/ω = 0.2 Keywords: Schrödinger equation, chronal dynamics, τ = ħ/E, χ = φ·τ, attractor, God number.
The paper introduces a fundamental quantity — the chronal radian χ = φ·τ, where φ is the phase (rad), τ is the local chronal field (c). It is shown that all the key relations of quantum mechanics, field theory and gravitation can be expressed in terms of χ in a simple and visual way. Action S = h·φ → S = h·( χ/τ) Energy E = ħ/τ → E = ħ·( dφ/dχ) Momentum p = h·k → p = h·(∇φ) Gravity G ∼ τ² → G ∼ (χ/φ)² The introduction of χ makes it possible to reformulate all the results of chronal dynamics (pp-cycle, dd-synthesis, RER, island of stability) in a single language. This makes the theory transparent, testable and ready for engineering implementation. The final part of the work outlines the transition from theory to engineering - the creation of the Chronal Shield and resonant energy sources.
A new fundamental quantity is introduced in the paper — the chronal radian χ = φ·τ, where φ is the phase (rad), τ is the local time (s). It is shown that χ is a natural measure of the system's position in phase space, combining the time and angular coordinates. With its help, all the key relations of quantum mechanics and chronal dynamics take on a simple and geometrically illustrative form. E = ħ/τ = ħ·( dφ/dχ), and the probability of synchronization is P ∼ cos²(Δχ/2). The introduction of the chronal radian makes it possible to divert the fundamental field τ from direct attacks by opponents, focusing the discussion on the observed value of χ.
A geometric interpretation of electron dynamics is presentedbased on phase-coherent helical motion constrained by relativistic kinematics.Building on de Broglie’s concept of internal periodicity and theHamilton–Jacobi formulation of mechanics, the electron is modeled asan intrinsic light-speed helical trajectory whose axial pitch correspondsto the de Broglie wavelength and whose transverse scale is set by thereduced Compton length. Within this framework, spin-1/2 symmetry,magnetic moment, rest energy, and bound-state quantization emerge asinterconnected consequences of phase closure and geometric constraints,rather than as independent postulates. The formal operator structure ofquantum mechanics is recovered as a statistical description of ensemblesof phase-coherent helical trajectories, with momentum and energy operatorsarising as generators of spatial and temporal phase evolution. The frameworkprovides a geometric visualization of interference, tunneling, and quantumtransitions, while remaining fully consistent with the standard probabilisticpredictions of quantum mechanics and the Lorentz invariance of specialrelativity. The helical phase interpretation is intended as a conceptualand pedagogical complement to orthodox formalisms, offering physicalintuition for otherwise abstract quantum structures without modifying theirmathematical foundations. Thus, this work does not propose a modificationof quantum theory, but offers a geometric interpretation of its formal structures aimed at clarifying their physical content.
A geometric interpretation of electron dynamics is presentedbased on phase-coherent helical motion constrained by relativistic kinematics.Building on de Broglie’s concept of internal periodicity and theHamilton–Jacobi formulation of mechanics, the electron is modeled asan intrinsic light-speed helical trajectory whose axial pitch correspondsto the de Broglie wavelength and whose transverse scale is set by thereduced Compton length. Within this framework, spin-1/2 symmetry,magnetic moment, rest energy, and bound-state quantization emerge asinterconnected consequences of phase closure and geometric constraints,rather than as independent postulates. The formal operator structure ofquantum mechanics is recovered as a statistical description of ensemblesof phase-coherent helical trajectories, with momentum and energy operatorsarising as generators of spatial and temporal phase evolution. The frameworkprovides a geometric visualization of interference, tunneling, and quantumtransitions, while remaining fully consistent with the standard probabilisticpredictions of quantum mechanics and the Lorentz invariance of specialrelativity. The helical phase interpretation is intended as a conceptualand pedagogical complement to orthodox formalisms, offering physicalintuition for otherwise abstract quantum structures without modifying theirmathematical foundations. Thus, this work does not propose a modificationof quantum theory, but offers a geometric interpretation of its formal structuresaimed at clarifying their physical content.