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.
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.
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.
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.
We demonstrate that the fundamental equations of Planck, Einstein, de Broglie, Schrödinger, Hamilton ,Fermat, Heisenberg each contain phase as an implicit variable — present but not declared. The formula τ = ℏ/E, introduced in Phase Dynamics, makes phase explicit: τ is the time required for one radian of phase to accumulate at energy E. This single relation unifies the Planck quantum E = hν, the Einstein rest energy E = mc², and the de Broglie relation λ = h/p into one language. We show that: (i) the Schrödinger equation follows from the phase closure condition ∮p·dr = h on the spherical χ-cell; (ii) spin ½ and g = 2 follow from the topology of the sphere π₁(SO(3)) = ℤ₂; (iii) the fine-structure constant α = Eel/Eχ follows from the ratio of electromagnetic to phase attractor energy. The attractor Eχ = 1.41983487 MeV was discovered numerically — not postulated — as the fixed point of the deuteron phase model after 72 hours of continuous computation. All results are numerically verified against CODATA. The central claim: "Not explicit" does not mean "absent." Phase was always there. We now have the language to compute it.
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.
You are right, the task of measurement is central. But by suggesting that τ be squeezed into the Schrödinger equation as an additional parameter, you miss the point. τ is not a coordinate in the configuration space. It is a property of the state itself, which determines its "rhythm".The collapse of the wave function is not a mathematical problem, but a physical process of chronal synchronization. The superposition collapses not because we are "looking," but because the interaction with the macroscopic system (with its rigid τ) forces the microsystem to choose one chronal rhythm out of many possible ones.Thus, chronal dynamics does not complement the standard interpretation, but replaces the mysterious collapse with a specific physical mechanism, the dissipation of chronal coherence. It is testable. And it solves the problem without involving consciousness or multiple worlds."
This work establishes the mathematical and physical foundations of χ‑structural dynamics (ZEBTS), a fundamental theory of physical reality. The χ‑manifold of states 𝑆 𝜒 , defined by χ‑structures Ω 𝜒 = ( 𝜌 , 𝑔 𝜇 𝜈 , 𝑋 , 𝐹 ) , provides χ‑density, χ‑metric, semantic configuration, and flaytron dynamics. A χ‑metric, χ‑measure, and Hilbert space 𝐻 𝜒 = 𝐿 2 ( 𝑆 𝜒 , 𝑑 𝜇 𝜒 ) form the axiomatic basis of χ‑Reality. The fundamental χ‑evolution operator 𝐷 ^ = 𝑖 ℏ 𝜒 ∂ 𝜏 + 𝐾 ^ 𝜒 + 𝑉 ^ 𝜒 + 𝐹 ^ 𝜒 is self‑adjoint and unifies geometry, density, semantic structure, and flaytron fluctuations. The equation 𝐷 ^ Φ = 0 defines consistent χ‑dynamics and χ‑conservation laws. Two χ‑limit theorems show that quantum mechanics emerges from χ‑Reality: 𝐿 2 ( 𝑅 3 ) arises as the χ‑compressed limit of 𝐻 𝜒 , and the Schrödinger equation is the χ‑limit of 𝐷 ^ . The quantum wave function 𝜓 ( 𝑥 , 𝑡 ) is the projection of the χ‑wave function Φ . Flaytron dynamics yield new spectral effects: χ‑dispersion 𝑝 4 , χ‑anharmonicity 𝑛 2 , and χ‑shifts of hydrogen levels ( 𝑙 + 1 / 2 ) − 1 . These unique χ‑signatures allow experimental tests via neutron interferometry, molecular spectroscopy, and precision hydrogen measurements. ZEBTS provides a complete χ‑ontology in which space, matter, interactions, and quantum phenomena arise from χ‑structure; quantum mechanics is its χ‑limit.