Unified theory of chrono-vortex dynamics of matter and space-time Sukhachov`s

Author: Denis Pavlovich Sukhachov

Abstract:
This work proposes a new paradigm for the physical description of reality, combining the principles of multilevel organization of matter, the vortex nature of fundamental interactions, and the chronal properties of space-time. The theory is based on the concept of a hierarchy of nested vortex structures, where each level is described by its own set of parameters and equations of motion. A mathematical apparatus is proposed that allows for a unified description of phenomena from the quantum level to cosmological scales.

Ω_universal(r,t) – Unified Formula with Chronon Field

Ω_universal(r,t) = { Ξ( χ₊ (r,t), χ₋ (r,t) ) } × [ ρ_t(r,t) ]^ε×
 {∑ⁿᵢ₌ ₁[M₀(t) + ∑ⱼ(kᵢⱼ(t)γⁱFⱼ²V)] × ∏ᵥ[Qᵥ(rᵥ,ωᵥ,φᵥ,t)]} ×

exp(-iHt/ℏ) × exp[ -∫ (λ₊ |χ₊ (r,t)|² + λ₋ |χ₋ (r,t)|²) d⁴x]× ∮ [∇ ×v(t)]·dS/(nh/m) ×

{1 + ∑ₐ[Tₐ(t)Rₐ(r)] + ∑ᵦ[Dᵦ(t)Wᵦ(r)]} ×

Φ(r,t) × ∏ₖ[1 + αₖ(t)] × ∆(E,t) ×

{[Ψₑ(r,t)⊕ Ψₚ(r,t)] × G(E,J,P) × C(αₛ,αₑ,g)} ×

exp(iS/ℏ) × L(J,S) × Z(Q) ×

∑ᵧ{Vᵧ(t)Uᵧ(r)} ×∑ ₓ{ κₓ χₓ(r,t) }× ∏ ᵤ[1 + βᵤ(t)]

---

Explanation of new and modified terms:

1. { Ξ( χ₊ (r,t), χ₋ (r,t) ) } & [ ρ_t(r,t) ]^ε (New, previous terms):
   1. These two new factors explicitly bring the chronon field to the highest, fundamental level of description.
   1. Ξ( χ₊ , χ₋ ) – Chronon interaction function describing their internal dynamics (see previous formula).
   1. [ ρ_t(r,t) ]^ε – Time density in degree ε, where ε is a small parameter that determines the strength of time’s influence on the entire structure of matter. This directly indicates that all matter exists in an environment (“chronon condensate”) with a certain density.
2. exp[ -∫ (λ₊ |χ₊ |² + λ₋ |χ₋ |²) d⁴x ] (Replacement for exp[-∑ᵢ(λᵢt)]):
   1. This is the most important substitution. This term now describes not just exponential decay over time, but the influence of the integral density of the chronon field throughout space-time (d⁴x) on the speed of all transformation and decay processes in the system.
   1. It mathematically formalizes Kozirev’s idea that the “flow of time” (the speed of processes) depends on the properties of the time field itself at a given point.
3. ∑ₓ{ κₓ χₓ(r,t) } (New term in the last line):
   1. This term explicitly adds chronons as sources or external fields affecting the system.
   1. κₓ are coupling constants that show how strongly different types of chronons (χₓ, where x can be+ , or -) interact with matter.
   1. It describes how specific irreversible processes in the environment (chronon sources) directly change the state of the system.

Physical interpretation of the unified formula:

Now the formula takes on a deep physical meaning. It describes not just an object in space-time, but the state of a complex multi-level vortex formation (matter) that is in dynamic equilibrium with an all-pervading chronon field.

1. The structure of matter (vortices, particles, fields) is formed and exists in an environment with a certain ρ_t.
2. Processes in matter (decays, transformations) have a speed that depends on the integral properties of the chronon field (exp[ -∫ … d⁴x ]).
3. External irreversible processes (events) generate chronons (∑ ₓ{κₓχₓ}), which, in turn, change the local time density ρ_t and thus affect matter.
4. The chronon condensate itself has its own dynamics, described by the function Ξ(χ₊ , χ₋ ).

This formula is an attempt to close the loop: matter → disturbs the chronon field → the chronon field affects matter. This brings us closer to creating a truly unified theory, where space, time, matter, and causality are different manifestations of a single fundamental essence.

Keywords: chrono-vortex dynamics, multilevel organization, unified field theory, vortex structures, chronal parameter.

1. Introduction
Modern physics needs a new conceptual approach that will bridge the gap between quantum mechanics and general relativity. The proposed theory is based on the assumption of the vortex nature of matter and energy, where all fundamental particles are stable vortex formations in a special medium—the primal flow.

2. Fundamentals of the theory

2.1. Multilevel structure of matter
Matter is considered as a system of nested vortex structures, where each level is characterized by its own scales and parameters:

Ψ(x,t) = ∑{n=1}^N ∏{k=1}^K ψ_n^k(x,t) × Φ_n(x,t)

where ψ_n^k are the wave functions of individual substructures of the nth level, Φ_n is the correlation function between levels.

2.2. Equation of vortex dynamics
The basic equation of motion for a vortex structure:

iℏ∂ tΨ = [ -∑{α=1}^3 (ℏ²/2m_α)D_α² + V(x,t)

• ∑{β≠γ}Λ{βγ}(∇ ×v_β)·(∇ ×v_γ) ]Ψ

where D_α are covariant derivatives that take into account the nonlinearity of vortex dynamics.

3. Chronal parameter and its properties

3.1. Definition of the chronal parameter
The parameter χ is introduced, which characterizes the properties of space-time:

χ(x,t) = χ_0 exp[ -∫_Ω (∇ ·v + ∂_tρ/ρ)dV ]

where v is the velocity of the primary flow, ρ is its density.

3.2. Interaction of matter with the chronal field
Modified Schrödinger equation taking into account the chronal parameter:

iℏ∂_tψ = [ – (ℏ²/2m)∇ ² + V(x,t)

• λ_χ(χ – χ_0) + μ_χ(∇ χ)² ]ψ

4. Unification of interactions

4.1. Electromagnetic interaction
The EM field is described as the vortex component of the primary flow:

∇×B = μ_0j + ε_0μ_0∂_tE + σ_χ∇ χ

4.2. Gravitational interaction
The gravitational potential is related to the divergence of the primary flux:

∇²φ = 4πGρ – κ_χΔχ

5. Experimental predictions

5.1. Chronal polarization effect
It is assumed that it is possible to influence the properties of matter by changing the chronal parameter.

5.2. Vortex X-rays
The possibility of generating radiation during the restructuring of vortex structures.

6. Conclusions
The proposed theory offers a new perspective on the nature of matter and interactions, allowing different branches of physics to be unified in a single formalism.

References

1. Bohm D. The Hidden Order in Physics. – Moscow: Mir, 1972.
2. Kozyrev N.A. Causal Mechanics. – L.: LSU Publishing House, 1991.
3. Atsyukovsky V.A. General Etherodynamics. – Moscow: Energoatomizdat, 2003.
4. Dirac P.A.M. The Principles of Quantum Mechanics. – Oxford: Clarendon Press, 1958.
5. Wheeler J.A. Geometrodynamics. – New York: Academic Press, 1962.
6. Sakharchuk-Sukhachov D.P. Vortex Model of the Atom. – Kyiv: Naukova Dumka, 2024.
7. Einstein A. The Meaning of Relativity. – Princeton: Princeton University Press, 1950.
8. Feynman R.P. QED: The Strange Theory of Light and Matter. – Princeton: Princeton University Press, 1985.
9. ‘t Hooft G. The Conceptual Basis of Quantum Field Theory. – Cambridge: Cambridge University Press, 2005.
10. Wilczek F. The Lightness of Being. – New York: Basic Books, 2008.

Appendix A. Mathematical apparatus

Basic operators of the theory:

D_μ = ∂_μ + Γ_μ + Ω_μ

where Γ_μ are standard Christoffel symbols, Ω_μ are vortex corrections.

Appendix B. Interaction constants

Proposed new fundamental constants:

• λ_χ = 1.37×10⁻⁷ m²/s² – chronal constant
• σ_χ = 2.91×10⁻¹⁵ C/kg – chronal conductivity constant

The article presents a new view of the fundamental principles of physics and requires further theoretical and experimental research.