TGI: Theory of Geometry

**Theory of Interference Geometry (TIG).** **Considering the main elements of the theory, we can propose the following general equation:** ``` Ψ(x, y, z, t, θ₁, θ₂, θ₃, ...) = Σ Aₙ exp[i(kₙ·r - ωₙt)] + Φ(θ₁, θ₂, θ₃, ...) ``` **Where:** * **Ψ:** Total wave function, representing the state of the system at any point in spacetime and in the extra dimensions. * **x, y, z, t:** Spatial coordinates and time. * **θ₁, θ₂, θ₃, ...:** Coordinates of the extra dimensions. * **Aₙ:** Amplitude of the nth component wave. * **kₙ:** Wave vector of the nth component wave. * **ωₙ:** Angular frequency of the nth component wave. * **i:** Imaginary unit. * **r:** Position vector. * **Φ:** Function representing the contributions of fundamental forces and interactions between particles, depending on the coordinates of the extra dimensions. **Justification:** * **Wave nature:** TIG seems to suggest a fundamental wave nature for all particles and interactions. The sum of plane waves represents this nature. * **Extra dimensions:** The coordinates θ₁, θ₂, θ₃, ... represent the extra dimensions proposed by the theory, where the most complex interferences and interactions occur. * **Fundamental forces and interactions:** The function Φ incorporates the contributions of the fundamental forces and interactions between particles, which are dependent on the coordinates of the extra dimensions. * **Flexibility:** This equation is general enough to accommodate a variety of physical phenomena, from quantum mechanics to gravitation. ### English Text Explanation: **The Theory of Interference Geometry (TIG)** proposes a fundamental wave nature for all particles and interactions. This theory introduces extra dimensions beyond the familiar three spatial dimensions and time, suggesting that the most complex interactions.