Temporal Dynamics Metric
Temporal Dynamics Metric The Temporal Dynamics Metric describes the geometry of spacetime influenced by underlying temporal flows and their interactions. These temporal flows are mapped across different dimensions of space and time. The metric g μ ν ( t ) g_{\mu\nu}(t) reflects the structure of spacetime, integrating these flows. Temporal Dynamics Metric: g μ ν ( t ) = [ α 1 ⋅ ∫ τ 1 ( t ) c d t + ∫ [ τ 1 ( t ) ⋅ τ 1 ( t ) ] d t ∫ [ τ 1 ( t ) ⋅ τ 2 ( t ) ] d t ∫ [ τ 1 ( t ) ⋅ τ 3 ( t ) ] d t ∫ [ τ 2 ( t ) ⋅ τ 1 ( t ) ] d t α 2 ⋅ ∫ τ 2 ( t ) c d t + ∫ [ τ 2 ( t ) ⋅ τ 2 ( t ) ] d t ∫ [ τ 2 ( t ) ⋅ τ 3 ( t ) ] d t ∫ [ τ 3 ( t ) ⋅ τ 1 ( t ) ] d t ∫ [ τ 3 ( t ) ⋅ τ 2 ( t ) ] d t α 3 ⋅ ∫ τ 3 ( t ) c d t + ∫ [ τ 3 ( t ) ⋅ τ 3 ( t ) ] d t ] g_{\mu\nu}(t) = \begin{bmatrix} \alpha_1 \cdot \int \frac{\tau_1(t)}{c} \, dt + \int \left[\tau_1(t) \cdot \tau_1(t)\right] \, dt & \int \left[\tau_1(t) \cdot \tau_2(t)\right] \, dt & \int \left[\tau_1(t) \cdot \tau_3(t)...