Simplifying the Temporal spacetime metric. (Edited)
Temporal spacetime metric. Scenario: Gravitational Field with Increasing Effect Suppose τ(t) represents a gravitational field effect that increases over time, such that τ(t) = g(t) = t². The generalized metric tensor would be: (edit removed the temproal aspect from the old model, minkowski to temporal) ημν(t) = [ 1 + α₀ · t² 0 0 0 1 + α₁ · t² 0 0 0 1 + α₂ · t² ] The spacetime interval is: ds² = (1 + α₀ · t²) dx² + (1 + α₁ · t²) dy² + (1 + α₂ · t²) dz² In this case, as time t increases, the spatial distances (dx², dy², dz²) are scaled more significantly due to the time-dependent factors, than in Minkowski space. This reveals new insights into how gravitational fields or other temporal factors alter spatial dimensions, which is not captured in the standard Minkowski spacetime model. To see how gravity is described by my metric, let’s examine the spacetime interval and its implications. ds² = (1 + α₀ · τ(t)) dx² + (1 + α₁ · τ(t)) dy² + (1 + α₂ · τ(t)) dz² General temporal Compon...