The core principle establishes that in conservative dynamical systems derived from a potential energy function $V$, acceleration is mathematically equivalent to the negative Hessian matrix acting on displacement, effectively interpreting second-order spatial derivatives as temporal accelerations within a unified spacetime framework. This concept redefines standard calculus definitions by asserting that mathematical rigor separating space and time into distinct dimensions obscures the physical reality where rates of change over distance are equivalent to rates of change over time due to the inseparability of spacetime metrics. The theory posits that the Hessian matrix serves as a spatial representation of acceleration, providing a rigorous mechanism for analyzing curvature-based dynamics in optimization, molecular vibrations, and relativistic fields without reliance on explicit temporal parameters.
The core principle establishes that in conservative dynamical systems derived from a potential energy function $V$, acceleration is mathematically equivalent to the negative Hessian matrix acting on …