Nonlinear physical processes arise via dimensional parameters scaling with energy. Parameter dimensions determine the scaling character at speed of light c, and at velocities < c. Reducing dimensional analysis to time and length dimensions only, resolves this scaling paradigm. A mode change occurs for running parameters for wave-particle velocities < c, consistent with symmetry breaking, where scaling is determined by the exponent on the length component. The fine structure constant alpha is found to have dimensions Hz, requiring dimensional amendments to a number of fundamental parameters. The gravitational constant G is found to have dimensions m-1, implying that gravity is not a force. Gravity is shown to have dimensions of linear density. Running parameters ought to resolve multiple anomalies within the standard model, leading to unification of gravity with electromagnetism.