The Force Created by What Cannot Exist: Rethinking the Casimir Effect

Natural Evolution of Actuality (NEA) begins with abstract, independently lawful parental responsibilities and primitive consequential joining. Positive, Negative, and Open Geometry respectively distinguish admitted configurations, definite obstructions, and unresolved physical realizations. In its developed electromagnetic sector, charge-sensitive phase transport, transverse radiative modes, and physical boundary conditions are separate responsibilities. The original flagship investigation proposed a boundary-mode response and a separation derivative of an admitted-mode generator, while a companion study separately proposed photon generation through time-dependent boundary transport. This paper fortifies those source results without turning forbidden modes into physical particles or claiming that merely deleting possibilities creates energy. We prove a finite-dimensional constrained-response theorem featuring an exact positive Woodbury suppression and a finite limit for compatible sources, and we give exact cutoff-controlled one-dimensional mode sums, including attractive Dirichlet–Dirichlet and repulsive Dirichlet–Neumann examples. We also reconstruct the ideal electromagnetic parallel-plate interaction energy per unit area—given by negative pi squared times the reduced Planck constant and the speed of light, divided by seven hundred twenty times the plate separation cubed—and the corresponding Casimir pressure, which scales inversely with the fourth power of the plate separation under standard declared quantized-field, boundary, and reference-subtraction assumptions. A distinct Gaussian constraint theorem shows how two individually imposed restrictions acquire an interaction proportional to the correlations connecting them, without an additional force carrier. We express the material-response generalization as a relative scattering determinant and distinguish static spectral stress from dynamical Casimir photon production. Finally, an NEA-compatible shape-response formulation specifies when generated geometry, History, and the Jeffers Response Tensor II must accompany a physical force calculation. These results make Negative Geometry quantitatively consequential in selected developed architectures, while preserving the absence of a unique primitive selection algorithm and the open status of physical parameter determination.