Scalar Casimir Effect from Bilocal Correlations in a Wormhole Foam

Abstract

We determine how spatially bilocal correlations induced by a dilute ensemble of virtual Euclidean wormholes modify the scalar Casimir interaction between parallel Dirichlet plates. From the leading monopole action, we isolate an equal-Euclidean-time sector and construct a point-throat, first-order matched spectator model with fixed foam statistics. Global two-plate inclusion-exclusion over all mouth-pair center positions yields a continuous fixed-separation kernel free of the logarithmic image structures produced by a restricted translation sector. The kernel is quadratically suppressed at coincidence, changes sign near 0.695 plate spacings, and tends to a positive large-separation plateau. Averaging over truncated-Gaussian, log-normal, and Gamma distributions with a common relative width yields closely spaced energy curves but a finite shape dependence. Differentiating the dimensional energy at fixed ensemble parameters gives a leading-order pressure threshold of 0.05 in the large-separation limit. In the truncated-Gaussian scan extending to twelve plate spacings, an amplitude of 0.06 yields a crossover near a separation ratio of 3.17, whereas amplitudes of 0.02 and 0.04 remain attractive and 0.05 is critical. The scalar cavity therefore provides a scale-selective probe of spatial bilocality whose leading boundary response can change sign within the declared model.