The Illusion of Spacetime Foam: Proving a Continuous Planck-Scale Continuum via Bounded Vacuum Elasticity

This paper presents a deterministic refutation of the standard quantum gravity "spacetime foam" hypothesis by applying the framework of The Unified Theory of Absolute Spatial-Temporal Geometric Tension. It demonstrates that the chaotic, probabilistic fragmentation predicted at the Planck scale is an artifact of treating Planck's constant as an immutable invariant in an observer-blind measurement model. By introducing a bounded elastic potential and a space tension field with an absolute physical yield ceiling, this research proves that infinite energy self-interactions are suppressed, maintaining a perfectly smooth, continuous, and finite spacetime manifold across all scales. The paper addresses the long-standing mathematical incompatibility between general relativity and quantum field theory at ultra-short distances, natively resolving the vacuum fluctuation divergences that traditionally required arbitrary mathematical cutoffs or discretized geometries. Furthermore, this continuous framework aligns with observational astrophysical data that has consistently failed to detect the Lorentz invariance violations or photon dispersion predicted by chaotic vacuum models.