Inverse Shell Theorem Via Hypothetical Simple Harmonic Motion: A Backward Approach from Dynamics

We present a reverse dynamical derivation of the shell theorem by assuming, hypothetically, that a particle inside a hollow spherical shell experiences a nonzero gravitational force. Such an assumption, constrained by spherical symmetry, necessarily leads to simple harmonic motion about the center. We demonstrate that this motion is incompatible with Newtonian gravity through multiple independent arguments, including violations of Gauss’s law and Laplace’s equation, contradictions with energy conservation and momentum conservation, and the absence of any physical mechanism capable of supporting a restoring force inside an empty cavity. This backward approach shows that the vanishing of the gravitational field inside a hollow shell is not merely a result of symmetry or integration, but a fundamental requirement imposed by the internal consistency of gravitational theory.