Inertia as the Geometric Cost of Projecting 5D Null Trajectories

While Space-Time-Matter (STM) literature has extensively identified four-dimensional inertial mass with extra-dimensional momentum (m ∝ |p5|), it lacks a dynamic explanation for why extra-dimensional motion manifests specifically as resistance to acceleration in 4D. We reformulate the origin of inertia not as an intrinsic material property, but as the geometric cost of altering the projection of a 5D null trajectory onto 4D spacetime. By analyzing the rigidity imposed by the null condition ds^2 = 0, we explicitly show that any 4D velocity variation forces a non-linear readjustment in the extra-dimensional component, naturally generating the relativistic γ^3 factor as an energy cost rate. Finally, we make this framework quantitative for composite systems, proving that the collective rigidity of coupled null trajectories accounts for emergent inertial mass even when individual constituents lack extra-dimensional momentum (p5,i = 0).