Finite Informational Capacity and the Emergence of the Speed of Light

We introduce a projectional framework—termed TAP (Transcendental Projection)—in which the observable (3!+!1)-dimensional universe arises as the projected image of a higher-dimensional informational manifold under an operator P. Finite temporal and spatial informational capacities on the projection surface enforce, through a constrained variational principle, a strictly hyperbolic effective field equation with characteristic velocity c =\( \sqrt{\beta_{\text{eff}}/\alpha_{\text{eff}}} \) Within this structure, non-retentive (massless) modes necessarily propagate at c, while retentive modes are restricted to subluminal velocities. An associated energy–flux inequality provides a local information-theoretic bound, establishing the universal speed limit as an emergent capacity ratio rather than a postulate. We further situate this result in relation to relativity, quantum field theory, holography, and cosmology.