The Causal Origin of the Generalized Uncertainty Principle

The Generalized Uncertainty Principle (GUP), characterized by a quadratic momentum correction, is a standard prediction of String Theory and Loop Quantum Gravity, typically attributed to a fundamental minimum geometric length scale. We propose that GUP is not an intrinsic geometric modification of space, but a kinematic consequence of the relativistic speed limit applied to quantum measurement durations. By enforcing Lorentz invariance of the quantum phase and Time-Energy uncertainty, we derive a "Spacetime Action Constraint." We validate this framework via three computational models: (1) a discrete phonon lattice (Control), (2) a fluctuating causal network (Mechanism), and (3) a temporal convolution model (Verification). We demonstrate that spatial discreteness alone preserves standard Heisenberg uncertainty, whereas introducing causal measurement latency reproduces the exact quadratic GUP scaling. Furthermore, applying this causal limit to information packing naturally recovers the Holographic Principle and the Bekenstein bound. These results suggest that the "minimum length" of quantum gravity can be reinterpreted as a "minimum causal latency," implying that spacetime geometry is emergent from causal information constraints.