Information-Union: A Unified Framework for Quantum Entanglement via the Information-Processing Invariance; 𝒄² = 𝒗 ⋅ 𝑳

This paper introduces the 'Information-Union' framework, a novel model for quantum entanglement derived from the foundational principle of Information-Processing Invariance, expressed as 𝑐²= 𝑣 ⋅ 𝐿. This principle posits a universal 'vacuum bandwidth' that governs the trade-off between a system's temporal update rate (𝑣) and its spatial expression (𝐿). We model entanglement as a physical phase transition termed the 'Information Union,' where constituent particles surrender local spatial metrics to a global, photonic mediator. Applying Landauer's principle and Vopson's mass-energy-information equivalence, we demonstrate that the establishment of this union requires quantifiable 'merger work' (𝑾𝚽) against the vacuum's inherent resistance. The mediator acts as a hardware channel coupling the system to the universe's minimal update rate, 𝜖, which we show correlates exactly with the Hubble constant (𝐻o). The framework culminates in a falsifiable prediction: entanglement maintained over cosmological distances must exhibit a distance-dependent degradation in synchronicity – a 'coincidence jitter' – proportional to √𝐿. This intrinsic decoherence, independent of environmental noise, provides a direct experimental test of the coupling between quantum nonlocality and cosmic expansion.