Universal Gravitational Bounds on Information, Computation, and Complexity

This paper investigates the fundamental limits imposed on computation by gravitational effects across all scales, from quantum to cosmic, through the lens of an extended quantum gravity framework that incorporates quantum informational measures into Einstein's field equations. This framework reveals intricate connections between spacetime geometry, quantum entanglement, and computational complexity, yielding novel bounds on information processing in curved spacetime with implications for quantum computing, black hole physics, and cosmology. Key findings include a generalized Margolus-Levitin theorem that accounts for gravitational time dilation, a modified holographic bound on information density incorporating quantum gravitational corrections, predictions for gravitationally induced decoherence rates in quantum systems, and an analysis of the total computational capacity of the observable universe. We derive scale-dependent computational limits and explore their consequences for specific quantum algorithms and error correction protocols. Additionally, we examine the philosophical implications of these gravitational constraints on computation, discussing their relevance to concepts such as determinism, free will, and the arrow of time, and propose experimental setups to test our theoretical predictions, ranging from table-top quantum experiments to astrophysical observations. Our results suggest that gravity plays a fundamental role in shaping the informational structure of the universe, potentially placing ultimate limits on knowledge acquisition, aiming to provide a unified perspective on the interplay between gravity, quantum mechanics, and information theory, offering new insights into the nature of space, time, and computation in our universe.