Information-Based Emergent Spacetime and Gravity

We propose a theoretical framework in which spacetime, gravity, and cosmological phenomena emerge from an underlying informational structure. The state of the universe is defined by a quantum state ψ and an associated information measure S. In this model, spatial distance is derived from shared information between subsystems, and geometry emerges from informational relationships. Time is defined as the evolution of entropy, with dS/dt governing temporal flow. We derive a modified dynamical equation in which gravitational behavior arises from gradients of information rather than purely mass-energy as in general relativity. This naturally leads to a modified velocity profile for galactic rotation curves: v²(r) ≈ A(1/r) + B where the constant term B emerges from hidden or non-local information contributions. This provides an alternative interpretation of dark matter as an informational effect rather than a particle. We further explore implications for black holes, entropy growth, and the emergence of complex systems, suggesting that highly structured information may lead to self-organizing systems analogous to consciousness. This framework offers a unified perspective linking quantum mechanics, gravity, and information theory, and provides testable predictions for galactic dynamics.