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 described by a quantum state ψ and an associated information measure S. In this model, spatial distance arises 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 emerges from gradients of information rather than purely mass-energy as in general relativity. This leads to a modified velocity profile for galactic rotation curves: v²(r) = A(1/r) + B where the constant term B represents contributions from non-local or hidden informational structure. This provides an alternative interpretation of dark matter as an emergent informational effect rather than a fundamental particle. We further explore implications for black holes, entropy growth, and the emergence of complex systems, including potential connections to self-organization and consciousness. This framework aims to unify quantum mechanics, gravity, and information theory, and offers testable predictions for astrophysical observations.