Informational theory of relativity

Assuming the minimal time to send a bit of information in the Einstein clock synchronization of two clocks located at different positions, we heuristically introduce the extended metric to the information space as an attempt to unify space-time and information. This modification of relativity changes the red-shift formula, keeping the geodesic equation intact. Extending the gauge symmetry hidden in the metric to the five-dimensional general invariance, we start with the Einstein-Hilbert action in the five-dimensional space-time. After the 4+1 decomposition we obtain the effective action, which includes the Einstein-Hilbert action for gravity, the Maxwell-like action for the velocity field, and the Lagrange multiplier term that ensures the normalization of the time-like velocity field. As an application, we investigate a solution of the field equations in the case that a four-dimensional part of the extended metric is spherically symmetric, which exhibits Schwarzschild-like space-time but with the minimal radius. As a discussion we present a possible informational model of the synchronization process as a trial model that is inherently stochastic. The model enables us to interpret the information quantity as a new spatial coordinate.