My idea. Perhaps time can be expressed as
Where S is the entropy of entanglement of an arbitrary closed surface. r is the radius to the surface point. Integration over a closed surface.
This is very similar to the analogy. Time behaves as a potential, and entropy as a charge.
From this formula there are several possible consequences.
1.Bekenstein Hawking entropy for the event horizon. Light cone case
2.Gravitational time dilation. The case if matter inside a closed surface processes information at the quantum level according to the Margolis-Livitin theorem.
3.The formula is invariant under Lorentz transformations.
4.If this definition is substituted instead of time, then the interval acquires a different look, which probably indicates a different approach of the Minkowski pseudometric with a complex plane
Where is the squared length of Planck
Is such an interpretation possible? Sincerely, Kuyukov V.P.