# Time is the potential?

Perhaps time can be expressed as

$$t = \frac {Gh} {c ^ 4} \int \frac {dS} {r}$$

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

$$ct = r$$

$$S = \frac {c ^ 3} {Gh} r ^ 2$$

1. Gravitational time dilation. The case if matter inside a closed surface processes information at the quantum level according to the Margolis-Livitin theorem.

$$dI = \frac {dM c ^ 2t} {h}$$

$$\Delta t = \frac {Gh} {c ^ 4} \int \frac {dI} {r} = \frac {GM} {rc ^ 2} t$$

1. The formula is invariant under Lorentz transformations.

2. 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

$$s ^ 2 = (l ^ 2_ {p} \frac {S} {r}) ^ 2-r ^ 2$$

Where is the squared length of Planck

$$l ^ 2_ {p} = \frac {Gh} {c ^ 3}$$

Is such an interpretation possible? Sincerely, Kuyukov V.P.