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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.

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