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.
- Bekenstein Hawking entropy for the event horizon. Light cone case
$$ ct = r $$
$$ S = \frac {c ^ 3} {Gh} r ^ 2 $$
- Gravitational time dilation. The case if matter inside a closed surface processes information at the quantum level according to the Margolis-Livitin theorem.
$$ dI = \frac {dM c ^ 2t} {h} $$
$$ \Delta t = \frac {Gh} {c ^ 4} \int \frac {dI} {r} = \frac {GM} {rc ^ 2} t $$
The formula is invariant under Lorentz transformations.
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.
