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### Formula is the Time?

Posted: Sun Jan 20, 2019 1:46 pm
My idea. 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

$ct=r$

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

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

$dI=\frac{Mc^2t}{h}$

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

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

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

Where is the squared length of Planck

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

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