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Formula is the Time?

Posted: Sun Jan 20, 2019 1:46 pm
by Kuyukov Vitaly
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.