Holography the time. Perhaps time can be expressed as
[math]$$ t=\frac{Gh}{c^4}\int\frac{dS}{r} $$[/math]
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
[math]$$ r=ct $$[/math]
[math]$$ S=\frac{c^3}{Gh}r^2$$[/math]
2.Gravitational time dilation. The case if matter inside a closed surface processes information at the quantum level according to the Margolis-Livitin theorem.
[math]$$ dI=\frac{dMc^2 t}{h} $$[/math]
[math]$$ \Delta t=\frac{Gh}{c^4}\int\frac{dI}{r}=t\frac{GM}{c^2r}$$[/math]
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
[math]$$ s^2=(l^2_{p}\frac{S}{r})^2-r^2 $$[/math]
Where is the squared length of Planck
[math]$$ l^2_{p}=\frac{Gh}{c^3} $$[/math]
Quantum tunneling of noncommutative geometry gives the definition of time in the form of holography, that is, in the form of a closed surface integral. Ultimately, the holography of time shows the dualism between quantum mechanics and the general theory of relativity.Attachment #1: 1_dualism_1.pdfAttachment #2: 1_Quantum_tunneling_approach_of_noncommutative_geometry.docx
