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Deriving the Entropy-Geometry Relationship in General Relativity
Theoretical physics involves making suggestions and exploring ideas to see where they lead. In the context of gravity, Jacobson proposed that the entropy of a region is always proportional to the area of its boundary. This suggestion implies that increasing the entropy of a region by enhancing entanglement also increases the energy inside the region, affecting the geometry of space. Jacobson's idea leads to a new law in general relativity where the area of every region is linked to the entropy inside, ensuring that the geometry adjusts to maintain this proportionality. By taking this suggestion seriously, an equation relating entropy to geometry can be derived.