Deriving the Entropy-Geometry Relationship in General Relativity

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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.

I suspect most loyal Mindscape listeners have been exposed to the fact that I’ve written a new book, Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime. As I release this episode on Monday 9 September 2019, the book will officially be released tomorrow, in print, e-book, and audio versions. To get in the mood, we’ve had several podcast episodes on quantum mechanics, but the “emergence of spacetime” aspect has been neglected. So today we have a solo podcast in which I explain a bit about the challenges of quantum gravity, how Many-Worlds provides the best framework for thinking about quantum gravity, and how entanglement could be the key to showing how a curved spacetime could emerge from a quantum wave function. All of this stuff is extremely speculative, but I’m excited about the central theme that we shouldn’t be trying to “quantize gravity,” but instead looking for gravity within quantum mechanics. The ideas here go pretty far, but hopefully they should be accessible to everyone.

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The end of this episode includes a bonus, a short snippet from the audio book, read by yours truly. Audio excerpted courtesy Penguin Random House Audio. And here are links to some of the technical papers mentioned in the podcast.