“The entropy of a black hole is proportional to the area of its event horizon, not its volume. This is a deep statement, suggesting that the information about everything that fell into the black hole is stored on its surface, like a kind of hologram.”Leonard Susskind · The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics · 2008 · The Black Hole War, Chapter 1: The Black Hole War Begins
The entropy and information of a black hole are stored on its two-dimensional surface, not in its three-dimensional volume.
Susskind explains the discovery by Jacob Bekenstein and Stephen Hawking: a black hole's entropy is measured by its event horizon's area. When an object falls in, its information is not lost but etched onto that surface. This defies our intuition, since entropy usually scales with volume. For instance, a solar-mass black hole has a horizon area of about 10^7 square meters, yet its entropy is 10^77 units, enormous compared to an ordinary star. This relationship led to the holographic principle, suggesting our entire three-dimensional space might be a projection from a two-dimensional surface.
Why it matters The notion that information resides on surfaces rather than volumes is timely as debates over the universe's initial entropy and the nature of time intensify, with this book bridging thermodynamics and quantum gravity.