Philipp Dorau and Albert Much argue that the semiclassical Einstein equations can follow from quantum relative entropy, reframing gravity as something emerging from quantum information.
Overview
This Physical Review Letters paper, From Quantum Relative Entropy to the Semiclassical Einstein Equations, argues that Einstein's semiclassical gravity equations can be derived from quantum relative entropy and its connection to horizon-area variation.
The authors use modular theory to show that relative entropy between the vacuum and coherent excitations of a scalar quantum field on a bifurcate Killing horizon is given by the energy flux across that horizon.
Assuming the Bekenstein-Hawking entropy-area formula, that energy flux becomes proportional to a change in horizon area. From there, the semiclassical Einstein equations follow from the identification.
That feels like a fundamental shift in how we talk about gravity: not gravity as just another force waiting to be quantized in the usual way, but gravity as an emergent bulk description of underlying quantum information.
This one also lands personally for me. It builds on Hawking's work, and I have a signed letter from Stephen Hawking congratulating me on earning Eagle Scout and encouraging my future success. I am grateful my father reached out to him for that acknowledgement, and I will always treasure it.
Video Notes
- Gravity may be an emergent property, more like thermodynamics describing gases or fluids than a fundamental force in the usual sense.
- The paper builds on Bekenstein and Hawking by tying the origin of gravity to entropy in quantum fields.
- By calculating quantum relative entropy between the vacuum and matter excitations, physicists can recover Einstein's equations.
- The framework may help explain why gravity behaves differently from the other forces and resists ordinary quantization.
Why It Matters
- The paper replaces classical thermodynamic entropy in Jacobson-style gravity arguments with quantum relative entropy.
- It builds directly on the Bekenstein-Hawking connection between entropy and horizon area.
- It suggests quantum information may sit at the root of what we experience macroscopically as gravity.
- Personally, this feels like one of the first plausible candidates I have seen for a unified way to think about gravity.
