Physicists Derive Einstein's Gravity Equations From Quantum Information Theory, Without Analogies
A Physical Review Letters paper shows that a measure of how distinguishable quantum states are, evaluated at a horizon, yields the semiclassical Einstein equations.
Physicists have derived the semiclassical Einstein equations, which describe how quantum matter curves spacetime, starting from quantum information theory. The paper, "From Quantum Relative Entropy to the Semiclassical Einstein Equations," appears in Physical Review Letters. Its authors include Philipp Dorau and Albert Much.
The result builds on a long-standing hint that gravity may not be fundamental. In 1995, Ted Jacobson showed that Einstein's equations can be obtained from thermodynamics, which suggested gravity might emerge from something deeper. For decades, however, the link between entropy and gravity leaned on analogies with classical thermodynamics rather than strict proof.
Dorau and Much replace those analogies with a quantity from quantum information theory called relative entropy. It measures how distinguishable two quantum states are. The team evaluates it at a horizon, a spacetime boundary beyond which no information can be received, and shows that it equals the energy flowing across that horizon. Combined with the Bekenstein-Hawking relation between a horizon's entropy and its area, that identity yields the semiclassical Einstein equations.
Much offers a picture. Imagine a wave on a rippling sea surface, where the ripples stand for the quantum vacuum. Relative entropy measures how well the wave can be told apart from that background. In his words, matter is the pluck, spacetime is the string, and Einstein's equations are the note. He said the derivation "uses mathematically rigorous and well-defined quantities, replacing earlier heuristic arguments."
The authors are open about what is new and what is not. "Most of the ingredients for our work have been known for decades," Dorau said, crediting recent progress in understanding relative entropy with supplying the missing link between quantum information, thermodynamics and gravity. The contribution is a precise mathematical framework where earlier work relied on physical intuition and suggestive arguments.
The paper does not deliver a full theory of quantum gravity, and the authors call their conclusion about the origin of gravity tentative. It also has no immediate practical use. Much pointed out that general relativity, once seen as purely theoretical, now underpins GPS, and that quantum information is the framework behind quantum computing.
Next, the team plans to extend the results to other forms of quantum matter, more general quantum states, and lightlike surfaces, which matter in black hole physics. They also want to work out the quantum side of the equation, to see whether Einstein's equations plus quantum corrections emerge on the other side. Much said the connection could serve as a test bed for the various theories of quantum gravity, and the pair's stated long-term goal is to clarify how far gravity can be derived from quantum information alone.
If the approach holds up, it would turn a decades-old analogy into a derivation, and it would give researchers a concrete tool for testing which proposals for quantum gravity are consistent with it. The work was originally reported by Leon Barkho of the University of Sharjah.
