Physicists link gravity and quantum information in Einstein equation derivation

Einstein's theory of general relativity describes gravity as the curvature of space and time caused by matter and energy. Quantum theory describes the microscopic world. Research reported by Phys.org on 12 October 2026 shows that gravity and quantum information are deeply connected, and that the shape of spacetime can be traced back to the way information is stored in quantum fields.

In 1995, the physicist Ted Jacobson showed that Einstein's equations can be derived from thermodynamics, the physics of heat and entropy, much like the laws governing a gas emerge from the motion of its molecules. According to Phys.org, this suggested gravity might not be fundamental but could emerge from something deeper. The new study, published in Physical Review Letters, reconstructs that derivation using mathematical methods that connect quantum information to spacetime geometry.

The authors use quantum relative entropy rather than the classical notion of entropy. According to Phys.org, relative entropy measures how well two quantum states can be told apart, like telling a passing wave apart from the constant rippling of the sea. Dr. Albert Much, assistant professor of quantum field theory and general relativity and a coauthor of the study, said: "We show that this quantity, evaluated at a horizon—a boundary in spacetime beyond which no information can be received—equals the energy flowing across that horizon."

Much said the relation between entropy and the area of horizons, illustrated by Bekenstein and Hawking, is well established. He said combining it with the relative entropy result leads directly to the equations that describe how quantum matter curves spacetime. The authors said the significance of their findings rests on the genuine novelty of their proof. They acknowledged that the fundamental ingredients of the connection between information and gravity were already known, and said the relationship was often presented through physical intuition and suggestive arguments rather than rigorous mathematical proofs.

Phys.org reported that the paper and extensive conversations with the authors suggest the research could provide new clues about the origin of gravity, a tentative conclusion based on their use of quantum relative entropy. According to the report, the connection between entropy and gravity relied for decades on analogies with classical thermodynamics. The authors said the work is a meaningful step toward understanding quantum gravity, the open problem of uniting general relativity with quantum theory.