Gravity emerges from quantum information, new mathematical proof suggests

Physicists have long faced a stubborn puzzle: Einstein's theory of gravity and the laws of quantum mechanics describe the same universe but speak entirely different languages. One treats space and time as a smooth, curved fabric. The other governs the probabilistic dance of particles at scales too small to see. Bridging that gap has remained one of the most pressing unsolved problems in physics. Now a team of researchers has published what they argue is a rigorous mathematical proof that gravity itself may not be fundamental at all—that it emerges instead from the structure of quantum information.

The intellectual roots of this idea run back three decades. In 1995, physicist Ted Jacobson demonstrated that Einstein's equations—the mathematical heart of general relativity—could be derived from thermodynamics, the physics of heat and entropy. It was a striking insight: just as the behavior of a gas emerges from the random motion of its molecules, gravity might emerge from something deeper still. But for decades, that connection remained largely intuitive, supported by physical reasoning and suggestive analogies rather than by rigorous proof.

The new work, published in Physical Review Letters, changes that. The researchers, led by Dr. Albert Much of the Institute for Theoretical Physics, reconstruct the thermodynamic derivation of general relativity using sophisticated mathematical tools drawn from quantum information theory. The key innovation is their use of quantum relative entropy—a precise measure from quantum information science that quantifies how distinguishable two quantum states are from each other. Much describes it with a simple image: imagine the surface of the sea, never perfectly still, its constant rippling like the quantum vacuum—the state we call empty space. Now imagine a wave passing across that surface. Quantum relative entropy tells you how well you can distinguish that wave from the background ripple.

The authors show that when this quantity is evaluated at a horizon—a boundary in spacetime beyond which no information can escape—it equals the energy flowing across that boundary. Combined with the well-established relationship between entropy and the area of horizons, discovered by Bekenstein and Hawking, this leads directly to Einstein's equations. The implication is profound: the curvature of spacetime, the very shape of gravity itself, may be governed by how quantum states can be told apart from one another. As Much puts it, using a musician's metaphor: matter is the pluck of a guitar string, spacetime is the string itself, and Einstein's equations are the note it produces.

What makes this work significant, the authors emphasize, is not that the individual ingredients are new. Physicists have understood for decades how quantum matter behaves near black hole horizons and how empty space carries thermal properties. Coauthor Philipp Dorau, a theoretical physicist at Leipzig University, notes that recent progress in understanding relative entropy provided the missing link—the mathematical bridge that connected quantum information, thermodynamics, and gravity into a single coherent framework. The real advance is replacing decades of heuristic argument and physical intuition with mathematically rigorous derivations and proofs. Much stresses that their work uses "mathematically rigorous and well-defined quantities," a shift he sees as a meaningful step toward understanding quantum gravity.

The researchers are careful to note that their findings do not yet have practical applications. But they point to history as their warrant for pursuing foundational work. General relativity, once purely theoretical, became essential to GPS technology. Quantum information theory, the language of their proof, now underlies quantum computing and emerging quantum technologies. If confirmed and extended, this work could help resolve one of physics' deepest divides: the still-unresolved tension between the quantum laws of the microscopic world and Einstein's theory of gravity.

The authors are already planning their next steps. They aim to generalize their findings to more complex scenarios—different forms of quantum matter, more general quantum states, and lightlike surfaces that play a central role in black hole physics. Much describes their long-term ambition plainly: to determine how far gravity can be derived from quantum information alone, and whether that derivation might guide the development of a complete theory of quantum gravity. The work, they suggest, could serve as a testing ground for competing theories of quantum gravity, a way to see which frameworks produce the right equations when quantum information is inserted into the mathematical machinery.