Physicists from Leipzig derived Einstein's famous equations from quantum information. Perhaps gravity and space itself are not fundamental, but merely how the information of a quantum field looks "from the outside"
An apple falls to the ground, the Moon circles the Earth, light bends near stars. More than a century ago, Albert Einstein explained why this happens: mass and energy curve spacetime, and everything else simply moves along those curves. His equations work flawlessly — from planetary orbits to black holes. But they do not answer a deeper question: why is space capable of curving at all? What is it, really? A new paper by theoretical physicists Philipp Dorau and Albert Much of the Institute for Theoretical Physics at Leipzig University, published in Physical Review Letters — one of the most authoritative physics journals in the world — offers a striking answer. Einstein's equations can be derived from quantum information — the information written in the quantum field, the invisible foundation permeating the entire Universe.
This idea has a famous backstory. In 1995, the American physicist Ted Jacobson showed that Einstein's equations can be obtained from the laws of thermodynamics — the science of heat and entropy. Gravity in his approach is like gas pressure: pressure does not exist as a separate force, it arises from the motion of countless molecules. Likewise, gravity may not be a fundamental force but a collective effect of something deeper — processes occurring in the quantum field. But Jacobson's approach had a weakness: ordinary entropy in quantum field theory turns out to be infinite, and for a long time it was impossible to bring his reasoning to a rigorous quantum form.
Dorau and Much found a workaround. Instead of ordinary entropy, they used the so-called quantum relative entropy — a measure of how distinguishable one state of a quantum field is from another, that is, how much quantum information separates them. This quantity in quantum field theory is always finite. The physicists compared two states of a quantum field. The first is the vacuum, its ground state. In physics this is not emptiness at all: there are no particles in it, but the quantum field continuously trembles with fluctuations, and all its regions are connected to one another by an invisible web of quantum entanglement. The second is the same field in which matter or energy has appeared. It turned out that the "distinguishability" of these two states is exactly equal to the flux of energy of the quantum field through a horizon, an imaginary boundary in spacetime. And according to the famous Bekenstein–Hawking law, the entropy of a horizon — that is, the amount of information it can store within itself — is proportional to its area. By linking one to the other, the authors obtained Einstein's equations describing how quantum matter curves spacetime.
The main conclusion of the paper sounds almost philosophical: the curvature of spacetime literally follows from how quantum information is stored in the quantum field. When matter appears in it, the pattern of entanglement changes, and a kind of informational trace remains in the field. It is precisely this trace that we perceive as gravity. This means that gravity may turn out to be not a fundamental force of nature but a secondary phenomenon. And along with it, space itself. What we perceive as geometry, curves and attraction is how quantum information looks "from the outside." Just as the picture on a screen is merely the outward appearance of the software code that draws it, space may be the outward appearance of information written in the quantum field. It curves not because mass presses into it like a ball into stretched fabric, but because the quantum information itself has changed. In previous installments of our series "The Code of Reality," we told how quantum information can build the geometry of space and give birth to matter. The work from Leipzig takes the next step: gravity itself, it seems, is also born from quantum information.
It is important to understand the limits of this result. This is not a final quantum theory of gravity; the main unsolved problem of physics remains unsolved for now. The authors work in the so-called semiclassical approximation: quantum fields are considered against the background of ordinary, non-quantum spacetime. The calculation is performed for a certain class of field states and relies on the Bekenstein–Hawking law as an initial assumption. The physicists themselves speak of their work as a rigorous argument rather than a completed theory, and they plan to extend the approach to a full-fledged quantum gravity. But the direction is already obvious. Perhaps an apple falls not because the Earth attracts it. But because that is how information is distributed in the quantum field from which the Universe is woven.
