An orchestra plays out of tune, and the sound seems like chaos. But if you record all the notes and analyze them mathematically, you can reconstruct the shape of the concert hall — where the walls are, how high the ceiling is. Roughly in this way, physicists propose to derive gravity from quantum theory.

In everyday life, space and time are the stage on which events unfold. But in the microcosm, the stage itself becomes shaky. It turns out that the equations of curved spacetime can be rewritten in the language of operators — mathematical "tools" that describe the creation and destruction of particles. The authors of the new work took the algebra of such operators and let the gravitational constant tend to zero. From this algebra, the metric, a way to measure distances in a curved world, naturally emerges. And the full Einstein equations, not their simplified version.

Earlier, Ted Jacobson performed a similar trick, but he relied on the connection between the area of a black hole horizon and its entropy — a measure of disorder. The new work does without this assumption. Instead, a more general principle is used: in the weak-gravity limit, the operator algebra becomes of a special type — the so-called type III. If you add a "modular Hamiltonian" (an operator describing time evolution from the perspective of a local observer), you get a type I algebra. Such an algebra already has minimal "building blocks"—projectors onto microstates, the very quantum cells that make up space.

For an eternal black hole, the size of this algebra exactly matches the Bekenstein–Hawking entropy plus universal logarithmic corrections. The authors also propose using the "complexity" of operators on the boundary of space as an indicator: when it becomes too large, the semiclassical description inside the volume stops working. Thus, quantum theory itself suggests where familiar physics ends and something deeper begins. In the finale, we return to the orchestra: its notes are quantum fields, and the hall is spacetime itself, whose shape we are learning to read.