Two synchronized swimmers dive into the sea. One hits calm water, the other a whirlpool. Their movements, perfectly coordinated at the start, diverge. Something similar happens to two quantum particles when one moves in flat space and the other in curved space. Alexander Friedmann was the first to show that space can expand; now physicists are studying how its curvature affects the subtlest quantum effects.

In the new work, the researchers equipped each particle with imaginary quantum clocks — an internal mechanism that ticks off the time spent in a given region. They calculated how the readings of these clocks correlate (agree) for two particles: independent and entangled (linked by a shared fate even at a distance). It turned out that curvature acts like an invisible spring, compressing or stretching the rhythm of each 'tick'. In a flat world, the correlations obey the classical limit, but in a curved one, for entangled particles, this limit can be surpassed.

The authors proposed turning this effect into an experiment akin to John Bell's test. If in flat space you tune the setup so that it barely reaches the classical boundary, then in curved space the same setup will break through it. Curvature acts as an unaccounted 'player' changing the rules. The calculations were performed for a two-dimensional curved background, where tidal forces create a kind of harmonic trap (as if the particles were swinging on invisible swings). This gives rise to a new idea: use entangled quantum clocks as a sensitive tool for measuring spacetime curvature.

Let's return to our swimmers. The one caught in the whirlpool moves along a twisted trajectory, and his stroke rhythm is disrupted. But now we know: if the swimmers were entangled at the quantum level, the rhythm distortions of one would instantly affect the other. It is this hypersensitive connection that physicists hope to harness to detect the bends of space where they are strongest — for example, near black holes.