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.
as written by the authors arXiv:2607.05715
Building on the framework developed by Perche [Phys. Rev. D 106, 025018 (2022)], we study two localized nonrelativistic quantum particles propagating along timelike geodesics in a curved spacetime background. Each particle is coupled to a quantum clock that operationally records the time spent in a prescribed spatial region. We compute the covariance of the resulting time observables for separable and entangled two-particle states, comparing flat and curved backgrounds. We then reformulate the protocol as a Bell-like experiment and show that the Bell parameter can acquire a curvature-induced correction. In particular, a protocol calibrated to saturate the classical bound in flat spacetime can be driven above this bound in curved spacetime for entangled states. We focus on two-dimensional curved backgrounds in which the local tidal term induces an effective harmonic potential in the Fermi-frame description. Our results show that spacetime curvature can modify operationally defined quantum correlations and suggest entangled quantum clocks as probes of spacetime curvature.
Quantum entanglement is so strong that changing the state of one particle instantly affects another — even if they are separated by billions of light-years. Einstein called it 'spooky action at a distance'.
In Carl Sagan's novel 'Contact', aliens send humans the blueprints for a machine that uses wormholes — tunnels through curved spacetime. Entangled quantum clocks could become the first step toward detecting such structures.