Gravity as a Quantum Channel: Entanglement Through Frame Dragging

Two spinning tops whirl in an invisible dance, tied together by a thread of spacetime. One of them, massive and rotating, is in a superposition of two opposite directions of rotation. The second, a light test particle, moves in a circle around the first. Their motions intertwine, generating quantum entanglement through the gravitational field. This is not fantasy but an exact calculation showing how the frame-dragging effect (a rotating mass twists spacetime around itself) can link quantum states.

Since the 1930s, physicists have debated whether gravity needs to be quantized. In 1957, at a conference in Chapel Hill, Feynman insisted on a quantum description, while others were skeptical. Today a criterion has been proposed: if a gravitational interaction creates entanglement between two massive bodies, then it cannot be a classical channel. Most proposals are limited to the Newtonian limit, where effects of the finite speed of light do not appear. The new work goes beyond this limit by considering the gravitomagnetic sector associated with angular momentum.

The authors consider an interferometric setup: a massive rotating source at the center of a circular interferometer is in a superposition of two opposite orientations of angular momentum, and a test particle moves along two arms corresponding to orbital angular momentum +l and −l. In the first approach, they take the Lense-Thirring Hamiltonian, quantize it by turning angular momenta into operators, and solve the Schrödinger equation in the limit of large angular momentum quantum numbers. In the second approach, they use a path integral in linearized quantum gravity: they compute the on-shell action taking into account retarded and advanced switching functions, and then apply the stationary phase approximation to the field and the particle trajectory. Both methods yield the same entanglement phase: Δ = 4πGJm₀/(ℏRc²), where J is the angular momentum of the source, m₀ is the mass of the test particle, and R is the radius of the interferometer. This phase matches the proper time difference between the arms, calculated earlier for quantum clocks.

The work demonstrates that the correspondence between effective entangling Hamiltonians and local linearized quantum gravity, previously established for the Newtonian case, also holds for the post-Newtonian gravitomagnetic interaction. This means that observing such entanglement under standard assumptions about locality and the mediator would indicate the nonclassicality of the gravitational interaction. Unlike neighboring works, which either restrict themselves to the Newtonian limit or consider entanglement via quantum clocks, here atomic interferometry without internal degrees of freedom is used, which simplifies the analysis and makes the entanglement phase explicit. Furthermore, the role of retardation is explicitly shown, which strengthens the conclusion about the existence of gravitons if the effect is detected. A natural next step is a detailed analysis of experimental conditions under which the entanglement phase becomes measurable in the laboratory, including realistic parameters of rotating masses and interferometers. It is also important to investigate how relativistic retardation suppresses or enhances correlations beyond the considered limiting cases. The approach could be extended to other post-Newtonian corrections, for example, those related to quadrupole moments or higher multipoles. The results will influence experimental programs aimed at testing quantum gravity with tabletop methods, especially in the fields of atomic interferometry and optomechanics. They will also sharpen the theoretical arguments in the debate over which observations could indicate the existence of gravitons.