Entanglement Through Frame Dragging: Gravity as a Quantum Channel
Context
The question of whether gravity needs to be quantized has remained open since the 1930s, when Leon Rosenfeld first quantized the linearized Einstein equations, but later doubted whether this was necessary. A debate at the 1957 Chapel Hill conference revealed a split: Feynman insisted on a quantum description, while other physicists, including Bondi, were skeptical. The modern approach uses gravity-induced entanglement (GIE) as evidence for the nonclassicality of the gravitational channel. Most proposals are limited to the Newtonian limit, where the phase survives as c→∞ and does not touch genuinely relativistic effects. This work belongs to a line of research extending GIE into the post-Newtonian regime, in particular to the gravitomagnetic sector associated with angular momentum.
Methods
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, while a test particle travels along two arms corresponding to orbital angular momentum +l and −l. In the first approach, they take the Lense-Thirring Hamiltonian, quantize it by promoting angular momenta to 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 with retarded and advanced switching functions, then apply the stationary phase approximation to the field and the particle trajectory.
Results
Both methods give 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 computed earlier for quantum clocks. The path-integral derivation explicitly shows how the retardation of the gravitational signal modifies the phase: it accumulates only along those parts of the trajectory where the source and the particle are in causal contact. In the limit where the source stays switched on long enough, the retarded corrections vanish and the Schrödinger-equation result is recovered.
Implications
The work demonstrates that the correspondence between effective entangling Hamiltonians and local linearized quantum gravity, established earlier 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 signal the nonclassicality of the gravitational interaction. Unlike neighboring works that either stop at the Newtonian limit or consider entanglement via quantum clocks, this one uses atomic interferometry without internal degrees of freedom, which simplifies the analysis and makes the entanglement phase explicit. In addition, the role of retardation is made explicit, which strengthens the conclusion that gravitons exist if the effect is detected.
Future development
The natural next step is a detailed analysis of the experimental conditions under which the entanglement phase becomes measurable in the lab, including realistic parameters for rotating masses and interferometers. It is also important to study how relativistic retardation suppresses or enhances correlations beyond the limiting cases considered. The approach could be extended to other post-Newtonian corrections, for example those associated with quadrupole moments or higher multipoles.
Impact
The results will influence experimental programs testing quantum gravity with tabletop methods, especially in atomic interferometry and optomechanics. They will also sharpen the theoretical arguments in the debate over which observations can provide evidence for the existence of gravitons.
Next steps
It is necessary to calculate the expected phase magnitudes for specific materials and apparatus sizes, and to assess the impact of decoherence and noise. Protocols for tomography of the entangled state should also be developed to test the predictions.
Key open problems
In quantum field theory, the question of whether gravity can be described as a local quantum field theory without contradictions remains unresolved. This work links an observable quantity (the entanglement phase) to fundamental assumptions about locality and the nature of the mediator, which speaks directly to the problem of quantizing gravity. It also touches on the long-standing problem of interpreting quantum mechanics for macroscopic superpositions, since it proposes a concrete experiment where such a superposition leads to measurable consequences.
The frame-dragging effect was first confirmed in 2004 by the Gravity Probe B satellite, which measured the precession of gyroscopes to an accuracy of about 1%. This work proposes using the same effect, but at the quantum level, where the rotating mass is in a superposition of two directions of rotation.
The idea of a superposition of spacetime geometries echoes Greg Egan's novel Quarantine, where quantum states affect the macroscopic structure of reality. Here, however, the focus is on weak fields and laboratory scales, not cosmological consequences.
Key numbers
- Interferometer radius R: on the order of micrometers in the proposed experiments
- Angular momentum of the source J: can reach 10-14 kg·m²/s for microparticles
- Entanglement phase Δ: on the order of 10-6 radians for realistic parameters
- Test particle velocity v: significantly less than the speed of light, v/c << 1