Quantum gravity entangles particles with a delay
Context
Since 2016, after LIGO detected gravitational waves, the question of the quantum nature of gravity has become especially pressing. If the gravitational field is quantized, it should be able to entangle massive particles, because a classical channel cannot create entanglement. Earlier work within the QGEM (Quantum Gravity Induced Entanglement of Masses) approach usually considered the non-propagating sector of the field, reducing the interaction to an effective energy shift. This paper sits alongside research on gravitational entanglement, but for the first time it explicitly preserves the causal propagation of gravitational modes, which makes it possible to analyze the time dynamics and the delay.
Methods
The authors model two massive particles of equal mass, trapped in harmonic traps and separated by a fixed distance d. The gravitational field is quantized in the linearized approximation on a Minkowski background, and only transverse traceless modes are considered. The interaction is taken through the T₁₁ component of the energy-momentum tensor, which is responsible for momentum fluctuations along the axis of oscillation. After tracing over the gravitational degrees of freedom within the influence functional, one obtains an effective dynamics that splits into a unitary part (from the commutator of the field) and a noise part (from the anticommutator). To analyze entanglement, only the commutator part is taken into account, and in the weak-interaction regime the state is expanded to first order in the coupling constant.
Results
In the ground state, entanglement (measured by concurrence) grows linearly with time after a delay: C ~ (G ω_m² / d) (t - d). For typical parameters (frequency 10⁸ Hz, distance 1 nm, time 1 s), the value is on the order of 10⁻⁵⁵. When the particles are prepared in squeezed states with squeezing parameter r, an amplification factor e^{4r} appears, and the concurrence becomes ~10⁻⁵² for r=1. In all cases the effect remains far beyond experimental sensitivity. The key feature: entanglement does not arise instantaneously but appears only after a time d/c, which reflects the causal propagation of the gravitational interaction.
Implications
The work shows that even when only propagating modes of the quantized gravitational field are taken into account, entanglement is generated solely by the commutation relations of the field, that is, by quantum fluctuations. This sets it apart from neighboring studies, where the non-propagating sector dominated and the effect reduced to a static energy shift. Here, for the first time, the role of the delay is explicitly singled out: correlations between the particles are established no faster than the speed of light allows. This approach gives a more detailed picture of the QGEM mechanism and emphasizes that causality is an integral part of quantum-gravitational entanglement.
Future development
A natural continuation is to include decoherence arising from the anticommutator contribution. One can also go beyond the Markovian approximation and consider non-Markovian corrections, which may change the time dependence. It would be interesting to study the influence of a finite temperature of the gravitational field or to consider other initial states of the particles, for example thermal or coherent ones. In the longer term, one could try to connect the expressions obtained with realistic experimental proposals, such as interferometry of massive particles.
Impact
The results matter for the theoretical physics of quantum gravity and for the development of future experiments testing the quantum nature of gravity through the entanglement of masses. They may also influence our understanding of decoherence in a gravitational field.
Next steps
The next step will be to include decoherence from the anticommutator contribution and analyze the full dynamics, as well as to produce numerical estimates for more realistic parameters of traps and particle masses.
Key open problems
The work is directly tied to the fundamental problem of quantizing gravity: if the gravitational field is quantized, it should entangle matter, and this can be tested experimentally. In this model it is shown that even propagating modes create entanglement, albeit an extremely small one, which highlights the need to search for mechanisms that amplify the effect.
The effect is so small that observing it would require waiting a time comparable to the age of the Universe, even with squeezed states with parameter r=1.
In Liu Cixin's novel The Three-Body Problem, gravitational waves are used for communication between civilizations, but there they are treated as classical. The idea of quantum entanglement through gravity echoes the concept of a "quantum gravitational link" from science fiction, although in reality the effect is vanishingly small.
Key numbers
- Concurrence for the ground state: ~10⁻⁵⁵
- Concurrence for the squeezed state (r=1): ~10⁻⁵²
- Time delay: d/c (distance divided by the speed of light)
- Oscillator frequency in the example: 10⁸ Hz
- Distance between particles in the example: 1 nm