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arXiv:2602.07622

A gravitationally induced decoherence model for photons in the context of the relational formalism

Max Joseph Fahn, Kristina Giesel, Roman Kemper

gr-qchep-thquant-phSubmitted Feb 7, 2026• Announced Feb 10, 2026• 0 citations
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Abstract

We formulate a model of gravitationally induced decoherence for photons starting from Maxwell theory coupled to linearised gravity, expressed in terms of Ashtekar-Barbero variables and treated as an open quantum field theoretic system. In contrast to quantum mechanical models, the interaction between the system (Maxwell field) and the environment (gravitational field) is not postulated phenomenologically, but is instead dictated by the underlying action in a post-Minkowskian approximation. This framework extends earlier models for a scalar field and enables a more detailed analysis of the role of dynamical reference fields (clocks) within the relational formalism. We show that, for a suitable choice of geometrical clocks together with a U(1)-Gauss clock, and by employing an appropriate combination of the observable map and its dual, the resulting Dirac observables are given directly by the transverse components of the photon field as well as the symmetric-transverse-traceless degrees of freedom of gravitational waves on the linearised phase space of the coupled system. In addition we also compare different choices of Dirac observables and their dynamics. Upon applying a Fock quantisation to the reduced system, we derive the time convolutionless (TCL) master equation, truncated at second order, and analyse its structural properties. These results provide a foundation for further investigations of the decoherence model, including its renormalisation and a detailed study of its one-particle sector, and are found to be structurally consistent with former master equations for photons derived using ADM variables and a specific gauge fixing.

Comments
47 pages + appendix

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We formulate a model of gravitationally induced decoherence for photons starting from Maxwell theory coupled to linearised gravity, expressed in terms of Ashtekar-Barbero variables and treated as an open quantum field theoretic system. In contrast to quantum mechanical models, the interaction between the system (Maxwell field) and the environment (gravitational field) is not postulated phenomenologically, but is instead dictated by the underlying action in a post-Minkowskian approximation. This framework extends earlier models for a scalar field and enables a more detailed analysis of the role of dynamical reference fields (clocks) within the relational formalism. We show that, for a suitable choice of geometrical clocks together with a U(1)-Gauss clock, and by employing an appropriate combination of the observable map and its dual, the resulting Dirac observables are given directly by the transverse components of the photon field as well as the symmetric-transverse-traceless degrees of freedom of gravitational waves on the linearised phase space of the coupled system. In addition we also compare different choices of Dirac observables and their dynamics. Upon applying a Fock quantisation to the reduced system, we derive the time convolutionless (TCL) master equation, truncated at second order, and analyse its structural properties. These results provide a foundation for further investigations of the decoherence model, including its renormalisation and a detailed study of its one-particle sector, and are found to be structurally consistent with former master equations for photons derived using ADM variables and a specific gauge fixing.
Abstract We consider the coupling of a scalar field to linearised gravity and derive a relativistic gravitationally induced decoherence model using Ashtekar variables. The model is formulated at the gauge invariant level using suitable geometrical clocks in the relational formalism, broadening existing gauge invariant formulations of decoherence models. For the construction of the Dirac observables we extend the known observable map by a kind of dual map where the role of clocks and constraints is interchanged. We also discuss a second choice of geometrical clocks existing in the ADM literature. Then we apply a reduced phase space quantisation on Fock space and derive the final master equation choosing a Gibbs state for the gravitational environment and using the projection operator technique. The resulting master equation is not automatically of Lindblad type, a starting point sometimes assumed for phenomenological models, but still involves a residual time dependence at the level of the effective operators in the master equation due to the form of the correlation functions that we express in terms of thermal Wightman functions. Furthermore, we discuss why in the model analysed here the application of a second Markov approximation in order to obtain a set of time independent effective system operators is less straightforward than in some of the quantum mechanical models.
We generalise the quantum mechanical toy model for gravitationally induced decoherence presented in Xu, Blencowe (2022) and Domi et al. (2024). In contrast to earlier formulations, in which the Hamiltonian of the system of interest is linearly coupled to the position operators of the oscillators in the environment, we consider an interaction formulated in terms of Weyl elements of the environment's position operators. This extension is motivated by polymer quantum mechanics, in which Weyl elements are fundamental operators, as well as by the possibility of generating non-linear interactions through suitable truncations of the exponential Weyl elements. Here we focus on a sinus-like coupling that is still quantised using the Schrödinger representation and, in the limit of a small Weyl parameter, reproduces the conventional linear interaction. To derive the corresponding master equation, we developed two complementary methods for the analytical calculation of the environmental correlation functions. The first utilises Wick's theorem for thermal expectation values in conjunction with annihilation and creation operators, while the second is based on the short-time Fourier transform and completely avoids the use of annihilation and creation operators, making it more readily transferable and generalisable to a polymer quantisation. Both approaches yield identical results. We further generalise the spectral density required for the exponential coupling structure. A numerical analysis shows that the environmental correlation functions decay rapidly with time, which supports the validity of the Markov approximation. Using a Taylor expansion in the Weyl parameter, we show that the first-order term reproduces the decoherence model of Xu, Blencowe (2022) and Domi et al. (2024). Finally, we derive the solution to the renormalised master equation.
The gravitational decoherence field studies the suppression of coherence in quantum systems caused by effects rooted in the gravitational interaction. This models are not just important to yield interesting ideas about the search, in regimes others than the Planck scale, for the interplay between quantum mechanics and general relativity, but also from a theoretical point of view. The fact that the gravitational field can not be shielded opens the question of how strong will the gravitational ‘environment’ decohere a quantum system? and if this decoherence can somehow explain the absence of macroscopical super- positions? This thesis studies in depth the ‘Classical Channel Gravity’ (CCG) model, a recent proposal of gravitational decoherence that assumes that the gravitational interac- tion is always accompanied with an intrinsic decoherence mechanism which ensures that there is no transmission of quantum information between the parties involved. This model can be understood a series of weak continuous quantum measurements accompanied with a feedback term produced by some underlying hidden gravitational degrees of freedom. We first study all the possible emergent dynamics from collisional Markovian dynamics; these ones range from exact unitary to arbitrary fast decoherence (Zeno effect). The second part of the thesis is devoted to study the Newtonian and post Newtonian limits of the CCG model, with particular focus on the testability features of CCG. In particular, we apply this model to coupled clocks and find that the amount of decoherence predicted by CCG is the same as the decoherence that an ‘environment of clocks’ will imprint in a single clock in the context of unitary evolution. On the other hand, we find that this effect is far from being detectable with the current achieved time accuracy. However, CCG as a model for multi partite systems and two systems with very different masses seems to yield an amount of decoherence that is not only able to be detectable with current experiments but also seems to indicate that this model is ruled out. Nevertheless, we also mention potential caveats with our assumptions and discuss other physically motivated directions to further study this result. Finally, we also explore the extension of CCG for the cosmological scenario. In this context the scale factor is being decohered by test particles ‘sitting’ on spacetime. We find that this decoherence will be seen by an observer unaware of the CCG fundamental mechanism as an emergent form of dark energy filling the universe.
We investigate the open quantum dynamics of a system of two masses interacting with an environment of linearized gravitational waves. We formulate the analysis in terms of the observable proper distance between the two masses, and show that the canonical variables obtained from the standard Lagrangian, expressed in terms of the Fermi normal coordinates, are not suitable for an effective description of the system. We resolve this issue through a unitary transformation that provides a physically meaningful system--environment decomposition and derive the master equation to leading order in GGG. Its dissipative sector reproduces the classical energy loss due to gravitational-wave emission, while the noisy contributions suppress coherences between states with different mass quadrupole, or effectively, different proper separations. In the regime where the proper distance can be described by considering small quantum fluctuations around an average distance l0l_0l0​, the dynamics reduces to a Caldeira--Leggett-type equation, with a decoherence rate dependent on the baseline length l0l_0l0​.
This thesis investigates the role of gravitational waves in quantum systems, motivated by advances in our understanding of the quantum–gravity interface and efforts to identify experimental signatures of quantum gravity. It focuses on gravitational decoherence and the interplay between internal energy and centre-of-mass dynamics in composite quantum systems, complemented by a study of internal-energy effects in gravitationally mediated entanglement. First, we develop relativistic Hamiltonian formulations showing that changes in a composite system’s internal energy increase its gravitational mass rather than alter its momentum. This removes earlier ad hoc arguments for eliminating “anomalous friction forces”. We show that gravitational waves act as a dynamical background, inducing curvature-dependent forces that modify total momentum. Second, we revisit a thought experiment in which tensions between causality and complementarity arise. We identify a scenario in which these tensions follow from energy–mass equivalence, making the effect specific to gravitational interactions. In a gravitationally mediated entanglement experiment using Newtonian gravity as mediator, we investigate whether decohering gravitational radiation can resolve the apparent conflict. Finally, we build upon a model of gravitational decoherence consistent with general relativity. This requires deriving a higher-derivative quantum Langevin equation and master equation. The resulting dynamics show that gravitational interactions induce decoherence in the canonical momentum basis of the quadrupole and generate acceleration- and jerk-dependent corrections absent in electrodynamics. Together, these results show that weak-field gravitational interactions leave distinct relativistic imprints on quantum systems, including effects unique to gravitational waves, providing potential signatures that distinguish gravity from other interactions.
We formulate the gravitationally induced quantum decoherence of a massive object prepared in a spatial superposition. Starting from linearized gravity coupled to a massive system particle and an environmental scalar field, we derive a closed-time-path influence functional governing the reduced system dynamics. In the nonrelativistic and quasi-static regime, the decoherence exponent can be written as a bilinear functional of the difference of the system stress-energy tensors and an effective noise kernel obtained by dressing the environmental stress-energy tensor correlator with graviton propagators. We then apply this framework to the Newtonian long-range gravitational interaction and evaluate the resulting decoherence function for a dilute nonrelativistic gas modeled by finite wave packets and coarse-grained in time and space. By performing controlled approximations, we obtain analytic expressions for the cumulative decoherence function and show that the dominant contribution is accumulated logarithmically over a broad range of distances, while remaining subdominant to conventional collisional decoherence under realistic conditions.