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arXiv:2605.15600

The role of Wigner rotation in estimating the specific angular momentum of a Kerr spacetime

F. J. Lobo, M. Rivera-Tapia, G. Rubilar, A. Delgado

gr-qcquant-phSubmitted May 15, 2026• Announced May 18, 2026

Abstract

We study the rotation of the polarization due to the gravitational field in the Kerr spacetime and the possibility of estimating the specific angular momentum that parameterizes this metric. Our approach is based on a geodesic interferometer, that is, a Mach-Zehnder interferometer whose arms are defined by null geodesics, and a single photon propagating within it. We show that the detection probability at the output ports of the interferometer is a function of two phase differences, one arising from the gravitational time delay and the other from the polarization rotation, both computed under the slow rotation and weak field approximations. Thereby, the interferometric visibility is a signature of two relativistic effects. Using the detection probability, we obtain an estimate for the specific angular momentum and characterize its uncertainty.

Comments: 17 pages, 5 figures

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Abstract In (Zych et al 2011 Nat. Commun. 2 505), the authors predicted that the interferometric visibility is affected by a gravitational field in way that cannot be explained without the general relativistic notion of proper time. In this work, we take a different route and start deriving the same effect using the unitary representation of the local Lorentz transformation in the Newtonian limit. In addition, we show that the effect on the interferometric visibility due to gravity persists in different spacetime geometries. However, the influence is not necessarily due to the notion of proper time. For instance, by constructing a ‘astronomical’ Mach–Zehnder interferometer in the Schwarzschild spacetime, the influence on the interferometric visibility can be due to another general relativistic effect, the geodetic precession. Besides, by using the unitary representation of the local Lorentz transformation, we show that this behavior of the interferometric visibility is general for an arbitrary spacetime, provided that we restrict the motion of the quanton to a two-dimensional spacial plane.

We investigate in a covariant manner the spin-induced non-geodesic motion of massive spin 1/2 particles in an arbitrary gravitational field for trajectories that are initially geodesic when spin is ignored. Using the WKB approximation for the wave function in curved spacetime, we compute the O(hbar) correction to the Wigner rotation of the spin 1/2 particle, whose O(1) contribution is zero on timelike geodesics. We develop conditions for the motion of observers in which the Wigner rotation is null. For the spherically symmetric Schwarzschild metric, we consider specific examples of particle motion in the equatorial plane for (i) circular orbits and (ii) radially infalling trajectories. For the former case we consider the entanglement for a perfectly anti-correlated EPR entangled pair of spins as the separate qubits traverse the circular orbit in same direction.

Complementarity plays a pivotal role in understanding a diverse range of quantum phenomena. Here, we show how the tradeoff between quantities of a complete complementarity relation is modified in an arbitrary spacetime for a particle with an internal spin. This effect stems from local Wigner rotations in the spacetime, which couple the spin to the system's external degrees of freedom. To conduct our study, we utilize two generalized delayed-choice interferometers. Despite differences in complementarity tradeoffs inside the interferometers, the interferometric visibility of both setups coincides in any relativistic regime. Our results extend the finding that general relativity induces a universal decoherence effect on quantum superpositions, as local Wigner rotations, being purely kinematical, preclude any spin dynamics. To illustrate, we analyze the Newtonian limit of our results.

The Hong-Ou-Mandel (HOM) effect is analyzed for photons in a modified Mach-Zehnder setup with two particles experiencing different gravitational potentials, which are later recombined using a beam-splitter. It is found that the HOM effect depends directly on the relativistic time dilation between the arms of the setup. This temporal dilation can be used to estimate the

γ

and

β

parameters of the parameterized post-Newtonian formalism. The uncertainty in the parameters

γ

and

β

are of the order $ 10^{-8}-10^{-12}$, depending on the quantum state employed.