Cosmic Strings as Knobs: Spacetime Defects Tune Quantum Information in a Relativistic Oscillator

Imagine a flaw in the fabric of the universe so narrow it is essentially a line, yet so massive it bends the geometry around it. Cosmic strings, hypothetical relics predicted by grand unified theories and forged during symmetry-breaking phase transitions in the early universe, are exactly that: one-dimensional topological defects whose conical spacetime leaves a permanent imprint on everything that travels through it. A new theoretical study published in Quantum Information Processing shows that these exotic defects, combined with rotation and electromagnetic fields, can act as genuine control knobs for the information content of a quantum particle. The work, led by Quezia R. D. S. Moreira of the Federal University of Ceará in Brazil together with Abdelmalek Bouzenada, Allan R. P. Moreira, Faizuddin Ahmed, and João B. R. Silva, demonstrates that the geometry of spacetime itself can be used to manipulate quantum uncertainty.

The team’s system of choice is the Dirac oscillator, a relativistic quantum model first formulated by Marcos Moshinsky and Pavel Szczepaniak in 1989. It describes spin-1/2 fermions, such as electrons, through the Dirac equation of 1928, modified by a coupling that makes the equation linear in both momentum and position. In the nonrelativistic limit it reduces to a harmonic oscillator with an additional spin-orbit coupling, and its exact solvability has made it a workhorse of relativistic quantum mechanics. The model has even been realized experimentally, in ion traps, photonic lattices, and microwave systems, which gives the new theoretical results a tangible connection to laboratory physics.

What makes the new study remarkable is the setting. The authors placed their Dirac oscillator in the spacetime of a spinning cosmic string, threading the system with a uniform magnetic field and an Aharonov-Bohm flux. The cosmic string metric is characterized by a deficit angle, determined by the parameter alpha, which is related to the string’s linear mass density. This conical geometry modifies particle motion, wave functions, and energy spectra through purely global constraints, in close analogy with the Aharonov-Bohm effect, where electromagnetic potentials alter quantum phases even in field-free regions. The rotation of the string, encoded in a parameter a proportional to its angular momentum, adds a further layer of nontrivial structure.

Solving the curved-spacetime Dirac equation with all these ingredients is no small feat, but the researchers obtained exact analytical expressions for both the energy spectrum and the wave functions. The key quantity is the effective angular momentum, which combines the ordinary angular quantum number, the Aharonov-Bohm flux, a spin-dependent geometric term, and a contribution from the string’s rotation proportional to the energy. The deficit angle alpha divides this effective momentum, shifting the energy levels and breaking their degeneracy in ways that depend directly on the topology of the background. In the limit where the defect vanishes and spacetime becomes flat, the familiar spectrum of the Dirac oscillator in a magnetic field is recovered, confirming the internal consistency of the calculation.

One subtle point deserves attention. The analysis must be restricted to radial distances larger than the ratio of the rotation parameter to the deficit angle. Inside that boundary, the angular coordinate becomes timelike, and closed trajectories around the string would correspond to closed timelike curves, paths that loop back into a particle’s own past. Such behavior would wreck the causal ordering on which relativistic quantum theory depends, undermining the Hermiticity of the wave operator and the probabilistic interpretation of the wave function. By working in the causally well-behaved exterior region, the authors ensure that their energy spectrum, wave functions, and information measures describe physically admissible states.

With exact solutions in hand, the team turned to the central question: how does all this geometry affect quantum information? Their tool was the Shannon entropy, the measure introduced by Claude Shannon in 1948 to quantify the average information or uncertainty of a probabilistic source. Applied to quantum mechanics, the Shannon entropy can be computed for the probability distribution of a particle’s position and, separately, for its momentum distribution obtained by Fourier transform. The sum of the two entropies obeys a fundamental bound formulated in 1975 by Beckner, Bialynicki-Birula, and Mycielski, which states that the total entropy can never fall below a fixed value determined by the spatial dimension. This entropic uncertainty relation is an information-theoretic strengthening of the familiar Heisenberg principle.

The numerical results reveal a striking pattern of competing effects. Increasing the Aharonov-Bohm flux pushes the probability peak of the ground state away from the origin, reducing positional entropy while raising momentum entropy, meaning the particle becomes easier to locate but harder to pin down in velocity. Increasing the oscillator frequency or the magnetic field does the opposite: the particle is squeezed toward the origin, positional entropy drops, and momentum uncertainty grows. The topological defect parameter alpha behaves differently, increasing both the positional entropy and the total entropy, a signature that the geometric distortion of the string genuinely injects additional quantum complexity into the system rather than merely redistributing it between conjugate variables.

Rotation adds yet another dial. As the rotation parameter a increases, the probability density of the ground state shifts toward larger radial distances while its amplitude grows, and in the entropy tables the positional entropy falls as the momentum entropy rises. The effect becomes more pronounced at higher energy levels, where the wave function develops additional probability peaks and increasingly intricate multi-peak structures. In every configuration examined, the total entropy remained safely above the theoretical lower bound of approximately 2.14473, confirming that the model fully respects the entropic uncertainty principle. The authors also mapped the entropic density, a spatial visualization of where quantum information concentrates, showing white zones of maximal localization that migrate and multiply as the parameters and energy levels change.

The broader significance of the work lies in its reframing of spacetime geometry as a quantum-information resource. Curvature, rotation, magnetic fields, and topological flux all act as tunable parameters that control the balance between spatial confinement and momentum delocalization, and therefore the distribution of information across the quantum state. The authors argue that their framework extends naturally to more refined measures, including entanglement entropy, quantum discord, and Fisher information, the last of which would quantify how precisely parameters such as the rotation rate can be estimated from the quantum state. That points toward quantum metrology in curved spacetime, where the geometry itself becomes part of the measurement apparatus.

Cosmic strings remain hypothetical, but their influence is not confined to speculation. They are actively studied in cosmology for their potential role in structure formation and anisotropies in the cosmic microwave background, and their conical geometry has direct analogues in condensed matter systems such as graphene and other defect-bearing materials, where similar topological structures modify the behavior of quantum particles. Combined with the experimental realizations of the Dirac oscillator in trapped ions and photonic systems, the new results sketch a plausible pathway toward engineered platforms in which topological defects deliberately shape quantum uncertainty. If spacetime topology can be harnessed as a control parameter, the boundary between gravitation and quantum information science becomes a little thinner, and a little stranger, than it was before.

Subject of Research: Shannon entropy of a Dirac oscillator in the spacetime of a spinning cosmic string with magnetic and Aharonov-Bohm fields

Article Title: Testing the influence of information entropy in the case of Dirac oscillator (spin-1/2) interaction with the cosmic string topological defect

Article References: Moreira, Q. R. D. S., Bouzenada, A., Moreira, A. R. P., Ahmed, F., & Silva, J. B. R. (2026). Testing the influence of information entropy in the case of Dirac oscillator (spin-1/2) interaction with the cosmic string topological defect. Quantum Information Processing, 25(11), Article 344. https://doi.org/10.1007/s11128-026-05363-2

Image Credits: AI Generated

DOI: 10.1007/s11128-026-05363-2

Keywords: Dirac oscillator, cosmic string, Shannon entropy, quantum information, topological defect, Aharonov-Bohm effect, curved spacetime, spin-1/2 fermions, entropic uncertainty relation, relativistic quantum mechanics, magnetic field, quantum metrology