Torsion Alters Mechanics Beyond Spin, Research Confirms

Researchers are investigating the impact of spatial torsion on quantum fluctuations within the framework of Metric-Affine Gravity (MAG) and employing the Stochastic Variational Method (SVM). Tomoi Koide from the Instituto de Física, Universidade Federal do Rio de Janeiro, and Armin van de Venn from the Frankfurt Institute for Advanced Studies (FIAS), working with colleagues at the Physics Department, Goethe University, demonstrate how torsion induces non-linearity in mechanics, extending beyond its traditionally understood influence on spin. This collaborative work reveals that torsion can affect spinless degrees of freedom via fluctuations and explores the interplay between Levi-Civita curvature and torsion within the Schrödinger equation, building upon previous findings. By establishing a structural parallelism between SVM and geometry, this research offers new avenues for exploring gravity with non-metricity and promises to contribute to solutions for outstanding cosmological challenges.

Their work suggests that twisting space, torsion, has a wider influence on quantum behaviour than previously understood, potentially offering fresh insight into some of cosmology’s most enduring puzzles. This combination reveals that torsion can influence even spinless particles through their quantum fluctuations, inducing non-linearity in mechanics where it was previously thought impossible.

For decades, torsion was considered relevant only to fermions, particles possessing intrinsic angular momentum, but this research demonstrates a broader impact on quantum behaviour. Understanding the fundamental forces remains a significant challenge for physicists. While the strong, weak, and electromagnetic forces are successfully described by quantum mechanics, gravity continues to resist complete quantization.

This study offers a potential pathway toward a more complete theory, addressing puzzles like dark energy and dark matter by exploring a richer geometric framework than standard general relativity. MAG introduces both torsion and non-metricity, properties absent in the simpler Riemannian geometry upon which Einstein’s theory is built. Torsion describes the twisting of spacetime, while non-metricity relates to changes in vector length during parallel transport.

SVM provides a means of quantizing systems while explicitly accounting for geometrical influences, sidestepping limitations inherent in traditional canonical quantization methods. Canonical quantization, while effective in flat spacetime, struggles with complex geometries and coordinate systems where the position operator’s spectrum is bounded. Instead, SVM treats quantum fluctuations as a stochastic process, offering a more adaptable approach to quantization in dynamic spacetimes.

By applying SVM within the MAG framework, researchers have uncovered a structural parallelism between stochastic processes and the geometry of statistical manifolds. Specifically, the research investigates the interplay between the Levi-Civita curvature, the standard curvature of spacetime, and torsion within the non-linearity of the Schrödinger equation, extending beyond previous findings.

This suggests that torsion’s influence isn’t merely additive but interacts with existing gravitational effects in a complex manner. These insights not only deepen our understanding of gravity but also open avenues for exploring extensions to theories incorporating non-metricity, potentially resolving long-standing cosmological problems.

Torsion and non-metricity characterise quantum fluctuations in generalised spacetime geometry

Metric-Affine Gravity (MAG) serves as the foundational framework for this work, a geometrical theory extending beyond standard general relativity by allowing both torsion and non-metricity to define spacetime curvature. Unlike Riemannian geometry, where the connection is solely determined by the metric, MAG treats the metric and affine connection as independent entities, fundamentally altering how gravity is understood.

This independence introduces torsion, representing the anti-symmetric component of the connection and describing the failure of parallel transport to commute, and non-metricity, indicating a change in vector length during parallel transport. SVM is a technique that allows for the quantization of systems by incorporating geometrical effects, proving particularly useful when dealing with stochastic processes. The core of the SVM approach involves transforming the time-dependent Schrödinger equation into a diffusion equation, effectively representing quantum evolution as a stochastic process.

This transformation necessitates splitting the time derivative, a step that mirrors the concept of dual connections found in statistical manifolds, revealing a structural parallelism between SVM and information geometry. The methodology extended beyond simply applying SVM to MAG; it involved a detailed examination of how torsion specifically influences quantum fluctuations.

By integrating these two frameworks, the research demonstrated that torsion induces non-linearity in quantum mechanics, a surprising result given its traditional association only with spin degrees of freedom. Instead, torsion can also affect spinless particles through these fluctuations, opening new avenues for understanding fundamental interactions.

The study went beyond previous analyses by investigating the interplay between the Levi-Civita curvature and torsion within the Schrödinger equation’s non-linear terms. This approach, combined with the power of SVM, allowed for a deeper exploration of the potential role of torsion in resolving long-standing cosmological problems and refining our understanding of gravity itself.

Torsion’s influence on quantum fluctuations and non-linear Schrödinger equation dynamics

Torsion induces non-linearity in mechanics, altering the behaviour of both spin and spinless particles. Researchers demonstrate that torsion, traditionally considered to affect only particles with spin, can also influence spinless degrees of freedom through quantum fluctuations, challenging the long-held view of torsion’s limited interaction scope within spacetime.

Extending previous analyses, the study investigates the interplay between the Levi-Civita curvature and torsion within the non-linearity of the Schrödinger equation. The core of this research lies in the quantification of how torsion impacts quantum fluctuations. The research highlights a structural parallelism between SVM and information geometry, where the splitting of time derivatives in stochastic processes mirrors the dual connections found in statistical manifolds.

The study establishes that torsion affects the quantum fluctuations governing particle motion, even for spinless particles lacking classical interaction with torsion. This is achieved through the application of SVM, a quantization method designed to incorporate geometrical effects. Inside this framework, researchers were able to demonstrate that torsion’s influence extends beyond fermions, impacting all particles at the quantum scale.

The analysis of the Schrödinger equation reveals a competitive relationship between Levi-Civita curvature and torsion, influencing the equation’s non-linear characteristics. Since the method successfully quantizes systems with non-trivial topologies, it offers a potential pathway for extending gravity theories to include non-metricity. The correspondence between stochastic processes and geometry is a key result, providing a new lens through which to view the relationship between quantum mechanics and geometry. These insights are expected to deepen our understanding of unresolved cosmological problems and pave the way for future extensions to gravity theories.

Torsion as a fundamental spacetime property and its implications for cosmology

For decades, physicists have sought a way to reconcile general relativity with quantum mechanics, a task hampered by the geometrical description of gravity itself. This is a departure from standard models where torsion is considered a secondary effect, and it opens up possibilities for understanding phenomena currently attributed to dark energy or modified gravity. By framing stochastic processes as manifestations of underlying geometrical structures, researchers reveal a structural equivalence that could provide new avenues for quantizing gravity, a long-sought goal.

Understanding how torsion affects fluctuations could refine cosmological models, potentially resolving discrepancies between predicted and observed expansion rates. Beyond cosmology, these insights might also inform our understanding of the very early universe, where quantum effects and strong gravitational fields were dominant. However, direct experimental verification remains a significant hurdle, requiring extremely precise measurements of spacetime curvature and torsion. Once new observational data becomes available, the interplay between Levi-Civita curvature and torsion will be better understood, and future research may explore the inclusion of non-metricity, further expanding the geometrical landscape of gravity.