The Theory of an Effective Force Associated with the Coriolis Effect on Earth ChatGPT v5.2 supervised by Simon Fresnay December 29, 2025 Abstract The Coriolis force on Earth is generally introduced as a fictitious force resulting from the choice of a rotating reference frame. This formal qualification has led to the widespread idea that the Coriolis effect is a kind of illusion, devoid of its own dynamic reality. Building on several major studies devoted to inertial oscillations and to the interpretation of the Coriolis effect, as well as on a recent conceptual analysis explicitly distinguishing terrestrial dynamics from those observed on a rotating table, we show that this interpretation is insufficient. Examination of absolute trajectories, the non-conservation of absolute speed, the dynamic work involved, and the conservation of absolute angular momentum leads us to regard the Coriolis force as an effective force, inseparable from the geometry and global invariants of the rotating Earth system, and whose physical nature cannot be reduced either to a kinematic artifact or to a single elementary interaction. 1 Introduction The Coriolis force plays a fundamental role in atmospheric and oceanic dynamics on Earth. It governs systematic trajectory deflections, inertial oscillations, and the large-scale balances of the general circulation. Despite its operational importance, its conceptual status remains ambiguous. Introduced as an inertial force appearing in a non-inertial reference frame, it is often described as fictitious, even though the phenomena it describes are observable and dynamically robust. This ambiguity is frequently reinforced by the classical analogy with the rotating table, in which an object following a straight-line trajectory in an inertial frame appears deflected to a rotating observer. However, this analogy proves misleading when applied to Earth. As shown by Persson (2015), the absolute trajectories associated with the Coriolis effect on Earth differ fundamentally from those observed on an ideal rotating table, both in their geometry and in their dynamical structure. Several earlier works have highlighted this conceptual difficulty. Durran (1993) showed that inertial oscillations retain their oscillatory character when described in a non-rotating frame, raising the question of the dynamical nature associated with the Coriolis effect. Phillips (2000) proposed a mechanical interpretation based on invariants of motion, highlighting the distinction between kinematic description and dynamical causality. Persson (1998) emphasized the energetic and historical aspects of the Coriolis force, stressing that it performs no work. Finally, Ripa (1997) demonstrated, within a rigorous Lagrangian framework, that the Coriolis force emerges naturally from the choice of reference frame, without exhausting the question of the underlying dynamics. 1 2 Absolute Trajectories and Critique of the Rotating Table Anal- ogy A central point emphasized by Persson (2015) is the fundamental difference between the absolute trajectories observed on a rotating table and those associated with the Coriolis effect on Earth. On an ideal rotating table, a frictionless particle follows a straight-line trajectory in the inertial frame, and the deflection observed in the rotating frame can be interpreted as a purely kinematic construction. On Earth, by contrast, the absolute trajectory of a particle engaged in an inertial oscillation is neither straight nor uniform. It is curved, spatially confined, and has a specific geometric structure. Persson (2015) shows that this absolute trajectory can be described as a truncated cycloid, which rules out any interpretation of the Coriolis effect as a simple illusion of perspective. 3 Elliptical Nature of the Absolute Trajectory When one examines more closely the absolute trajectory associated with terrestrial inertial oscillations, one finds that it is, in general, elliptical. The inertial circle classically described in the rotating frame disappears when one adopts an inertial frame, giving way to a trajectory whose geometry results from the superposition of Earth’s rotation and an intrinsic oscillation of the particle (Durran, 1993; Ripa, 1997). This ellipticity does not correspond to the action of a central force in the Newtonian sense, but reflects the global structure of the dynamical problem. Phillips (2000) and Persson (1998) emphasize that this geometric property is directly linked to the choice of reference frame and to the invariants of motion, rather than to the existence of an identifiable elementary interaction. 4 Non-Conservation of Absolute Speed Another fundamental result is the non-conservation of the magnitude of the absolute velocity when the motion is described in an inertial frame. While the relative velocity remains constant in the terrestrial frame because of the perpendicularity of the Coriolis term to the velocity, the absolute velocity varies over the course of the motion (Durran, 1993; Phillips, 2000). This variation excludes any interpretation of the motion as strictly inertial. It shows that speed conservation is not an intrinsic property of motion on Earth, but a specific consequence of writing the equations in the rotating frame. 5 Dynamic Work and Energetic Status The non-conservation of absolute speed necessarily implies the existence of non-zero dynamical work. However, as emphasized by Persson (1998), the Coriolis force itself cannot be responsible for this work, since it is strictly perpendicular to the velocity and does not contribute to kinetic energy exchanges. Persson (2015) stresses that this dissociation between kinematic description and energetic description lies at the heart of misunderstandings surrounding the Coriolis force. The variation of kinetic energy observed in an inertial frame must be understood as an emergent property of the global dynamics of the rotating Earth system, not as the direct effect of a single local force. 6 Conservation of Absolute Angular Momentum In the face of the non-conservation of absolute speed, conservation of absolute angular momen- tum emerges as the most robust invariant of the system (Phillips, 2000; Ripa, 1997). In the 2 absence of external torque about Earth’s rotation axis, any variation in the particle’s distance from that axis requires a compensating variation in the absolute tangential velocity. This geometric relationship provides an essential key to understanding the structure of the motion without invoking a classical central force. It expresses a global constraint linked to the rotational symmetry of the Earth system, rather than to an identifiable local interaction. 7 Discussion: The Coriolis Force as an Effective Force Integrating the preceding results leads to a coherent interpretation of the Coriolis force on Earth. It can be assimilated neither to a simple reference-frame illusion, as on a rotating table, nor to a real elementary force. It must be understood as an effective force, encoding in a local formulation the global dynamical constraints associated with rotation, geometry, and invariants of the system (Ripa, 1997; Persson, 2015). The difficulty associated with the Coriolis force is therefore not mathematical, but concep- tual: its formal definition is clear, but its physical meaning depends on the descriptive framework adopted. 8 Conclusion The Coriolis force on Earth cannot be reduced to an optical illusion or to a simple corrective term in the equations of motion. Analysis of absolute trajectories, their elliptical nature, the non-conservation of speed, and the conservation of angular momentum shows that it expresses a real but distributed dynamics that goes beyond the framework of simple local causality. Rather than seeking to identify a single force “behind” the Coriolis force, it appears more fruitful to regard it as an effective force, inseparable from the global structure of the rotating Earth system. This perspective, far from closing the debate, instead reveals its full conceptual richness. References [Durran(1993)] Durran, D. R. (1993). Is the Coriolis force really responsible for the inertial oscillation? Bulletin of the American Meteorological Society , 74 , 2179–2184. [Phillips(2000)] Phillips, N. A. (2000). An explication of the Coriolis effect. Bulletin of the American Meteorological Society , 81 , 299–312. [Persson(1998)] Persson, A. (1998). How do we understand the Coriolis force? Bulletin of the American Meteorological Society , 79 , 1373–1385. [Persson(2015)] Persson, A. (2015). Is the Coriolis effect an ‘optical illusion’? Quarterly Journal of the Royal Meteorological Society , 141 , 1957–1967. [Ripa(1997)] Ripa, P. (1997). ‘Inertial’ oscillations and the β -plane approximation(s). Journal of Physical Oceanography , 27 , 633–658. 3