Gazing into the vastness of the universe, imagine if the secrets to its most complex laws were written not in complicated equations, but in the very shapes and curves of space and time itself. This intriguing premise is at the heart of a groundbreaking study aiming to shed light on the mysteries of how particles behave and how forces act upon them by examining the universe’s geometry. By delving into the geometric nature of the cosmos, the study unveils a novel perspective where the intricate dance of celestial bodies and the subtle interactions of subatomic particles might all follow a common geometric blueprint. This approach opens the door to understanding the universe’s foundational principles through the lens of geometry, suggesting a profound connection between the cosmos’s vast expanses and the minute details of physical phenomena.

Through this innovative work, Professor Güngör Gündüz from Middle East Technical University (Orta Doğu Teknik Üniversitesi) brings to light a perspective where the universe’s laws appear to spring from its geometric makeup. Professor Gündüz explains, “Exploring the deformable spacetime, we’ve seen the dominance of Möbius transformations over traditional Lorentz transformations. This shift offers us a fresh lens to view the fabric of reality, where the motion of surfaces under minimality conditions reveals a helicoidal pattern, akin to a Möbius helicoid, representing the most elementary mass with inherent properties like charge and spin.”

The study published in the peer-reviewed journal, Results in Physics, delves into shapes like helicoids and catenoids, known for their unique geometric features. By transforming these two isometric shapes in specific ways, Gündüz showed that the transformation relations between helicoid and catenoid also reveal the Lorentz factor of relativity without getting involved with the Maxwell equations. The unified properties of helicoid and catenoid create a new shape, so-called Möbius helicoid, brings to light a fascinating geometric foundation for mass formation, charge, and spin,” says Gündüz.

Digging deeper, Professor Gündüz shares, “Our method suggests a model where the basic properties of particles are inherently tied to their geometric structure in spacetime. For instance, the Möbius helicoid serves as a foundational figure for understanding the zitterbewegung behavior of the Dirac electron and the mass-velocity relationship, a cornerstone of special relativity”. De Broglie equation takes a new form in deformable spacetime and the relativistic increase of mass with velocity corresponds to the increase of the windings of the Möbius helicoid as seen in the figure at different β = v/c values.

By taking into consideration the structure of Möbius helicoid a master equation was derived for the dynamical behavior in deformable spacetime. The electromagnetic wave, Schrödinger, Klein–Gordon, Dirac, quantum telegrapher, and quantum torsion equations could be easily obtained from this master equation by making some simplifying assumptions for the parameters involved.

A key finding of the research involves the process through which particles acquire mass. “Our results indicate that the process of mass formation, including the role of the Higgs potential, is closely related to spacetime’s geometric properties,” Gündüz points out. This connection between mass formation and the geometry of spacetime opens new doors to understanding one of the most enigmatic aspects of physics: how mass comes to be.

This study by Gündüz not only questions traditional physics models but also highlights potential avenues for future discoveries. “Our model offers a new way of looking at the connection between deformable spacetime geometry and physics, suggesting the universe’s very essence might be intricately tied to the fundamental forces and particles in ways we’re just starting to comprehend,” Gündüz reflects. This exploration into the geometric foundation of physical laws invites us to rethink the universe’s nature, potentially altering our understanding of both the cosmic and quantum domains.

Through Professor Güngör Gündüz’s work, we are presented with a captivating view of the universe, suggesting that the rules it follows might originate from its geometrical structure induced in deformable spacetime. This perspective could revolutionize our understanding of everything from the smallest particles to the vast cosmos, drawing us closer to unraveling the universe’s deepest mysteries. In conclusion, this pioneering research provides a compelling glimpse into how the fundamental laws of physics might be deeply intertwined with the geometric nature of the universe. By bridging the gap between geometry and physics, Professor Gündüz’s work paves the way for a new understanding of the cosmos, where the intricacies of space and time are not just the backdrop of physical phenomena but the very foundation from which these laws emerge. As we delve deeper into this fascinating interplay between geometry and physics, the universe’s secrets may become increasingly accessible, offering new insights into the grand design of everything around us.


Güngör Gündüz, Physics in deformable spacetime: Physical laws emerging from the surface minimality principle and the masses of particles, Results in Physics, Volume 56, 2024, 106981. DOI: