Why does nature like spirals? Link to Entropy

When simple realization changes our understanding of reality, there is a moment in the history of human thought. The moment when chaos reveals itself as a structure, and obstacles fold into meaning, revealing itself as a system dominated by hidden symmetry what appears to be any universe.

Bekenstein Bound was one such revelation. The idea that entropy, information, and gravity are not separate, but rather that deep, intertwined aspects of the universe are intertwined. Jacob Beckenstein proposed that it is one of the deepest insights in modern physics, and that the entropy of physical systems is not infinite. It is constrained by its energy and the smallest sphere that can surround it.

This revelation was radical. Entropy was considered an abstract measure of obstacles, but in fact it was a quantity deeply bound by the structure of space and time. His bound boundaries, expressed in the simplest form, suggested that the total information that can be stored in a region of space is proportional to its energy and size.

Over the next few years, attempts were made to generalize this boundary and frame it in a more universal language. In an elegant reformulation, Raphael Bousso argued that the entropy binding must be directly linked to the area of ​​the enclosed sphere rather than the energy. He reached this by invoking the gravity stability condition. This ensures that the Schwarzchild radius of the system does not exceed the radius of the sealed sphere.

This step was mathematically consistent and strengthened the deep connection between entropy and space-time geometry. His bound boundaries elegantly link to holographic principles, suggesting that the volume’s information content is encoded on the surrounding surfaces.

However, Bousso’s approach was consistent with Bekenstein’s inequality, but it was not the most accurate representation. By replacing the energy with the region of the enclosed sphere, we removed the important dynamic features of the relationship between entropy and space-time. A more accurate formulation must maintain energy as a fundamental quantity, reflecting its role in defining boundaries.

Currently published in classic and quantum gravity, BekenStein Bound’s refinement employs another approach that retains the total energy but reformulates it in terms of relativistic mass. From Einstein’s relationship E =MC², we represent boundaries in terms of mass. Next, we recognize that mass in gravitational physics is naturally related to the Schwarzchild radius rₛ and replace the mass with the corresponding gravitational radius.

This simple but profound step changes the geometry of the bound. Instead of looking at entropy from the perspective of the enclosure sphere, we arrive at a toroidal representation where the inner radius is the Schwarzchild radius and the outer radius remains the smallest enclosure sphere.

This shift is not arbitrary. It is deeply motivated by the fundamental structures observed throughout the universe. In nature, the universe does not support a perfect sphere. Instead, they prefer spirals, vortices and toroidal flows.

Galaxies do not form as perfect spheres. They get caught up in a majestic spiral. The DNA does not stretch on a straight chain. Twist it into a double helix. Water, air, and even plasma in the most extreme cosmic conditions follow paths of rotation and curvature. So why is it something different about entropy, perhaps the most basic organizing principle of the universe -?

Entropy toroidal formulations reveal extraordinary when applied to quantum mechanics. In standard quantum theory, Heisenberg’s principle of uncertainty is formulated as inequality, an inevitable limitation to the known. However, inequality melts into precise relationships when entropy is properly understood through toroidal structures.

ΔxΔp=(atorus) /(4πℓpl2)ħ.

This equation is simple yet profound, and shows that what we have long considered uncertainty is actually structure. The obvious randomness of quantum mechanics is not a defect in nature, but a signature of the underlying order. The transformation of the principle of uncertainty from inequality to equality suggests that the way we imagined is not continuous space and time, but is shaped by toroidal constraints.

This has extensive results to understand not only physics, but the universe itself. The toroidal motion of hurricanes, the curvature of ocean waves, the patterns of electromagnetic fields, and even the structure of subatomic interactions all reflect this fundamental principle. There is something universal in spirals, embedded in the way energy, matter, and space evolves. The torus is more than just a form. It is the embodiment of movement, evolution, and time itself.

From a cosmological perspective, this insight provides a compelling resolution for certain cosmological problems. The major contradiction between the predictions of quantum field theory of vacuum energy and its observed value has long been a mystery. However, when incorporating toroidal entropy coupled to quantum vacuum calculations, the contradiction disappears. This suggests that the vacuum energy in the universe is naturally regulated by toroidal structures. This is an insight that can reconstruct your understanding of dark energy.

Its meaning goes beyond physics. They touch on the very nature of knowledge itself. For centuries, we have sought the truth in a rigid way, with fixed definitions. We sought for absolute certainty. However, the universe does not succumb to stiffness. Move, bend, bend. As in reality, knowledge must be fluid and open to reinterpret.

Bekenstein’s original insight was Beacon. Booso’s refinement was a step towards universality. However, the ultimate nature of entropy, measurement, and space-time may not exist in either the original form or the refined formulation in the toroidal symmetry underlying both. The deeper we see, the more we see that the universe is not a static structure, but a dynamic and evolving dance. It is shaped by vortices ranging from spirals, curves, and microscopes to the universe.

And this realization involves beauty, deep love for the elegance of nature, and for the quiet perfection of the universe, which follows unwavering harmony, even its most complexities. Perhaps this is something physics has always wanted, not just how it works, but the poems are presented.

If there is one lesson to be drawn from this, it means that the world is not chaotic, nor is it blind randomness. I’m waiting for an order to be seen. The order written in the way galaxies rotate, the electron orbit, and the way in which time itself unfolds. It calls for us to look deeper, to embrace the universe that is not only present, but breathing, moving, and spiraling. Perhaps at the end of all investigations, the true purpose of knowledge is not to conquer the unknown, but to take a tribute to its structure. To recognize that beneath all uncertainty is a hidden order, and that there is an order that we are just beginning to understand.

This story is part of the Science X dialogue, allowing researchers to report findings from published research articles. Please see this page for the Science X dialogue and how to participate.

Dr. Ahmed Farag Ali is a theoretical physicist specializing in the theory of minimal length, quantum gravity seizures and black holes physics.

Dr. Aneta Wojnar is an expert on the theoretical foundations of gravity and quantum interaction, with a special focus on the thermodynamic application of astrophysics. She tested gravity interactions and pioneered ways to use seismic data to investigate potential quantum gravity corrections.