Geometric Origin of Quantization on an Adiabatically Evolving Manifold

For most of the twentieth century, physics has operated as if the universe were a stage that never changes. In this view, the laws of nature are fixed, and the space in which matter moves is a rigid, unchanging grid. This assumption allowed scientists to build two incredibly successful, yet separate, theories. One theory, quantum mechanics, explains the behavior of the very small, such as atoms and electrons, predicting that energy comes in discrete, indivisible packets. The other, general relativity, explains gravity and the motion of planets and stars across the vast cosmos. While both theories work perfectly within their own domains, they rest on different foundations. Quantum mechanics relies on a mysterious number called the Planck constant, which sets the scale for these tiny energy packets, but the theory offers no explanation for where this number comes from or why it has the value it does. It is simply accepted as a fundamental rule of the universe. Meanwhile, astronomers have long known that the universe is not static; it is expanding, and that expansion is accelerating. This means the stage itself is stretching and changing, yet the standard equations of physics were written as if the stage were frozen in time.

A researcher at the University of Sonora, Anton Lipovka, has proposed a new way to look at this disconnect. He suggests that the strange rules of the quantum world are not separate from the expanding universe but are actually a direct result of it. His work, titled "Geometric Origin of Quantization on an Adiabatically Evolving Manifold," attempts to unify the behavior of light, the motion of charged particles, and the expansion of space into a single, continuous story. Instead of treating the Planck constant as a random, unexplained number, Lipovka argues that it is a measurable consequence of the universe's slow, steady growth. By treating space not as a fixed grid but as a shape that changes over time, he shows how the discrete energy levels found in atoms emerge naturally from the geometry of the cosmos itself.

The core of this idea rests on a simple observation: light traveling through an expanding universe loses energy. This loss of energy is what astronomers see as the redshift of distant galaxies. Lipovka takes this fact and asks what happens to the electromagnetic field, the invisible structure that carries light, when the space it travels through is constantly stretching. In a static universe, the energy of a light wave would be perfectly conserved. But in an expanding universe, the field is forced to adapt to the changing geometry. Lipovka demonstrates that this adaptation creates a specific, nearly unchanging quantity known as an adiabatic invariant. In physics, an invariant is a value that remains constant even as other things change around it. In this case, the invariant has the physical dimensions of action, a quantity that combines energy and time.

What makes this finding remarkable is the value of this invariant. When Lipovka calculates it using only observable data about the universe—specifically the rate at which the universe is expanding and the rate at which that expansion is accelerating—he arrives at a number that matches the Planck constant to within about one percent. This suggests that the Planck constant is not a fundamental, unchangeable rule of nature, but rather a local measurement of how fast the universe is evolving right now. If the universe were not expanding, this number would be zero, and the quantum world as we know it would disappear, leaving only the smooth, continuous laws of classical physics.

To test this idea, Lipovka developed a new set of equations called Complete Electrodynamics. These equations describe how charged particles and electromagnetic fields interact when the space they inhabit is changing. Unlike standard theories that assume a fixed background, these equations treat the geometry of space as a dynamic participant in the drama. The theory uses a type of geometry called Finsler geometry, which allows the rules of space to depend not just on where you are, but also on how fast you are moving. This might sound abstract, but it is a necessary step to describe a universe where the very fabric of space is stretching.

When Lipovka applies these equations to a hydrogen atom, the results are striking. In standard quantum mechanics, the electron can only exist at specific energy levels, a fact that is usually imposed as a rule. In Lipovka's framework, these specific levels appear automatically. The electron and the electromagnetic field it creates must form a stable, repeating pattern to survive in a changing universe. If the pattern does not fit perfectly with the geometry of the expanding space, the system becomes unstable and cannot exist. The only solutions that survive are those where the electron's orbit matches a specific condition, leading directly to the discrete energy levels observed in experiments. The famous spectrum of the hydrogen atom, which has been a cornerstone of quantum physics for a century, emerges here not as a mystery, but as a natural consequence of the universe's expansion.

This approach also offers a new perspective on other puzzling phenomena, such as the Aharonov-Bohm effect. In this effect, a charged particle is influenced by a magnetic field even when it travels through a region where the magnetic field is zero. Standard physics explains this by invoking "potentials," mathematical constructs that seem to have physical effects without a visible source. Lipovka's theory suggests that this effect arises because the particle is moving through a space that is subtly different at the start of its journey than at the end, due to the expansion of the universe. The changing geometry creates a kind of anisotropy, or directional difference, that guides the particle, removing the need for mysterious, invisible potentials.

The paper does not claim to have solved every problem in physics, nor does it dismiss the success of existing theories. Instead, it proposes that quantum mechanics and general relativity are two sides of the same coin, both arising from the interaction between matter and an evolving spacetime. The theory satisfies the correspondence principle, meaning that if the universe were to stop expanding, the new equations would smoothly turn back into the familiar laws of classical electrodynamics. This ensures that the theory remains consistent with everything we already know, while offering a deeper explanation for the quantum world.

Lipovka's work suggests that the separation between the very small and the very large is an illusion created by our assumption of a static universe. The Planck constant, the discrete steps of energy, and the strange behavior of particles are all linked to the slow, adiabatic stretching of the cosmos. By calculating this connection using real astronomical data, the study bridges the gap between the laboratory and the edge of the observable universe. It proposes that the quantum nature of reality is not a fundamental axiom, but a geometric feature of a universe that is constantly in motion. While further work is needed to fully explore the implications and test the theory against more complex systems, the results offer a compelling vision of a unified physics where the expansion of the stars and the dance of the atoms are driven by the same underlying geometry.