The role of the generalized uncertainty principle

In their ongoing quest to understand the fundamental laws that govern the universe, researchers have ventured into the fields of string theory, loop quantum gravity, and quantum geometry. These advanced theoretical frameworks have revealed a particularly compelling concept: the generalized uncertainty principle (GUP).

This principle fundamentally challenges traditional physics by proposing a minimum measurable length, which could profoundly change our fundamental understanding of space and time. It challenges the foundations of classical mechanics and invites a reevaluation of quantum mechanics and general relativity.

The GUP has catalyzed an impressive range of research efforts, from the microscopic realm of atomic physics to the cosmic scales of astrophysics and cosmology. Research has explored phenomena such as gravitational bar detectors, condensed matter systems, and the dynamics of quantum optics.

Each study contributes to a broader understanding of the potential implications of the GUP, suggesting that it could fundamentally transform our understanding of physics across different scales and systems.

Rethinking Planck’s constant

Building on this knowledge, our research, published in the International Review of Modern Physics Dintroduces a transformative concept: an “effective” Planck constant. This idea challenges the traditional view of the Planck constant as a static, unchanging value, proposing instead that it can vary depending on specific experimental or environmental conditions, in particular the momentum or position of the observed system.

This hypothesis emerges from the GUP, suggesting that Planck’s constant is not simply a universal constant but interacts dynamically with the momentum and position of the physical systems being measured.

This new perspective encourages a rethinking of the fundamental constants of physics, implying that they could be dynamical properties interacting significantly with the physical attributes of systems, such as their mass, size, and quantum state.

A bridge between quantum mechanics and the cosmos

At the heart of our investigation is a simple but profound formula: mrc = ℏ’

This formula demonstrates that by entering the Planck mass and length as mass and radius, respectively, we obtain what we call the “traditional” Planck constant, ℏ. This result highlights a significant and intrinsic connection between fundamental physical constants and the structure of the universe.

When this formula is applied specifically to the electron, the results are particularly illuminating: ℏ’ corresponds to the fine structure constant multiplied by ℏ, which perfectly matches the values ​​established by quantum mechanics. This precise alignment reinforces the robustness of our formula and its relevance to fundamental particle physics.

For particles like pions, kaons and gauge bosons, the calculated ℏ’ remains comparable in magnitude to ℏ, demonstrating the universal applicability of our formula to different scales and particle types.

However, when applied to larger systems, such as chemical elements like helium and oxygen, ℏ’ considerably exceeds ℏ by a few orders of magnitude (10 to 10³), suggesting a scale-dependent variability of the effective Planck constant.

More importantly, when the formula is applied to the entire universe, it yields a value for ℏ’ that offers a potential solution to the cosmological constant problem. This intriguing result suggests a new approach to solving one of the most difficult and persistent problems in theoretical physics. By bridging the observed gaps in vacuum energy densities with empirical observations, the formula provides a reconciled understanding of cosmic phenomena.

Link to Bekenstein’s entropy limit

Furthermore, our research establishes a critical link between the variable Planck constant ℏ’ and the Bekenstein entropy limit, a fundamental principle that limits the amount of information that can be contained in a given physical system.

This connection not only confirms the theoretical validity of the Bekenstein limit, but also significantly improves our understanding of the role of entropy and information at the quantum level at different scales and in different systems. This discovery suggests a deeper and more nuanced understanding of the relationships between information, entropy and the fundamental constants of the universe.

Conclusion

The implications of our findings are both profound and potentially transformative. By bridging quantum mechanics, thermodynamics, and cosmology, our research opens new avenues for a deeper understanding of the universe at its most fundamental level.

This work not only enriches our theoretical knowledge, but also invites the scientific community to reconsider the persistent mysteries of physics, such as the nature of dark matter and the problem of the cosmological constant.

We hope this research will inspire new explorations and lively discussions within the scientific community. By examining the universe through this innovative theoretical lens, we advocate for a more holistic and comprehensive understanding of the fundamental principles that govern everything from the tiniest particles to the vast expanses of space.

This journey into the depths of physical laws is far from over, and we look forward to the new insights and discoveries it will bring.

This article is part of Science X Dialog, where researchers can present the results of their published research papers. Visit this page for information about Science X Dialog and how to participate.

Ahmed Farag Ali is an Assistant Professor of Physics at Essex County College, USA. Jonas Mureika is a Professor of Physics at Loyola Marymount University, USA. Elias C. Vagenas is a Professor of Physics at Kuwait University, Kuwait. Ibrahim Elmashad is an Assistant Professor of Physics at Benha University, Egypt.