Bridging Quantum Mechanics and General Relativity: The Emergence of Unified Geometric Dynamics (UGD) Through Torsional Geometry

Abstract

The quest to unify quantum mechanics (QM) and general relativity (GR) remains a central challenge in modern theoretical physics. Despite significant efforts, most unification attempts, including string theory and loop quantum gravity, have introduced mathematical constructs that often lack direct physical observability. Unified Geometric Dynamics (UGD) proposes a novel approach, embedding torsional geometry into spacetime as the missing link between QM and GR. UGD extends Einstein's field equations to include torsion, offering a robust framework to resolve major cosmological puzzles, including dark matter, dark energy, and cosmic inflation. Unlike other theories, UGD is grounded in physically observable phenomena and generates testable predictions that align with contemporary experiments. This article explores UGD's core innovations, mathematical structure, and predictions, showing how it naturally integrates fundamental constants and eliminates the need for hypothetical gravitons. By leveraging the torsional geometry of spacetime, UGD opens new avenues for empirical validation, making it one of the most promising unification frameworks in modern physics.

Introduction: The Need for a New Approach

Since the advent of quantum mechanics and general relativity, physics has faced the challenge of reconciling these two domains into a unified theory. GR successfully describes spacetime and gravity on cosmic scales, while QM governs the probabilistic behavior of particles at microscopic scales. However, the two frameworks are inherently incompatible—general relativity relies on spacetime's smooth, continuous curvature, while quantum mechanics operates on discrete, probabilistic principles.

Several unification attempts—most notably, string theory and loop quantum gravity—have introduced higher-dimensional spaces and abstract mathematical constructs. While elegant, these models remain speculative and lack the direct empirical validation required to bridge quantum and gravitational phenomena.

Unified Geometric Dynamics (UGD) takes a fundamentally different approach by introducing torsion into the fabric of spacetime, a physical mechanism grounded in observable phenomena. UGD extends Einstein's field equations by incorporating torsion, allowing spacetime to twist and interact with quantum fields and energy-momentum distributions. This framework provides a natural connection between the quantum and relativistic realms, offering intuitive and testable predictions that could reshape our understanding of the universe.

The Core Innovations of Unified Geometric Dynamics

At the heart of UGD is the modification of the Einstein field equations to include a torsion tensor, denoted as:

Gμν+Tμνλ=(8πG/c4)Tμν, (Due to the limitations of this platform in displaying special characters and scientific notation, the formulas and mathematical expressions presented here may not be shown exactly as intended. For the correct and complete representation of these formulas, please refer to the official scientific document)

where Gμν is the Einstein tensor describing spacetime curvature, Tμν is the energy-momentum tensor, and Tμνλ represents the torsion tensor, introducing additional degrees of freedom. In contrast to the traditional view where spacetime is solely governed by curvature, UGD suggests that torsion plays a pivotal role at quantum scales, interacting with intrinsic spin and energy densities.

The introduction of torsion is not merely a mathematical convenience; it serves as the physical mechanism for explaining quantum phenomena such as spin and quantization. Torsion couples directly to quantum spin, leading to spin-torsion interactions that manifest naturally in the geometry of spacetime. In this view, quantum phenomena, including superposition and entanglement, are not arbitrary postulates but emerge from the torsional properties of spacetime itself.

Emergent Equations and Testable Predictions

UGD's power lies in its ability to generate testable predictions across various phenomena. Among its most promising predictions are:

Gravitational Atoms and Torsion Waves

UGD predicts the existence of gravitational atoms—quantized gravitational systems formed by torsional effects, analogous to the energy levels of electrons in atomic orbitals. These systems are expected to exist near extreme gravitational environments, such as black holes, where torsion-induced quantization could be detectable. These gravitational atoms could emit torsion waves, introducing subtle corrections to gravitational waveforms. Current and future detectors like LIGO and LISA could observe these signals, providing a potential empirical test of UGD.

Torsion-Modified Gravitational Waveforms

UGD predicts that the torsional contributions to spacetime will introduce oscillatory corrections to gravitational waves. In particular, systems involving rapidly spinning black holes or neutron stars could exhibit gravitational wave signals that deviate from GR's predictions. The next generation of gravitational wave observatories, equipped with higher sensitivity, will be able to detect these deviations, providing a critical test for UGD.

Torsion and Cosmic Structure Formation

Torsion significantly shapes the universe's large-scale structure, influences galaxy formation, and alters galactic rotation curves. UGD offers an alternative to dark matter by attributing anomalous galactic rotation to torsional effects. This provides a testable alternative to dark matter models, with observational data from upcoming astronomical surveys, such as those from the Vera Rubin Observatory, serving as a key validation platform.

Resolving the Hubble Tension

UGD also offers a solution to the Hubble tension, the discrepancy between the local and early universe measurements of cosmic expansion. By introducing torsion into the spacetime fabric, UGD modifies the expansion dynamics, offering a coherent explanation for the varying expansion rates observed in different epochs of the universe. This prediction could be tested with James Webb Space Telescope data, further validating UGD's cosmological implications.

Torsion as a New Explanation for Dark Matter and Dark Energy

One of UGD's most exciting contributions is its potential to resolve dark matter and energy mysteries without invoking exotic particles or fields. In the standard cosmological model, dark matter is posited to explain galactic rotation anomalies, while dark energy accounts for the universe's accelerated expansion. UGD suggests that torsion-induced effects in spacetime geometry can explain both phenomena.

Dark Matter as Torsional Curvature

Rather than invoking unseen matter, UGD attributes the gravitational anomalies observed in galaxies to the additional curvature introduced by torsion. This reimagining of galactic dynamics aligns with observed data and offers a natural explanation for the behavior traditionally ascribed to dark matter.

Dark Energy and Cosmic Expansion

Similarly, UGD modifies the expansion of spacetime by introducing torsion-driven fluctuations in the curvature. These torsional effects can drive the accelerated expansion of the universe without requiring the existence of dark energy as a separate entity. This theory unifies the explanation of cosmic acceleration and inflation under a single geometric framework, providing a simpler and more elegant solution to one of cosmology's greatest mysteries.

Emergence of Fundamental Constants from Spacetime Geometry

UGD offers a groundbreaking reinterpretation of fundamental constants, suggesting that quantities such as the speed of light c, Planck's constant h, and Newton's gravitational constant G emerge directly from the geometric structure of spacetime:

• Speed of Light: The constant c emerges as the maximum propagation speed of torsional waves in spacetime.
• Planck's Constant: UGD derives quantization as a natural result of torsion-spin interactions, with h acting as the fundamental scaling factor for these quantum effects.
• Gravitational Constant: G arises from the interaction between mass-energy and torsion, providing new insights into gravitational strength.

These derivations offer a profound shift in understanding, grounding these constants in the fundamental geometry of the universe.

The End of Gravitons and Exotic Gravity Particles

A significant implication of UGD is that it eliminates the need for hypothetical particles such as gravitons, often invoked in quantum gravity theories, to mediate the gravitational force. In UGD, gravity emerges purely from spacetime geometry, specifically from the interaction between curvature and torsion. This eliminates the need for gravitons, providing a fully geometric description of both quantum and classical gravity.

Conclusion: A New Perspective for Unification

Unified Geometric Dynamics (UGD) introduces torsional geometry, a revolutionary approach to unifying quantum mechanics and general relativity. UGD addresses major unresolved issues in modern physics, including dark matter, dark energy, and cosmic inflation, by offering a physically grounded, testable framework. The theory provides a compelling alternative to abstract unification models and positions itself as a prime candidate for experimental validation in the near future. As observational capabilities continue to improve, UGD could offer the key to unlocking a unified theory of the universe. The following are the new equations that complete Einstein Field Equations and Dirac Equations.

References

1. Ramon (Raymond) Caldas, Unified Geometric Dynamics (UGD) Theory From Quantum Fields to Cosmic Structures. A New Framework for Matter, Energy, and Gravity (2024).
2. Wald, R. M., General Relativity (University of Chicago Press, 1984).
3. Sakurai, J. J., Napolitano, J., Modern Quantum Mechanics (Cambridge University Press, 2021).
4. Peskin, M. E., Schroeder, D. V., An Introduction to Quantum Field Theory (Westview Press, 2018).
5. Burgess, C. P., Moore, G. D., The Standard Model: A Primer (Cambridge University Press, 2007).

The author: Raymond Caldas is an accomplished professional with over 35 years of leadership experience in power generation, power utilities, energy infrastructure, IT, material sciences, applied and quantum physics, and supply chain management, having led operations for a $6B utility company. He also developed a new advanced alloy, MX2669, an advanced energy storage technology named Q-Cell, and a hydrogen on-demand production system named TPN. In Physics, after more than four decades, he recently completed a research titled Unified Geometric Dynamics (UGD) Theory: From Quantum Fields to Cosmic Structures, which introduces a novel theoretical and experimental framework that unifies quantum mechanics and general relativity, offering new insights into dark matter, gravitational waves, and black hole dynamics. Mr. Caldas is dedicated to advancing industry innovation, material sciences, and theoretical physics.