Quantum GS Field and Explanation of Dark Matter

Abstract

Quantum gravity is regarded as a pivotal theoretical objective in unifying general relativity and quantum mechanics. This paper proposes a novel approach within the framework of the Generalized Gauge Equation (GGE), whereby quantum gravitational effects are induced by quantized fields such as the electromagnetic field. Specifically, we demonstrate that under GGE transformations, the quantized electromagnetic field generates a gravitational gauge potential with quantum characteristics, enabling the construction of corresponding quantum Weyl tensors and gravitational soliton solutions. In the weak-field limit, the model naturally reduces to a two-photon-to-graviton conversion process, consistent with linear quantum gravity theories. We further establish nonlinear Gravitational Spinor (GS) equations. It is particularly noteworthy that, via the quantized spinorial Weyl-electromagnetic relation, we have for the first time rigorously derived the nonlinear term in these equations as | ∇ ψ | 2 . This nonlinear term is not only a necessary requirement for theoretical self-consistency but also the key to why the solutions can reproduce dark matter phenomena on galactic scales—the resulting solutions naturally exhibit dark matter-like behavior and align closely with the observational predictions of MOND theory. This finding may reveal a more profound geometric and quantum relational nature of natural gravity. Within the G L ( m ) principal bundle geometry framework, we demonstrate that the four fundamental interactions can be unified at the classical level, with quantization serving as an effective description at microscopic scales. The proposed “gravitational spinor (GS)” acts as the fundamental quantum unit of the vacuum gravitational field, mediating gravitational interactions through virtual particle exchange. Our study indicates that quantum gravity serves as a bridge connecting physical phenomena across different scales, where the classical geometry of general relativity and quantum descriptions coexist consistently across different levels. This research not only provides a new theoretical pathway for exploring quantum gravitational effects but also directly links quantum gravity to galactic dynamics through precise nonlinear extensions, thereby advancing further reflection on the theoretical foundations and research paradigms of quantum gravity.