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February 26, 20260 citationsOpen Access

Quantum Geometric Algebra: A Theory of Emergent Spacetime and Matter based on Quantum Relational Networks

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TZTao Zhou

Key Points

  • The objective is to propose a theoretical framework that models spacetime and matter as emergent phenomena from quantum relationships.
  • Developed a framework called Quantum Geometric Algebra.
  • Utilized non-commutative geometry and category theory.
  • Constructed a mathematical model known as the Dynamic Quantum Spectral Triple.
  • Unified interpretations of gravity, quantum measurement, and black hole thermodynamics.
  • Resolved the cosmological constant problem.
  • Predicted observable quantum geometric imprints in the early universe.

Abstract

This paper proposes a novel theoretical framework termed "Quantum Geometric Algebra," which models the fundamental reality of the universe as a dynamic "quantum relational network," wherein both spacetime geometry and matter fields emerge as low-energy phenomena. This "relational ontology" paradigm aims to fundamentally resolve the deep incompatibility between general relativity and quantum mechanics, as well as the cosmological constant problem. By employing non-commutative geometry and category theory, we construct a rigorous mathematical model of this network—the Dynamic Quantum Spectral Triple—and elucidate how classical continuous spacetime and its physical laws derive from discrete quantum correlations. Under this framework, phenomena such as gravity, quantum measurement, and black hole thermodynamics receive unified and natural reinterpretations. The theory not only intrinsically resolves the cosmological constant problem but also predicts observable quantum geometric imprints in the early universe and the potential evolution of the dark energy equation of state, thereby paving the way for a background-independent, inherently unified theory of quantum gravity.

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Cite This Study

Tao Zhou (2026) studied this question.

synapsesocial.com/papers/699f95a81bc9fecf3dab3a71https://doi.org/10.5281/zenodo.18752134
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