Quadratic Gravity and Asymptotic Freedom
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The quest for a unified theory of gravity and quantum mechanics has led to renewed interest in quadratic gravity frameworks, where spacetime dynamics are governed by higher-order curvature terms. Within the Fractal Spacetime Dynamics project, this research explores how graviton interactions exhibit asymptotic freedom at high energies, suggesting a self-consistent and predictive theory of quantum gravity.
Theoretical Background: Beyond Einstein Gravity
Classical general relativity successfully describes gravity on large scales but breaks down at quantum energies. Quadratic gravity extends the Einstein-Hilbert action by incorporating curvature-squared terms, enabling renormalizable behavior in the ultraviolet regime.
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Curvature-Squared Contributions
Terms involving squared curvature tensors modify spacetime dynamics at microscopic scales, introducing new degrees of freedom that stabilize quantum behavior.
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Gravitons as Quantum Excitations
In this framework, gravitons emerge as quantum fluctuations of a geometrically rich spacetime, interacting through well-defined high-energy scattering processes.
Analysis I: Asymptotic Freedom in Graviton Collisions
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High-Energy Scattering Behavior
At increasing energies, graviton interaction strengths decrease, indicating asymptotic freedom analogous to non-Abelian gauge theories.
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Ultraviolet Stability of Spacetime
The weakening of gravitational coupling at short distances prevents uncontrolled divergences, allowing spacetime to remain well-defined even at Planck-scale energies.
Analysis II: Fractal Geometry and Quantum Structure
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Scale-Dependent Spacetime Dimensions
Fractal spacetime models predict that effective dimensionality changes with scale, influencing how quantum fields propagate and interact.
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Emergence of Classical Geometry
At macroscopic scales, the fractal structure averages out, recovering smooth spacetime consistent with general relativity.
Discussion: Implications for Unified Physics
Asymptotically free gravity offers a compelling route toward unifying fundamental forces. By reconciling quantum consistency with geometric spacetime, quadratic gravity frameworks may bridge the gap between particle physics and cosmology.
Conclusion: A Predictive Quantum Theory of Gravity
The Fractal Spacetime Dynamics project demonstrates that quadratic gravity can yield a stable, asymptotically free description of graviton interactions. These results suggest that spacetime itself may be the key to unlocking a unified theory of nature.
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