Exploring Quantum Gravity New Mathematical Approaches to Unifying Gravity and Quantum Mechanics
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2025
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| _version_ | 1866901602646884352 |
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| author | Stewart, Chris |
| author_facet | Stewart, Chris |
| contents | <h3><strong>Abstract:</strong></h3> <p>This paper explores <strong>new mathematical approaches</strong> to resolving the long-standing challenge of <strong>unifying general relativity and quantum mechanics</strong>. Traditional formulations of quantum gravity—such as string theory and loop quantum gravity—offer promising but incomplete frameworks. Here, we propose a novel approach that integrates <strong>differential geometry, topological field theory, and modified metric formulations</strong> to bridge the conceptual gap between curved spacetime and quantum uncertainty.</p> <p>We introduce <strong>non-commutative spacetime structures</strong>, explore the impact of quantum fluctuations on metric tensors, and examine the potential role of <strong>higher-dimensional symmetries</strong> in defining a self-consistent theory of quantum gravity. Our derivations include new <strong>gravitational wave modifications</strong>, predictions for <strong>Planck-scale deviations from classical relativity</strong>, and an evaluation of how our approach aligns with existing observational constraints from black hole physics and cosmology.</p> <h3><strong>Key Highlights:</strong></h3> <ul> <li><strong>Mathematical unification framework</strong> combining <strong>general relativity and quantum field theory.</strong></li> <li><strong>New metric formulations</strong> incorporating <strong>quantum fluctuations</strong> and <strong>non-local effects.</strong></li> <li>Predictions for <strong>gravitational wave deviations</strong> at extreme energy scales.</li> <li>Potential applications to <strong>black hole interiors, early-universe cosmology, and quantum vacuum effects.</strong></li> </ul> <p>By reanalyzing the fundamental structure of spacetime and its interaction with quantum fields, this paper provides a theoretical foundation for future <strong>experimental and computational</strong> efforts in quantum gravity research.</p> <p><strong>Keywords:</strong> <em>Quantum gravity, general relativity, gravitational waves, non-commutative geometry, higher-dimensional physics, quantum fluctuations, Planck-scale physics, modified metric tensors, space-time topology, unified field theory.</em></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15032530 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
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| spellingShingle | Exploring Quantum Gravity New Mathematical Approaches to Unifying Gravity and Quantum Mechanics Stewart, Chris Physics Physics Mathematical physics Physics/methods Physics/standards Transport (physics) Quantum physics Physics/education <h3><strong>Abstract:</strong></h3> <p>This paper explores <strong>new mathematical approaches</strong> to resolving the long-standing challenge of <strong>unifying general relativity and quantum mechanics</strong>. Traditional formulations of quantum gravity—such as string theory and loop quantum gravity—offer promising but incomplete frameworks. Here, we propose a novel approach that integrates <strong>differential geometry, topological field theory, and modified metric formulations</strong> to bridge the conceptual gap between curved spacetime and quantum uncertainty.</p> <p>We introduce <strong>non-commutative spacetime structures</strong>, explore the impact of quantum fluctuations on metric tensors, and examine the potential role of <strong>higher-dimensional symmetries</strong> in defining a self-consistent theory of quantum gravity. Our derivations include new <strong>gravitational wave modifications</strong>, predictions for <strong>Planck-scale deviations from classical relativity</strong>, and an evaluation of how our approach aligns with existing observational constraints from black hole physics and cosmology.</p> <h3><strong>Key Highlights:</strong></h3> <ul> <li><strong>Mathematical unification framework</strong> combining <strong>general relativity and quantum field theory.</strong></li> <li><strong>New metric formulations</strong> incorporating <strong>quantum fluctuations</strong> and <strong>non-local effects.</strong></li> <li>Predictions for <strong>gravitational wave deviations</strong> at extreme energy scales.</li> <li>Potential applications to <strong>black hole interiors, early-universe cosmology, and quantum vacuum effects.</strong></li> </ul> <p>By reanalyzing the fundamental structure of spacetime and its interaction with quantum fields, this paper provides a theoretical foundation for future <strong>experimental and computational</strong> efforts in quantum gravity research.</p> <p><strong>Keywords:</strong> <em>Quantum gravity, general relativity, gravitational waves, non-commutative geometry, higher-dimensional physics, quantum fluctuations, Planck-scale physics, modified metric tensors, space-time topology, unified field theory.</em></p> |
| title | Exploring Quantum Gravity New Mathematical Approaches to Unifying Gravity and Quantum Mechanics |
| topic | Physics Physics Mathematical physics Physics/methods Physics/standards Transport (physics) Quantum physics Physics/education |
| url | https://doi.org/10.5281/zenodo.15032530 |