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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2506.08165 |
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| _version_ | 1866915335166230528 |
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| author | Hateley, James |
| author_facet | Hateley, James |
| contents | We introduce a two-dimensional temporal framework in which time is represented by a compact manifold $T^2 = (t_1, t_2)$, with $t_1$ encoding classical causal structure and $t_2$ representing quantum coherence. This construction unifies unitary evolution, decoherence, measurement collapse, and gravitational dynamics within a consistent geometric and algebraic formalism. Compactification of the coherence time $t_2$ yields a minimal temporal resolution $Δt_2 \sim \sqrt{α'}$, leading to a discretized spectrum of temporal modes and regularized ultraviolet behavior in quantum field theory and string-theoretic gravity. We formulate an extended Schrödinger equation and generalized Lindblad dynamics on $T^2$, and demonstrate the compatibility of this structure with local gauge symmetry through a complexified BRST quantization procedure. Using para-Hermitian geometry and generalized complex structures, we derive a covariant formulation of temporal T-duality that accommodates both Lorentzian and Euclidean signatures. The $T^2$ framework provides new insights into modular thermodynamics, black hole entropy, and the emergence of classical time from quantum coherence, offering a compact and quantized model of temporal geometry rooted in string theory and quantum gravity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08165 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Compact Temporal Geometry and the $T^2$ Framework for Quantum Gravity Hateley, James High Energy Physics - Theory Mathematical Physics We introduce a two-dimensional temporal framework in which time is represented by a compact manifold $T^2 = (t_1, t_2)$, with $t_1$ encoding classical causal structure and $t_2$ representing quantum coherence. This construction unifies unitary evolution, decoherence, measurement collapse, and gravitational dynamics within a consistent geometric and algebraic formalism. Compactification of the coherence time $t_2$ yields a minimal temporal resolution $Δt_2 \sim \sqrt{α'}$, leading to a discretized spectrum of temporal modes and regularized ultraviolet behavior in quantum field theory and string-theoretic gravity. We formulate an extended Schrödinger equation and generalized Lindblad dynamics on $T^2$, and demonstrate the compatibility of this structure with local gauge symmetry through a complexified BRST quantization procedure. Using para-Hermitian geometry and generalized complex structures, we derive a covariant formulation of temporal T-duality that accommodates both Lorentzian and Euclidean signatures. The $T^2$ framework provides new insights into modular thermodynamics, black hole entropy, and the emergence of classical time from quantum coherence, offering a compact and quantized model of temporal geometry rooted in string theory and quantum gravity. |
| title | Compact Temporal Geometry and the $T^2$ Framework for Quantum Gravity |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2506.08165 |