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SynchronoGeometry
editSynchronoGeometry is a proposed theoretical framework in differential geometry and the philosophy of time, introduced by independent researcher Saadat Samadi in 2025. The concept integrates localized temporal rhythms into the spatial configuration of manifolds, treating time as an intrinsic and dynamic property of each point in space rather than as an external parameter.
Background
editIn classical geometries such as Euclidean, Riemannian, and pseudo-Riemannian models, time is typically considered a linear and external dimension. General relativity partially incorporates time into spacetime curvature, but assumes globally synchronized time scales. SynchronoGeometry advances this notion by proposing that each point on a manifold possesses its own temporal rhythm, which directly influences its local geometric structure.
Core Definitions
editLet M be a smooth manifold. Define a local time function t(x) for each point x ∈ M. The metric tensor is expressed as a function of both spatial coordinates and localized time:
Geodesic paths in this framework are modulated by temporal variations across the manifold, rather than spatial curvature alone.
Structural Characteristics
edit- Geometric entities such as angles, distances, and curvature exhibit rhythm-based modulations.
- Surface area and volume become time-dependent functions.
- Geodesics may bifurcate or oscillate due to asynchronous time gradients.
Conceptual Examples
edit- A triangle whose vertices experience different time rhythms morphs cyclically.
- A hypersurface pulses periodically due to embedded rhythm fields.
- A manifold’s topology shifts in response to propagating wave-like time pulses.
Applications
editSynchronoGeometry may offer modeling frameworks for:
- Dynamic perception theories and cognitive simulation
- Temporal narrative structures in interactive environments
- Quantum models with localized time variation
Future Research
editFurther work is needed to:
- Formalize curvature equations and topological constraints
- Explore connections to geometric flows and field theories
- Develop visual simulations of temporally fluctuating geometries
References
edit- Samadi, Saadat. SynchronoGeometry: A New Geometric Framework for Local Time Rhythms. ResearchGate, July 2025. DOI: [1](https://doi.org/10.13140/RG.2.2.11938.95686)
- Bakas, I. (2005). [Geometric flows and (some of) their physical applications](https://arxiv.org/abs/hep-th/0511057). arXiv:hep-th/0511057.
- Adom, R. (2025). [Manifestation of Quantum Forces in Spacetime](https://link.springer.com/article/10.1007/s10701-025-00857-y). Foundations of Physics.
- Ahn, J. et al. (2022). [Riemannian geometry theory for nonlinear optical properties](https://www.nature.com/articles/s41567-021-01496-6). Nature Physics.
- Maldacena, J. (2018). [Quantum mechanics and the geometry of spacetime](https://www.icts.res.in/sites/default/files/adscft20-2018-05-22-Juan-Maldacena-Lect1.pdf). IAS Lectures.
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