Why Infinity Can Exist: Geometry as Invariant, Non-Participatory Structure
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2025
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| _version_ | 1866901145843138560 |
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| author | Doumbouya, Lisa |
| author_facet | Doumbouya, Lisa |
| contents | <p dir="ltr">Infinity appears repeatedly in physical theory, yet consistently fails when treated as a physical quantity. Singularities diverge, infinite energies are forbidden, and infinite densities collapse into boundaries or require renormalization. These outcomes are typically framed as technical problems to be regulated or removed. In this paper, we argue that they instead reflect a category error: infinity has been misassigned to participatory physical systems. We propose that infinity is admissible only within invariant, non-participatory structure—specifically geometry understood as constraint rather than dynamics. Geometry does not evolve, dissipate, or resolve degrees of freedom, and therefore can be infinite without contradiction. Matter, energy, fields, and time, by contrast, necessarily participate in resolution and entropy and must therefore be finite. This distinction clarifies the physical meaning of singularities as boundary conditions rather than infinities, explains why infinities arise in mathematical descriptions but not in observation, and resolves longstanding tensions between mathematical idealization and physical realization while preserving the regime validity of existing physical theories.</p> <p> </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18097945 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Why Infinity Can Exist: Geometry as Invariant, Non-Participatory Structure Doumbouya, Lisa geometry infinity invariant structure participation singularities spacetime geometry regime validity Mathematical physics physics non-participatory structure constraints theoretical physics <p dir="ltr">Infinity appears repeatedly in physical theory, yet consistently fails when treated as a physical quantity. Singularities diverge, infinite energies are forbidden, and infinite densities collapse into boundaries or require renormalization. These outcomes are typically framed as technical problems to be regulated or removed. In this paper, we argue that they instead reflect a category error: infinity has been misassigned to participatory physical systems. We propose that infinity is admissible only within invariant, non-participatory structure—specifically geometry understood as constraint rather than dynamics. Geometry does not evolve, dissipate, or resolve degrees of freedom, and therefore can be infinite without contradiction. Matter, energy, fields, and time, by contrast, necessarily participate in resolution and entropy and must therefore be finite. This distinction clarifies the physical meaning of singularities as boundary conditions rather than infinities, explains why infinities arise in mathematical descriptions but not in observation, and resolves longstanding tensions between mathematical idealization and physical realization while preserving the regime validity of existing physical theories.</p> <p> </p> |
| title | Why Infinity Can Exist: Geometry as Invariant, Non-Participatory Structure |
| topic | geometry infinity invariant structure participation singularities spacetime geometry regime validity Mathematical physics physics non-participatory structure constraints theoretical physics |
| url | https://doi.org/10.5281/zenodo.18097945 |