The Action Space of the Scalar Temporal Field Ontology: Axioms, Equivalent Lagrangians, and Model Variants
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| Format: | Recurso digital |
| Language: | English |
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2025
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| _version_ | 1866901568578650112 |
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| author | Howe, Cale Scott |
| author_facet | Howe, Cale Scott |
| contents | <p>We formulate the Scalar Temporal Field Ontology (STFO) as a covariant field theory of a scalar time field τ(x^μ) coupled to gravity and matter. Starting from explicit axioms—time as a dynamical scalar, a normalized temporal congruence, variational dynamics with second-order equations of motion, and no additional fundamental fields beyond (g_{μν}, τ)—we construct a minimal reference action and characterize its action space: the family of Lagrangians compatible with these axioms.</p> <p>We show how different formulations involving the kinetic scalar X, the unit temporal vector n_μ, the expansion scalar Ω, and the deformation tensor C_{μν} are equivalent under field redefinitions and constraints. We then identify physically distinct model branches via generalized kinetic structure, higher-order temporal elasticity, and disformal matter couplings.</p> <p>This paper formally anchors the Lagrangian foundation of the Scalar Temporal Field Ontology and provides the reference action used by related black hole, cosmological, and thermodynamic STFO applications.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17862237 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Action Space of the Scalar Temporal Field Ontology: Axioms, Equivalent Lagrangians, and Model Variants Howe, Cale Scott Scalar Temporal Field Ontology STFO time as a scalar field modified gravity generalized scalar–tensor Einstein–æther k-essence disformal metric black holes cosmology Lagrangian field theory <p>We formulate the Scalar Temporal Field Ontology (STFO) as a covariant field theory of a scalar time field τ(x^μ) coupled to gravity and matter. Starting from explicit axioms—time as a dynamical scalar, a normalized temporal congruence, variational dynamics with second-order equations of motion, and no additional fundamental fields beyond (g_{μν}, τ)—we construct a minimal reference action and characterize its action space: the family of Lagrangians compatible with these axioms.</p> <p>We show how different formulations involving the kinetic scalar X, the unit temporal vector n_μ, the expansion scalar Ω, and the deformation tensor C_{μν} are equivalent under field redefinitions and constraints. We then identify physically distinct model branches via generalized kinetic structure, higher-order temporal elasticity, and disformal matter couplings.</p> <p>This paper formally anchors the Lagrangian foundation of the Scalar Temporal Field Ontology and provides the reference action used by related black hole, cosmological, and thermodynamic STFO applications.</p> |
| title | The Action Space of the Scalar Temporal Field Ontology: Axioms, Equivalent Lagrangians, and Model Variants |
| topic | Scalar Temporal Field Ontology STFO time as a scalar field modified gravity generalized scalar–tensor Einstein–æther k-essence disformal metric black holes cosmology Lagrangian field theory |
| url | https://doi.org/10.5281/zenodo.17862237 |