Recovering Einstein Mature View of Gravitation: A Dynamical Reconstruction Grounded in the Equivalence Principle
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arXiv
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| Format: | Preprint |
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2026
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| author | de Haro, Jaume Elizalde, Emilio |
| author_facet | de Haro, Jaume Elizalde, Emilio |
| contents | The historical and conceptual foundations of General Relativity are revisited, putting the main focus on the physical meaning of the invariant ds, the Equivalence Principle, and the precise interpretation of spacetime geometry. It is argued that Albert Einstein initially sought a dynamical formulation in which ds encoded the gravitational effects, without invoking curvature as a physical entity. The now more familiar geometrical interpretation (identifying gravitation with spacetime curvature) gradually emerged through his collaboration with Marcel Grossmann and the adoption of the Ricci tensor in 1915. Anyhow, in his 1920 Leiden lecture, Einstein explicitly reinterpreted spacetime geometry as the state of a physical medium (an ether endowed with metrical properties but devoid of mechanical substance) thereby actually rejecting geometry as an independent ontological reality.
Building upon this mature view, gravitation is reconstructed from the Weak Equivalence Principle, understood as the exact compensation between inertial and gravitational forces acting on a body under a uniform gravitational field. From this fundamental principle, together with an extension of Fermat Principle to massive objects, the invariant ds is obtained, first in the static case, where the gravitational potential modifies the flow of proper time. Then, by applying the Lorentz transformation to this static invariant, its general form is derived for the case of matter in motion. The resulting invariant reproduces the relativistic form of Newton second law in proper time and coincides with the weak field limit of General Relativity in the harmonic gauge. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16246 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Recovering Einstein Mature View of Gravitation: A Dynamical Reconstruction Grounded in the Equivalence Principle de Haro, Jaume Elizalde, Emilio History and Philosophy of Physics General Relativity and Quantum Cosmology The historical and conceptual foundations of General Relativity are revisited, putting the main focus on the physical meaning of the invariant ds, the Equivalence Principle, and the precise interpretation of spacetime geometry. It is argued that Albert Einstein initially sought a dynamical formulation in which ds encoded the gravitational effects, without invoking curvature as a physical entity. The now more familiar geometrical interpretation (identifying gravitation with spacetime curvature) gradually emerged through his collaboration with Marcel Grossmann and the adoption of the Ricci tensor in 1915. Anyhow, in his 1920 Leiden lecture, Einstein explicitly reinterpreted spacetime geometry as the state of a physical medium (an ether endowed with metrical properties but devoid of mechanical substance) thereby actually rejecting geometry as an independent ontological reality. Building upon this mature view, gravitation is reconstructed from the Weak Equivalence Principle, understood as the exact compensation between inertial and gravitational forces acting on a body under a uniform gravitational field. From this fundamental principle, together with an extension of Fermat Principle to massive objects, the invariant ds is obtained, first in the static case, where the gravitational potential modifies the flow of proper time. Then, by applying the Lorentz transformation to this static invariant, its general form is derived for the case of matter in motion. The resulting invariant reproduces the relativistic form of Newton second law in proper time and coincides with the weak field limit of General Relativity in the harmonic gauge. |
| title | Recovering Einstein Mature View of Gravitation: A Dynamical Reconstruction Grounded in the Equivalence Principle |
| topic | History and Philosophy of Physics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2601.16246 |