The emergence of the relativistic Lagrangian from the non-relativistic multiplicative Lagrangian
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913916359016448 |
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| author | Surawuttinack, Kittikun Supanyo, Suppanat Yoo-Kong, Sikarin |
| author_facet | Surawuttinack, Kittikun Supanyo, Suppanat Yoo-Kong, Sikarin |
| contents | The multiplicative Lagrangian and Hamiltonian introduce an additional parameter that, despite its variation, results in identical equations of motion as those derived from the standard Lagrangian. This intriguing property becomes even more striking in the case of a free particle. By manipulating the parameter and integrating out, the statistical average of the multiplicative Lagrangian and Hamiltonian naturally arises. Astonishingly, from this statistical viewpoint, the relativistic Lagrangian and Hamiltonian emerge with remarkable elegance. On the action level, this formalism unveils a deeper connection: the spacetime of Einstein's theory reveals itself from a statistical perspective through the action associated with the multiplicative Lagrangian. This suggests that the multiplicative Lagrangian/Hamiltonian framework offers a profound and beautiful foundation, one that reveals the underlying unity between classical and relativistic descriptions in a way that transcends traditional formulations. In essence, the multiplicative approach introduces a richer and more intricate structure to our understanding of physics, bridging the gap between different theoretical realms through a statistical perspective. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04224 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The emergence of the relativistic Lagrangian from the non-relativistic multiplicative Lagrangian Surawuttinack, Kittikun Supanyo, Suppanat Yoo-Kong, Sikarin General Relativity and Quantum Cosmology Classical Physics The multiplicative Lagrangian and Hamiltonian introduce an additional parameter that, despite its variation, results in identical equations of motion as those derived from the standard Lagrangian. This intriguing property becomes even more striking in the case of a free particle. By manipulating the parameter and integrating out, the statistical average of the multiplicative Lagrangian and Hamiltonian naturally arises. Astonishingly, from this statistical viewpoint, the relativistic Lagrangian and Hamiltonian emerge with remarkable elegance. On the action level, this formalism unveils a deeper connection: the spacetime of Einstein's theory reveals itself from a statistical perspective through the action associated with the multiplicative Lagrangian. This suggests that the multiplicative Lagrangian/Hamiltonian framework offers a profound and beautiful foundation, one that reveals the underlying unity between classical and relativistic descriptions in a way that transcends traditional formulations. In essence, the multiplicative approach introduces a richer and more intricate structure to our understanding of physics, bridging the gap between different theoretical realms through a statistical perspective. |
| title | The emergence of the relativistic Lagrangian from the non-relativistic multiplicative Lagrangian |
| topic | General Relativity and Quantum Cosmology Classical Physics |
| url | https://arxiv.org/abs/2505.04224 |