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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2507.08815 |
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| _version_ | 1866913938807980032 |
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| author | Etesi, Gabor |
| author_facet | Etesi, Gabor |
| contents | In this short note we argue that, even if, as sometimes remarked, a Lorentzian manifold does not model correctly the structure of the spatio-temporal continuum as it is, yet a Lorentzian manifold should describe its macroscopic structure as we experience it.
More precisely, theoretically motivated by von Weizsäcker's chronological relative frequency interpretation of probability, and taking the Diaconis--Mosteller principle (also called the law of truly large numbers) as an empirical evidence in the macroscopic world, we argue that large collections of physical events appear in a composition of two fundamentally different patterns, termed as a progression and a sample here, making it unavoidable to use a Lorentzian-type metric on a manifold to describe matter-filled macroscopic regions of the spatio-temporal continuum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08815 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the emergence of the Lorentzian metric structure of space-time in general relativity Etesi, Gabor General Physics In this short note we argue that, even if, as sometimes remarked, a Lorentzian manifold does not model correctly the structure of the spatio-temporal continuum as it is, yet a Lorentzian manifold should describe its macroscopic structure as we experience it. More precisely, theoretically motivated by von Weizsäcker's chronological relative frequency interpretation of probability, and taking the Diaconis--Mosteller principle (also called the law of truly large numbers) as an empirical evidence in the macroscopic world, we argue that large collections of physical events appear in a composition of two fundamentally different patterns, termed as a progression and a sample here, making it unavoidable to use a Lorentzian-type metric on a manifold to describe matter-filled macroscopic regions of the spatio-temporal continuum. |
| title | On the emergence of the Lorentzian metric structure of space-time in general relativity |
| topic | General Physics |
| url | https://arxiv.org/abs/2507.08815 |