Rao-Fisher information geometry and dynamics of the event-universe views distributions
We developed the novel mathematical model for event-universe by representing events as branches of dendrograms (finite trees) expressing the hierarchic relation between events. At the ontic level we operate with infinite trees. Algebraically such mathematical structures are represented as p-adic num...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-09-01
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| Series: | Heliyon |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844023070718 |
| _version_ | 1827803129981173760 |
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| author | Oded Shor Felix Benninger Andrei Khrennikov |
| author_facet | Oded Shor Felix Benninger Andrei Khrennikov |
| author_sort | Oded Shor |
| collection | DOAJ |
| description | We developed the novel mathematical model for event-universe by representing events as branches of dendrograms (finite trees) expressing the hierarchic relation between events. At the ontic level we operate with infinite trees. Algebraically such mathematical structures are represented as p-adic numbers. We call this kind of event mechanics Dendrogramic Holographic theory (DHT). It can be considered as a fundamental theory generating both GR and QM. In this paper we endower DHT with Rao-Cramer's information geometry. Following Smolin's derivation of QM from the event-universe, we introduce views from one event to others and by using their probability distributions we invent stochastic geometry. The important mathematical result is that all such views' distributions can be parametrized by four real parameters that are a part of the shape complexity measure introduced by Barbour in his particle shape dynamics theory – adapted to DHT. Hence, within DHT all possible event-universes can be embedded in four-dimensional real space. Asin GR, we introduce proper time. This “proper time” depends only on the change between one distribution of an observer to the other. The linkage of time to change is highlighted in the ideology of Rovelli and Barbour's shape dynamics. |
| first_indexed | 2024-03-11T20:50:09Z |
| format | Article |
| id | doaj.art-fa7889407cd14c2dbeac0b806d4c6f19 |
| institution | Directory Open Access Journal |
| issn | 2405-8440 |
| language | English |
| last_indexed | 2024-03-11T20:50:09Z |
| publishDate | 2023-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj.art-fa7889407cd14c2dbeac0b806d4c6f192023-10-01T06:01:35ZengElsevierHeliyon2405-84402023-09-0199e19863Rao-Fisher information geometry and dynamics of the event-universe views distributionsOded Shor0Felix Benninger1Andrei Khrennikov2Felsenstein Medical Research Center, Beilinson Hospital, Petach Tikva, Israel; Faculty of Medicine, Tel Aviv University, Tel Aviv, 6997801, IsraelFelsenstein Medical Research Center, Beilinson Hospital, Petach Tikva, Israel; Faculty of Medicine, Tel Aviv University, Tel Aviv, 6997801, Israel; Department of Neurology, Rabin Medical Center, Petach Tikva, 4941492, IsraelFaculty of Technology, Department of Mathematics, Linnaeus University, 3 51 95 Växjö, Sweden; Corresponding author. Faculty of Technology, Department of Mathematics, Linnaeus University, 351 95 Växjö, Sweden.We developed the novel mathematical model for event-universe by representing events as branches of dendrograms (finite trees) expressing the hierarchic relation between events. At the ontic level we operate with infinite trees. Algebraically such mathematical structures are represented as p-adic numbers. We call this kind of event mechanics Dendrogramic Holographic theory (DHT). It can be considered as a fundamental theory generating both GR and QM. In this paper we endower DHT with Rao-Cramer's information geometry. Following Smolin's derivation of QM from the event-universe, we introduce views from one event to others and by using their probability distributions we invent stochastic geometry. The important mathematical result is that all such views' distributions can be parametrized by four real parameters that are a part of the shape complexity measure introduced by Barbour in his particle shape dynamics theory – adapted to DHT. Hence, within DHT all possible event-universes can be embedded in four-dimensional real space. Asin GR, we introduce proper time. This “proper time” depends only on the change between one distribution of an observer to the other. The linkage of time to change is highlighted in the ideology of Rovelli and Barbour's shape dynamics.http://www.sciencedirect.com/science/article/pii/S2405844023070718 |
| spellingShingle | Oded Shor Felix Benninger Andrei Khrennikov Rao-Fisher information geometry and dynamics of the event-universe views distributions Heliyon |
| title | Rao-Fisher information geometry and dynamics of the event-universe views distributions |
| title_full | Rao-Fisher information geometry and dynamics of the event-universe views distributions |
| title_fullStr | Rao-Fisher information geometry and dynamics of the event-universe views distributions |
| title_full_unstemmed | Rao-Fisher information geometry and dynamics of the event-universe views distributions |
| title_short | Rao-Fisher information geometry and dynamics of the event-universe views distributions |
| title_sort | rao fisher information geometry and dynamics of the event universe views distributions |
| url | http://www.sciencedirect.com/science/article/pii/S2405844023070718 |
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