Shor Oded, Benninger Felix, Khrennikov Andrei
Felsenstein Medical Research Center, Beilinson Hospital, Petach Tikva, Israel.
Faculty of Medicine, Tel Aviv University, Tel Aviv, 6997801, Israel.
Heliyon. 2023 Sep 9;9(9):e19863. doi: 10.1016/j.heliyon.2023.e19863. eCollection 2023 Sep.
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 -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 . 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.
我们通过将事件表示为表达事件之间层次关系的树状图（有限树）的分支，开发了一种用于事件宇宙的新型数学模型。在本体层面，我们使用无限树进行操作。代数上，这种数学结构表示为(p)-adic数。我们将这种事件力学称为树状全息理论（DHT）。它可以被视为一种同时产生广义相对论（GR）和量子力学（QM）的基础理论。在本文中，我们用拉奥 - 克莱姆信息几何赋予DHT。遵循斯莫林从事件宇宙推导量子力学的方法，我们引入从一个事件到其他事件的视角，并利用它们的概率分布创造了随机几何。重要的数学结果是，所有这些视角的分布都可以由四个实参数参数化，这四个实参数是巴伯在其粒子形状动力学理论中引入的形状复杂度度量的一部分——适用于DHT。因此，在DHT范围内，所有可能的事件宇宙都可以嵌入到四维实空间中。与广义相对论一样，我们引入(\tau)。这个“固有时”仅取决于观察者的一种分布到另一种分布的变化。时间与变化的联系在罗韦利和巴伯的形状动力学思想中得到了强调。
