论文标题
因果关系 - 相对论和概率方面
Causality and time order -- relativistic and probabilistic aspects
论文作者
论文摘要
我们研究了当代物理理论的结构中的时间和因果线，重点是经验和操作方面。基于J. Ehlers，F。Pirani和A. Schild提出的一般相对论的公理化以及由R. Penrose，S.W。详细阐述的全球时空结构。 Hawking，B。Carter和其他人认为，当前做相对主义物理学的方式以将时间和因果关系视为原始概念，它们都不是“更原始”。关于哪些概念假定为原始的决定以及将公理视为哪些陈述取决于我们考虑整体的角度的选择。这种标准方法基于以下前提：点状粒子的概念是一个可行的近似值。但是，这种假设不受现实的物理学，尤其是量子理论的现实方法的支持。我们通过分析M. Eckstein和T. Miller的最新作品来消除这一假设。他们考虑了时空$ m $的空间$ p（m）$ p（m）$ p（m）$ \ p（m）$中的元素$ \ $μ（k）$指定与时空区域$ k $相关的某些事件的可能性。这样，不应将$ m $视为时空事件的集合，而应被视为对相应概率度量的支持。如埃克斯坦（Eckstein）和米勒（Miller）所示，空间$ p（m）$从基本的时空继承了因果秩序，并促进了“概率测量的因果进化”的严格概念。我们查看这些作品中分析的时间和因果结构的演绎链，以突出其运营（或准行动）方面。如果考虑到相关实验中观察到的相对频率和相关性，这是不可能的。
We investigate temporal and causal threads in the fabric of contemporary physical theories with an emphasis on empirical and operationalistic aspects. Building on the axiomatization of general relativity proposed by J. Ehlers, F. Pirani and A. Schild and the global space-time structure elaborated by R. Penrose, S.W. Hawking, B. Carter and others, we argue that the current way of doing relativistic physics presupposes treating time and causality as primitive concepts, neither of them being `more primitive' than the other. The decision regarding which concepts to assume as primitive and which statements to regard as axioms depends on the choice of the angle at which we contemplate the whole. This standard approach is based on the presupposition that the concept of a point-like particle is a viable approximation. However, this assumption is not supported by a realistic approach to doing physics and, in particular, by quantum theory. We remove this assumption by analysing the recent works by M. Eckstein and T. Miller. They consider the space $P(M)$ of probability measures on space-time $M$ such that, for an element $μ\in P(M)$, the number $μ(K)$ specifies the probability of the occurrence of some event associated with the space-time region $K$ and the measure $μ$. In this way, $M$ is not to be regarded as a collection of space-time events, but rather as a support for corresponding probability measures. As shown by Eckstein and Miller, the space $P(M)$ inherits the causal order from the underlying space-time and facilitates a rigorous notion of a `causal evolution of probability measures'. We look at the deductive chains creating temporal and causal structures analysed in these works, in order to highlight their operational (or quasi-operational) aspect. This is impossible without taking into account the relative frequencies and correlations observed in relevant experiments.
