On the Growing Universe of Causal Set Theory—An Order-Type Approach

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY

Foundations of Physics Pub Date : 2024-06-20 DOI:10.1007/s10701-024-00767-5

Tomasz Placek, Leszek Wroński

引用次数: 0

Abstract

We investigate a model of becoming—classical sequential growth (CSG)—that has been proposed within the framework of causal sets (causets), with the latter defined as order types of certain partial orderings. To investigate how causets grow, we introduce special sequences of causets, which we call “csg-paths”. We prove a number of results concerning relations between csg-paths and causets. These results paint a highly non-trivial picture of csg-paths. There are uncountably many csg-paths, all of them sharing the same beginning, after which they branch. Every infinite csg-path achieves in the limit an infinite causet, and vice versa, every infinite causet is achieved in the limit by an infinite csg-path. However, coalescing csg-paths, i.e., ones that achieve the same causet even after forking off at some point, are ubiquitous.

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论因果集合论的成长宇宙--一种秩序型方法

我们研究了在因果集（causets）框架内提出的经典连续增长（CSG）模型，后者被定义为某些部分排序的排序类型。为了研究因果集如何增长，我们引入了因果集的特殊序列，我们称之为 "因果路径"。我们证明了一些关于 csg-paths 和因果集之间关系的结果。这些结果描绘了 csg-paths 的非难图景。csg-路径的数量不可计数，所有csg-路径都有相同的起点，起点之后又有分支。每条无限的 csg 路径都能在极限中实现无限的因果集，反之亦然，每条无限的因果集都能在极限中通过无限的 csg 路径实现。然而，凝聚的 csg 路径，即即使在某点分叉后仍能实现相同因果集的路径，是无处不在的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Foundations of Physics 物理-物理：综合

CiteScore

2.70

自引率

6.70%

发文量

104

审稿时长

6-12 weeks

期刊介绍： The conceptual foundations of physics have been under constant revision from the outset, and remain so today. Discussion of foundational issues has always been a major source of progress in science, on a par with empirical knowledge and mathematics. Examples include the debates on the nature of space and time involving Newton and later Einstein; on the nature of heat and of energy; on irreversibility and probability due to Boltzmann; on the nature of matter and observation measurement during the early days of quantum theory; on the meaning of renormalisation, and many others. Today, insightful reflection on the conceptual structure utilised in our efforts to understand the physical world is of particular value, given the serious unsolved problems that are likely to demand, once again, modifications of the grammar of our scientific description of the physical world. The quantum properties of gravity, the nature of measurement in quantum mechanics, the primary source of irreversibility, the role of information in physics – all these are examples of questions about which science is still confused and whose solution may well demand more than skilled mathematics and new experiments. Foundations of Physics is a privileged forum for discussing such foundational issues, open to physicists, cosmologists, philosophers and mathematicians. It is devoted to the conceptual bases of the fundamental theories of physics and cosmology, to their logical, methodological, and philosophical premises. The journal welcomes papers on issues such as the foundations of special and general relativity, quantum theory, classical and quantum field theory, quantum gravity, unified theories, thermodynamics, statistical mechanics, cosmology, and similar.