Indeterminism in General Relativity

广义相对论中的非决定论

• 批准号: 2870539
• 金额: --
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2870539
• 关键词: Indeterminism; General; Relativity

One of the perennial philosophical questions is whether our world is deterministic. If we believe that physical theories tell us what the world is really like, we may just as well ask if these theories are deterministic. It would be desirable if determinism was a feature of the theory's formalism - we could just look at it and settle the issue right away. But this is not so: determinism is a feature of what the theory describes, and so we need to know what exactly the theory says about our physical reality, i.e. we need to have our theories interpreted.In the case of general relativity (GR), it seems at first sight that we have a good grip on what the theory says about the world (at least much better than in the case of quantum theories). Nevertheless, the question of GR's determinism is not yet settled. On the one hand, there are general issues with the notion of determinism in spacetime theories. First, how to find a plausible definition of determinism (Butterfield 1989, Earman 1986, Melia 1999), which both (i) does justice to clearly (in)deterministic toy examples (Melia 1999, Cudek 2023a), and (ii) is sufficiently independent of our metaphysical commitments (see Earman and Norton 1987). Second, how to understand the relation between the theory's models and the possible situations these models represent: for conflicting views on this, see Weatherall 2018, Fletcher 2020 and Belot 2018. This, in turn, is closely related to the vast topic of symmetry and structure (Dewar 2022 is a recent overview). These two issues will preoccupy the first two chapters of my thesis. On the other hand, there are issues specific to GR, which seem to pose a threat to any plausible account of determinism. First, there are well-known examples such as spacetimes with closed time-like curves or naked singularities (for more examples, see Earman 1995 and Doboszewski 2019).But the question of whether these anomalies are genuinely physically possible, and thus a threat to determinism, remains open (Earman 1995, Manchak 2011). Second, a significant strand of contemporary cutting-edge research in GR investigates formal prerequisites for a certain appealing formal criterion for determinism (namely, inextendibility of maximal future Cauchy development of given initial data). Recent results seem to suggest that, quite surprisingly, the value of the cosmological constant plays a significant role in establishing this criterion (see Dafermos and Luk 2017 and Kehle 2022). The third and fourth chapters of my thesis will discuss the philosophical significance of these results.In my doctoral project, I shall seek to gather these loose threads together, and investigate the possibility of a unified account of determinism in the context of GR. The sections on definitions of determinism, the relationship between determinism and modal metaphysics, and the representation of possibilities by models, will expand on my previous work (Cudek 2023a, 2023b). The conclusion of this project should be relevant not only to philosophy of physics and our general understanding of relativity theory, but also to metaphysics, epistemology, and general philosophy of science.My intended method for addressing the research questions set out above combines: (a) expertise in the philosophical literature covering the issues of: determinism in physical theories (with an emphasis on spacetime theories), modality in physics, and the relationship between the formalism and the interpretation of a theory, with (b) technical proficiency in graduate-level GR, and familiarity with contemporary research in mathematics of GR. Thus, my research method will involve both standard philosophical methodology of reading and reviewing papers, attending discussion groups and seminars, as well as covering any relevant technical material by auditing graduate classes in mathematics or physics departments, or through self-study.

一个长期存在的哲学问题是，我们的世界是否是决定论的。如果我们相信物理理论告诉我们世界的真实面貌，我们不妨问问这些理论是不是决定论。如果决定论是该理论形式主义的一个特征，那将是可取的--我们可以只看它，然后立即解决问题。但事实并非如此：决定论是该理论所描述的一个特征，因此我们需要知道该理论对我们的物理现实到底说了什么，即我们需要对我们的理论进行解释。就广义相对论(GR)而言，乍一看，我们似乎很好地掌握了该理论对世界的描述(至少比量子理论要好得多)。然而，GR的决定论问题尚未得到解决。一方面，时空理论中的决定论概念存在普遍问题。首先，如何找到一个似是而非的决定论定义(Butterfield 1989，Earman 1986，Melia 1999)，它既符合明确的决定论玩具例子(Melia 1999，Cudek 2023a)，又充分独立于我们的形而上学承诺(参见Earman和Norton 1987)。其次，如何理解该理论的模型与这些模型所代表的可能情况之间的关系：关于这一点的相互矛盾的观点，请参见Weatherall 2018、Fletcher 2020和Belot 2018。这反过来又与对称性和结构的广泛主题密切相关(《杜瓦2022》是最近的概述)。这两个问题将是我论文前两章的重点。另一方面，还有一些特定于GR的问题，这些问题似乎对任何关于决定论的合理解释都构成了威胁。首先，有一些众所周知的例子，比如具有封闭的类时间曲线的时空或赤裸裸的奇点(更多的例子，见Earman 1995和Doboszewski 2019)。但是，这些反常是否真的在物理上是可能的，从而对决定论构成威胁，这个问题仍然悬而未决(Earman 1995，Manchak 2011)。其次，GR中当代前沿研究的一大部分调查了某个有吸引力的决定论形式标准的形式先决条件(即，给定初始数据的最大未来柯西发展的不可拓展性)。最近的结果似乎表明，相当令人惊讶的是，宇宙常量的值在建立这一标准方面发挥了重要作用(见Dafermos和Luk 2017和Kehle 2022)。论文的第三章和第四章将讨论这些结果的哲学意义。在我的博士项目中，我将试图将这些松散的线索收集在一起，并探讨在GR的背景下统一解释决定论的可能性。关于决定论的定义、决定论和情态形而上学之间的关系以及通过模型表示可能性的部分，将在我之前的工作(Cudek 2023a，2023b)的基础上展开。这个项目的结论不仅应该与物理哲学和我们对相对论的一般理解有关，而且应该与形而上学、认识论和一般科学哲学有关。我打算用来解决上述研究问题的方法包括：(A)哲学文献中的专业知识，涵盖以下问题：(A)物理理论中的决定论(重点是时空理论)、物理学中的形态、形式主义和理论解释之间的关系，以及(B)研究生水平的GR技术熟练程度，以及对GR数学当代研究的熟悉。因此，我的研究方法将包括阅读和审查论文、参加讨论小组和研讨会的标准哲学方法论，以及通过审计数学或物理系的研究生班或通过自学来涵盖任何相关的技术材料。