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.

多年生的哲学问题之一是我们的世界是否是确定性的。如果我们相信物理理论告诉我们世界的真实面貌，那么我们也可以问这些理论是否是确定性的。如果确定论是理论形式主义的特征，那将是可取的 - 我们可以立即查看并立即解决问题。但事实并非如此：确定论是理论所描述的特征，因此我们需要知道该理论对我们的物理现实的确切说明，即我们需要解释理论。在总体相对论（GR）的情况下，似乎乍一看，我们对理论对世界的看法很好（至少比量级量的情况都更好）。然而，GR的决定论的问题尚未解决。一方面，在时空理论中确定论的概念存在一般问题。首先，如何找到对确定论的合理定义（Butterfield 1989，Earman 1986，Melia 1999），这两个（i）（i）在确定性的玩具实例（Melia 1999，Cudek 2023a）和（ii）中都非常明确地公正，并且（II）足够独立于我们的世俗承诺（请参阅Earman和Norton 1987）。其次，如何了解理论模型与这些模型所代表的可能情况之间的关系：有关此的相互矛盾的观点，请参见Weatherall 2018，Fletcher 2020和Belot 2018。这反过来又与对称和结构的广泛主题密切相关（Dewar 2022是最近的概述）。这两个问题将占据我论文的前两章。另一方面，有一些特定于GR的问题，似乎对确定论的任何合理描述构成了威胁。首先，有一些众所周知的例子，例如具有闭合时间曲线或裸奇异点的空间（有关更多示例，请参见Earman 1995和Doboszewski 2019）。但是，这些异常在物理上确实可能是可能的，因此对确定性的威胁是开放的（Earman 1995，Manchak 2011）。其次，一大批当代尖端研究在GR中调查了一定有吸引力的确定性正式标准的正式先决条件（即，最大的未来Cauchy开发给定初始数据的最大未来的不可扩展性）。最近的结果似乎表明，令人惊讶的是，宇宙常数的价值在建立该标准中起着重要作用（参见Dafermos和Luk 2017和Kehle 2022）。我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，我将寻求将这些松散的线程聚集在一起，并研究在GR背景下确定性的统一说明的可能性。关于确定论的定义，确定论与模态形而上学之间的关系以及模型代表的部分，将扩展我以前的工作（Cudek 2023a，2023b）。该项目的结论不仅应与物理学哲学和我们对相对论理论的一般理解有关，而且还与形而上学，认识论和科学的一般哲学有关。对理论的解释，（b）研究生水平的GR技术水平，以及对GR数学研究的熟悉。因此，我的研究方法将涉及阅读和审查论文，参加讨论小组和研讨会的标准哲学方法，以及通过审核数学或物理部门的研究生班或通过自学来涵盖任何相关的技术材料。