An investigation into temporal becoming within timeless strategies in physics Facoltà di Lettere e Filosofia Dipartimento di Filosofia Corso di laurea in Filosofia Emilia Margoni Matricola 1538340 Relatore Relatore esterno Prof. Emiliano Ippoliti Prof. Mauro Dorato A.A. 2019-2020 Contents Introduction ...................................................................................................................... 2 Chapter 1. Ordinary experience time and physical time ................................................ 11 1.1. Introduction ......................................................................................................... 11 1.2. The challenge of dynamism in accounting for experienced time ........................ 12 1.3. The adynamism of the block universe ................................................................. 23 1.4. Concluding remarks ............................................................................................. 30 Chapter 2. On processual becoming ............................................................................... 31 2.1. Introduction ......................................................................................................... 31 2.2. Point-like occurrences and the dismissal of becoming ........................................ 32 2.3. Processual becoming ........................................................................................... 37 2.4. Concluding remarks ............................................................................................. 48 Chapter 3. Shape dynamics: A review ............................................................................ 49 3.1. Introduction ......................................................................................................... 49 3.2. Relational dynamics ............................................................................................ 50 3.3. Shape dynamics ................................................................................................... 56 3.4. What is left of time? ............................................................................................ 62 3.5. Barbour’s relationalism: becomingless but not timeless ..................................... 68 3.6. Concluding remarks ............................................................................................. 72 Chapter 4. General covariance and Quantum Gravity: a discussion .............................. 74 4.1. Introduction ......................................................................................................... 74 4.2. The principle of general covariance and gauge theories ..................................... 76 4.3. The gauge-theoretic formulation of GR and its conceptual interpretation .......... 81 4.4. Gauge invariance and Quantum Gravity ............................................................. 84 4.5. Rovelli’s Evolving Constant approach ................................................................ 86 4.6. Concluding remarks ............................................................................................. 93 Conclusions .................................................................................................................... 94 Bibliography ................................................................................................................... 97 1 Introduction In the last two centuries, human beings’ understanding of time has undergone momentous changes. The advent of relativistic physics along with the advances in quantum mechanics have overridden previous conceptualizations of physical time and also profoundly ques- tioned the time of ordinary experience. It comes as no surprise that one of the persisting conundrums in foundational physics and the philosophy of physics is the gap that this epochal shift has introduced between physics and human experience. This work does not certainly dare to resolve such a basic problem. Rather, it intends to analyze how the con- ceptual toolkit elaborated within the frame of those contemporary physical theories es- pousing timelessness – in the sense that physical time is deemed not to be part of the fundamental ontology – can contribute to a better understanding of one of the key aspects of temporal experience, that is, (temporal) becoming. Indeed, not all theoretical strategies to implement a timeless physics do away with becoming, although they all treat time as non-fundamental. To bring out this difference, I will mainly look into Julian Barbour’s shape dynamics and Carlo Rovelli’s evolving constant approach. “In a timeless world, verbs of becoming like ‘happen’ have no place”, says Barbour (1999, p. 45). “This impossibility [of a single simple succession of global instants] is not absence of becoming. It is the fact that becoming is more complex than a naive non-relativistic extrapolation assumed”, writes Rovelli (2019, 1332). Evidently, ad- dressing these theories requires treating time and becoming as distinct phenomena. Based on a rich wealth of literature, my analysis will come to the conclusion that Barbour’s denial of time is denial of temporal becoming, while Rovelli’s more nuanced notion of becoming successfully rules out time. Contrary to Barbour’s straightforward rejection of becoming, for Rovelli, the naïve notion of becoming is to be described in terms of a one- parameter of evolving constants of motion. Obviously, this work cannot accommodate a full-fledged analysis and a subsequent juxtaposition of such complex theories. So, I will scrutinize them with the aid of a partic- ular conceptual lens, that is, the notion of process. I will take Barbour’s view to be the most radical and coherent refutation of process as a physical notion and Rovelli as the advocate of processes (not states or objects or other entities) being at the heart of physics. “There is a long tradition, going back at least to Hamilton, that seeks to make process the 2 most basic thing in the world. Roughly, the idea is that physics should be built up using verbs, not nouns […]. It all sounds very exciting, but I just do not think it can be done” says Barbour (1999, p. 329). “The universe is an ensemble of processes that happen”, writes Rovelli (2020, p. 124). It will be my claim that one of the crucial differences in Barbour’s and Rovelli’s timeless theories is that theirs are differing types of relationalism that diverge on what is implicated in relation. Barbour’s shape dynamics is an adynam- ical, configurational relationalism, in the sense that configurations, as I will concisely indicate below, are non-dynamical entities. Relationalism is but of locations and scale (see Gomes, 2020). On the contrary, Rovelli makes room for processual dynamics, to the extent that speaking of objects or states is but a way to offer a partial understanding of something that happens within the process. Yet, to make this latter claim clearer, it is worth briefly expounding its meaning at this initial stage. As I will argue more extensively in Chap. 2 and Chap. 4, the processual approach entails a four-dimensional theory of spacetime which admits no “natural breakup” of spacetime into spaces and times. Any such breakup comes from the introduction of an arbitrary frame of reference (a time-like fibration or a space-like foliation of the region of spacetime) whereby a given state of (what hence becomes) an observed system arises. In this sense, the state of a system is but a partition of a continuous process by means of a frame of reference which does not belong to the system1. According to John Stachel (2006; 2014), in physics processes precede states. For him, a processual view takes seriously the distinction between physical processes and physical events (Stachel, 2006, p. 56). The former has an extension in the sense that it occupies a finite region of spacetime, while a physical event occupies a point of spacetime. But insofar as spacetime is represented by a continuum, an event is nothing but “the limit of a portion of some physical process as all the dimensions of the region of spacetime occupied by this portion are shrunk to zero” (ibid.). To put it otherwise, an 1 I would like to stress again that I will address processual views within the set of theories that dismiss time as fundamental. This is the reason why I will not take into consideration other significant approaches that regard processes as “the stuff” of physics but treat time as fundamental. For example, Lee Smolin (2001, p. 53) avers that the world is a “history of processes”, where dynamical change is primary. But Smolin’s processual view pivots on time’s being fundamental, not emergent. Accordingly, his understanding of pro- cess implies time in the sense that the process is an activity generating a thick present, that is to say, two events that can be causally related to each other in a present that is continually growing by addition of new events. As to events in the thick present lose their ability to influence future events, they move into the always growing past (see e.g. Smolin 2001, 2020; Cortês, Gomes & Smolin, 2015). 3 extensionless event is an ideal limit2. However, it is of primary importance to specify what extension amounts to in this context. While it is wrong to think of processual exten- sion as something unfolding through time (as this would beg the question of what time is), a process, as Stachel recommends, should rather be conceived of as related to the issue of the identity that a given entity takes up within a