Relativistic spacetimes and definitions of determinism

Abstract

I discuss candidates for definitions of determinism in the context of general relativistic spacetimes, and argue that a definition which does not make recourse to any particular region of spacetime should be preferred over alternatives; one such notion is discussed in detail in the light of various physical examples. The emerging picture of determinism is a pluralist one: sometimes there is no unique way of making our intuitive concept of determinism precise. Instead, what is crucial for assessment of determinism of the theory are auxiliary conditions under which it counts as deterministic or indeterministic, and justification for using them in a given situation.

Singularities, Black Holes, and Cosmic Censorship: A Tribute to Roger Penrose

“…53 See Doboszewski [63,64] and Manchak [131,132] for conceptual studies of the (in)extendibility of space-times. 54 As pointed out to me by Julius Doboszewski, Chruściel et al [43] as well as Chruściel and Isenberg [42] only consider smooth extensions, so that looking at lower regularity seems a refinement postdating this early phase.…”

“…as described by something like the Kerr metric (at least outside its Cauchy horizon and more safely even outside its event horizon). As such, on the one hand they gain focus, but on the other hand they can be thought of as forming part of a broader conjecture that also originated with Penrose himself and is often called the final state conjecture: 64 A body, or collection of bodies, collapses down to a size comparable to its Schwarzschild radius, after which a trapped surface can be found in the region surrounding the matter. Some way outside the trapped surface region is a surface which will ultimately be the absolute event horizon.…”

“…See the Penrose diagram at the end of §2.6.2 of Dafermos and Rodnianski [61] for an example. 64 This is sometimes stated somewhat differently, in that 'generic asymptotically flat vacuum initial data (...) evolve to a solution which either disperses (in which case there are no black holes) or else eventually asymptotes to finitely many Kerr solutions (...) moving away from each other' [47, p. 78]. See also the fascinating lecture by Klainerman [113].…”

Interdisciplinarity: A complexity approach towards academic research

“…The Newton's logic was a result of the deterministic thinking, for which the linear thinking is the simplest way of manifestation. Without entering the philosophical debates, ‘determinism is typically spelled out as the statement that the state of the physical system at one moment of time, together with dynamical equations describing the evolution of the system, uniquely fixes the state of the physical system at any other moment of time’ (Doboszewski, 2019: 1). When the dynamical equations are linear, the evolution of the system is easily understood and anticipated.…”

Four Attitudes Towards Singularities in the Search for a Theory of Quantum Gravity

“…Recent work has emphasised the difficulty of defining determinism in precise terms;Doboszewski (2019) gives a pluralistic definition.6 This fact is already recognised in the literature, e.g.,(Wald, 1992, p. 182).…”