Spacetime singularities and a novel formulation of indeterminism

TL;DR

This paper proposes a new, broader interpretation of spacetime singularities in general relativity as signals of indeterminism, expanding traditional notions to include non-uniqueness, non-specification, and incoherence of states.

Contribution

It introduces a novel, comprehensive framework for understanding indeterminism in classical theories, specifically addressing the interpretative issues posed by spacetime singularities.

Findings

Singularities signal indeterminism in a broader sense.

The new formulation captures non-uniqueness, non-specification, and incoherence.

This approach explains the breakdown signaled by singularities.

Abstract

Spacetime singularities in general relativity are commonly thought to be problematic, in that they signal a breakdown in the theory. We address the question of how to interpret this breakdown, restricting our attention to classical considerations (though our work has ramifications for more general classical metric theories of gravity, as well). In particular, we argue for a new claim: spacetime singularities in general relativity signal indeterminism. The usual manner in which indeterminism is formulated for physical theories can be traced back to Laplace. This formulation is based on the non-uniqueness of future (or past) states of a physical system -- as understood in the context of a physical theory -- as a result of the specification of an antecedent state (or, respectively, of a subsequent state). We contend that for physical theories generally, this formulation does not comprehensively capture the relevant sense of a lack of determination. And, in particular, it does not comprehensively capture the sense(s) in which a lack of determination (and so, indeterminism) arises due to spacetime singularities in general relativity. We thus present a novel, broader formulation, in which indeterminism in the context of some physical theory arises whenever one of the three following conditions holds: future (and/or past) states are (i) not unique -- as for Laplacian notions of indeterminism; (ii) not specified; or (iii) `incoherent' -- that is, they fail to satisfy certain desiderata that are internal to the theory and/or imposed from outside the theory. We apply this formulation to salient features of singularities in general relativity and show that this broader sense of indeterminism can comprehensively account for (our interpretation of) the breakdown signaled by their occurrence.