Creative and geometric times in physics, mathematics, logic, and philosophy

TL;DR

This paper argues that time in physics and mathematics is best understood as comprising two distinct notions: geometric time, the parametric, deterministic time that plagues the block universe picture, and creative time, the process by which indeterministic events actualize new information. Grounded in ontic indeterminacy and a naturalistic view of information, it uses a weather analogy and quantum-mechanical considerations to show how potentialities become determinate, producing the present as the boundary between past and future. It then develops parallel perspectives across mathematics and logic, contrasting classical Platonism with constructive intuitionism and explaining how open-future semantics and tense logic naturally model creative time while preserving non-contradiction. The work further maps geometric time to B-theory and creative time to A-theory, proposes a relativistically compatible, locally defined notion of present, and discusses implications for relativity, quantum theory, and thermodynamics, highlighting how a dual-time framework clarifies the arrow of time and the logical structure of physical propositions.

Abstract

We distinguish two different concepts of time that play a role in physics: \textit{geometric time} and \textit{creative time}. The former is the time of deterministic physics and merely parametrizes a given evolution. The latter is instead characterized by real change, i.e. novel information that gets created when a non-necessary event becomes determinate in a fundamentally indeterministic physics. This allows one to give a naturalistic characterization of the present as the moment that separates the potential future from the determinate past. We discuss how these two concepts find natural applications in classical and intuitionistic mathematics, respectively, and in classical and intuitionistic logic, as well as how they relate to the well-known A- and B-theories in the philosophy of time. We acknowledge that we do not offer here a unified concept or a new philosophy of time. However, we contend that none of the existing philosophical accounts fully integrate both the geometric and creative concepts of time.

Figures (2)

• Figure 1: Typical evolution of a classical chaotic system in phase space. The initial state (a) has some ontic indeterminacy, i.e., the position and momentum are in this case not determinate further than the finite region depicted in figure. When evolved through the deterministic equations of motions (b), the indeterminacy spreads (while preserving the same volume), leading to multiple potential future evolutions, i.e. to indeterminism. However, only one of these potential evolutions will actualize (c), while ruling out the other previously potential futures (dashed); it is this process of actualization that makes creative time process.
• Figure 2: Illustration of determinacy propagation within the light cone. Dotted lines indicate states of indeterminacy, while solid lines represent determinacy.