The Garden of Forking Paths : Time as an Expanding Labyrinth By

The gifted 20 th century Argentine writer, Jorge Luis Borges, once described time as the " one essential mystery. " Indeed our mundane experience of time can be baffling. Moments slip away—sometimes in a trickle, other times in a stampede—and it is impossible to return to the past. Through our memories and dreams, distant times sometimes seem clear and immediate, and other times foggy and remote. Years sometimes fly by; days sometimes drag on. For physicists, eager to pin down elusive properties and assign measurable parameters to natural phenomena, the nature of time offers many fundamental enigmas. Various subfields of physics provide clashing visions of time's behavior. Classical mechanics offers a clockwork view of a steady rhythm of causes followed by effects. It is eminently deterministic and fully reversible. Complexity theory advices us, however, that a wide range of systems, even ones modeled by only a few parameters, can be deterministic in principle yet as hard to predict in practice as a coin toss. Edward Lorentz, for example, brilliantly showed why long-range weather forecasting is tricky; a minute discrepancy in one parameter can lead to overwhelming differences over time [1]. Yet this is not a violation of causality and determinism; rather it represents a statement of the imperfection of measuring devices. In principle, with absolutely precise instruments, the future could be predicted indefinitely. Another vision of time is as something akin to space. Einstein emphasized that by setting time as a parameter by which motion is measured—along with three spatial coordinates—Newton effectively rendered it a kind of fourth dimension (without saying such). Indeed, as early as 1754, a French encyclopedia entry written by the mathematician Jean d'Alembert discussed the idea of duration being the fourth dimension [2]. D'Alembert's definition, and a similar statement by Joseph Lagrange found in his 1797 text, The Theory of Analytical Functions, clearly drew this idea from Newtonian physics. Special relativity, particularly in the version framed by Hermann Minkowski, solidified the concept of time as being on par with space as members of a dimensional quartet—what became known as a spacetime manifold. Through general relativity, Einstein showed how mass and energy rendered this manifold dynamic—its geometry responding to the matter-energy distribution. This dynamics is fundamentally different from the Newtonian succession of