Two Arrows of Time in Nonlocal Particle Dynamics.pdfVIP

Two Arrows of Time in Nonlocal Particle 8 Dynamics 0 0 2 ∗ Roderich Tumulka p e S July 21, 2007 8 1 2 v Abstract 7 0 Considering what the world would be like if backwards causation 2 0 were possible is usually mind-bending. Here I discuss something that 1 is easier to study: a toy model that incorporates a very restricted sort 2 of backwards causation. It defines particle world lines by means of a 0 / kind of differential delay equation with negative delay. The model pre- h sumably prohibits signalling to the past and superluminal signalling, p - but allows nonlocality while being fully covariant. And that is what t n constitutes the model’s value: it is an explicit example of the possi- a bility of Lorentz invariant nonlocality. That is surprising in so far as u q many authors thought that nonlocality, in particular nonlocal laws for : particle world lines, must conflict with relativity. The development of v i this model was inspired by the search for a fully covariant version of X Bohmian mechanics. r a In this paper I will introduce to you a dynamical system—a law of mo- tion for point particles—that has been invented [5] as a toy model based on Bohmian mechanics. Bohmian mechanics is a version of quantum mechanics with particle trajectories; see [4] for an introduction and overview. W