Our aim is to determine whether there is any qualitative difference in predictability between Lorentz invariant classical theories which permit superluminal propagation and those that do not. In this paper, rather than focusing on causality violation, we will investigate predictability. The reason that causality violation would be problematic is that it implies a breakdown of predictability. This means that the argument is open to criticism on various grounds. However, this argument is heuristic: the causality-violating solution is not constructed, it is simply asserted to exist. The argument for this is to consider two lumps of non-trivial field with a large relative boost: it is claimed that there exist solutions of this type for which small perturbations will experience closed causal curves. It is sometimes claimed that such theories are unviable because the superluminality can be exploited to construct causality violating solutions, i.e., РІР‚Сљtime machinesРІР‚Сњ. Many Lorentz invariant classical field theories permit superluminal propagation of signals around non-trivial background solutions. In this sense, superluminal equations exhibit better predictability than generic subluminal equations.

In particular, we prove that superluminal equations always admit a unique maximal globally hyperbolic development. For a general quasilinear wave equation, we prove theorems establishing why this lack of uniqueness occurs, and identify conditions on the equation that ensure uniqueness. This problem does not arise in the superluminal theory, for which there is a unique maximal globally hyperbolic development. For the subluminal theory, there can exist multiple maximal globally hyperbolic developments arising from the same initial data. Surprisingly, we find that the subluminal theory is less predictive than the superluminal theory in the following sense. This equation can be formulated in either a subluminal or a superluminal form. To investigate this, we study the BornРІР‚вЂњInfeld scalar in two spacetime dimensions.

It is sometimes claimed that Lorentz invariant wave equations which allow superluminal propagation exhibit worse predictability than subluminal equations.

Superluminal waves