  The standard model of modern cosmology, which is based on the
Friedmann-Lema\^itre-Robertson-Walker metric, allows the definition of an
absolute time. However, there exist (cosmological) models consistent with the
theory of general relativity for which such a definition cannot be given since
they offer the possibility of time travel. The simplest of these models is the
cosmological solution discovered by Kurt G\"odel, which describes a
homogeneous, rotating universe. Disregarding the paradoxes that come along with
the abolishment of causality in such spacetimes, we are interested in the
purely academical question how an observer would visually perceive the time
travel of an object in G\"odel's universe. For this purpose, we employ the
technique of ray tracing, a standard tool in computer graphics, and visualize
various scenarios to bring out the optical effects experienced by an observer
located in this universe. In this way, we provide a new perspective on the
space-time structure of G\"odel's model.
