People often make use of a spatial "mental time line" to represent events in time. We investigated whether the eyes follow such a mental time line during online language comprehension of sentences that refer to the past, present, and future. Participants' eye movements were measured on a blank screen while they listened to these sentences. Saccade direction revealed that the future is mapped higher up in space than the past. Moreover, fewer saccades were made when two events are simultaneously taking place at the present moment compared to two events that are happening in different points in time. This is the first evidence that oculomotor correlates reflect mental looking along an abstract invisible time line during online language comprehension about time. Our results support the idea that observing eye movements is likely to "detect" invisible spatial scaffoldings which are involved in cognitively processing abstract meaning, even when the abstract meaning lacks an explicit spatial correlate. Theoretical implications of these findings are discussed.