Everyday linguistic expressions in many languages suggest that temporal concepts of past and future are projected onto back and front space (as in “we are years ahead of them”). The present experiments tested the psychological reality of a different space-time conceptual metaphor, projecting past to left space and future to right space, for which there are no linguistic traces in any language. In the first experiment, participants categorized words as referring to the past or to the future. Irrelevant to this task, words appeared either to the left or right of the screen and responses were given by pressing a key with either the left or right hand. Judgements were faster and/or more accurate when word position and response mapping were congruent with the left-past right-future conceptual metaphor. Experiment 2 used an analogous task that did not resource to language. Participants saw short silent movies. After each movie, they were presented with several trials in which two frames appeared in succession. Their task was to judge whether the latter scene happened before or after the former in the movie, by pressing a left or a right key. The first frame was always the central frame of the movie, and the second was sampled from 10 equally-spaced points along the movie. Latencies showed both a distance effect (the closer the two scenes, the longer the response time) and a response congruency effect (faster responding when “before” was mapped to the left key and “after” to the right key than the converse), suggesting that the movie was conceptualized as flowing from left to right along a mental spatial line. A final experiment used an implicit variant of this task. Movies were presented in pairs. Then, pairs of frames were presented simultaneously on left and right positions of the screen. The task was to decide whether both frames belonged to the same movie. In “yes” trials, response times were faster when the left frame occurred before the right frame in the movie than in the opposite arrangement. These results support the psychological reality of a left-right space-time conceptual projection and its routinary activation at least in certain tasks, both linguistic and non-linguistic. The fact that the origin of this metaphor may lie in left-to-right writing habits has implications for the possible mechanisms by which conceptual metaphors can be acquired. Finally, several predictions for future research are outlined. (Julio Santiago, Juan Lipiáñez, Elvira Pérez and María Jesús Funes)