Languages around the world use a recurring strategy to discuss abstract concepts: describe them metaphorically, borrowing language from more concrete domains. We "plan ahead" to the future, "count up" to higher numbers, and "warm" to new friends. Past work has found that these ways of talking have implications for how we think, so that shared systems of linguistic metaphors can produce shared conceptualizations. On the other hand, these systematic linguistic metaphors might not just be the cause but also the effect of shared, non-linguistic ways of thinking. Here, we present a case study of a variety of American English in which a shared, non-linguistic conceptualization of time has become crystallized as a new system of linguistic metaphors. Speakers of various languages, including English, conceptualize time as a lateral timeline, with the past leftward and the future rightward. Until now, this conceptualization has not been documented in the speech of any language. In two studies, we document how members of the U.S. military, but not U.S. civilians, talk about time using conventionalized lateral metaphors (e.g., "move the meeting right" to mean "move the meeting later"). We argue that, under the right cultural circumstances, implicit mental representations become conventionalized metaphors in language.