This paper presents an argument for the conceptual and physical impossibility of time travel. According to the author, the reason why most people in Western culture nowadays think time travel is conceivably possible – or, at least, speak as if it might be possible, as evidenced by many works of fiction where time travel takes place – is because we largely rely on spatial metaphors in order to conceptualize time. For example, if time is conceptualized as a medium that agents move through (like space), as in the “Moving Observer” metaphor for time described by Lakoff and Johnson (1980), it is easy to imagine the agent moving backwards through the same medium, i.e. “traveling to the past”, while time itself does not admit such a thing. The author argues that all talk of time travel derives from a similar projection of conceptual metaphors onto the actual nature of reality. The article’s main conclusion is that time travel, if conceptualized in the way we usually speak and think of it nowadays, is nonsense.