Let us draw an arrow arbitrarily. If as we follow the arrow we find more and more of the random element in the state of the world, then the arrow is pointing towards the future; if the random element decreases the arrow points towards the past. That is the only distinction known to phsyics. This follows at once if our fundamental contention is admitted that the introduction of randomness is the only thing which cannot be undone. I shall use the phrase ‘time’s arrow’ to express this one-way property of time which has no analogue in space. [Eddington, The Nature of the Physical World, 1928]
I'd always assumed that an arrow was the metaphor of choice here because, you know, it points in a certain direction. Latterly, though, I find myself wondering whether the other aspects of the metaphor are not more important; the skill, for instance, in the directing and loosing of the arrow; our alarm at its speed; the pain upon its impact in our bodies. The bullet of time would work just as well as a way of talking about these things, wouldn't it?