Donald Williams in his famous “The Myth of Passage” argued that time cannot flow, because if it did, then it would require either a meta-time to flow in or would flow at a rate of 1 (i.e., one second per second = one hour per hour = etc.) I’ve always been puzzled by what’s supposed to be wrong with the second option. Is it that if something flows at some rate, then it could have flowed at a different rate? But light appears to be a counterexample to that—it cannot flow but at c.
Here’s another take on what’s wrong with time flowing at a rate of 1. The flow of time is supposed to be intrinsically directional. But there is nothing intrinsically directional with a flow at a rate of one. Imagine that, somehow, our universe is divided into two halves, and in one of them time flows in one direction and in the other in the other direction. In our half, from 1 to 3 pm, it flows at a rate of 2 hrs / 2 hrs = 1. In the other half, from their 3 pm to their 1 pm it flows at a rate of −2 hrs / −2 hrs = 1. So regardless of the direction that time flows, the rate is 1: it is never −1, say. And that makes the flow of time as measured against time itself a kind of triviality that cannot capture the myth of passage.
It seems that only when we measure the flow against a meta-time do we have a non-trivial flow. That said, perhaps Williams is wrong that we need a regress of meta-times. Maybe time’s flow can be measured against a meta-time that itself does not flow.
