In his famous arrow paradox, the Greek philosopher Zeno of Elea (490 – 430 BCE) stated the obvious; for motion to occur, an object must change the position it occupies in space. Using the example of an arrow in flight, he further observed that at any instant in time, the arrow is motionless in space. The arrow, he reasoned, cannot move to where it is because it is already there. At the same time, it cannot move to where it is going because no time elapses to move there.
That being the case, at any (and, importantly, every) instant in time, the arrow is at rest and no motion is occurring. Thus, the apparent paradox: If the arrow is motionless at every instant in time, and if time consists entirely of such instants, then motion would seem impossible. How does the arrow ever get from the archer to the target? Indeed, how do we explain motion or change of any kind?
It seems to me that Zeno’s arrow paradox implicitly assumes that time is continuous and made up of discrete, durationless instants. But what if time is not continuous, but discrete? That is, what if it consists of small but non-zero increments, perhaps something approaching or even exceeding Planck time? What would be the implications?
One of the implications is there would theoretically exist an exceedingly brief but non-imaginary “gap” between the units of time. If so, it raises the question, “What happens in the gaps?”
Using the analogy of a high-speed movie film, our experience of time/change could be likened to individual frames of film separated by empty frame borders. Each frame represents an accurate reflection of reality at a single instant with previous and successive frames being almost, but not quite, indistinguishable. If so, it is actually the frame borders that explain time and change.
So, what happens in these gaps? One possibility is that nothing happens in them: literally, nothing. Just as electrons only exist in discrete radii from the nucleus and briefly cease to exist as they jump from one quantum state to the next, so what we perceive as physical reality might very briefly cease to exist during the gaps between the rapidly pulsing “frames,” only to be completely regenerated a fraction of a moment later but with ever-so-slight differences that we subjectively experience as time and/or change. This would explain Zeno’s famous motionless arrow in flight, as well as all other forms of change, from human aging to geological erosion to an expanding universe.
Why is each successive instant in time different from the one before? I don’t know. Perhaps regenerating reality obeys a law that explains both the difference and the direction of change.
On the other hand . . . I suppose time could be continuous but composed of indivisible increments of non-zero durations such that there is technically no such thing as a durationless instant in time. If that were the case, then Zeno’s arrow is never really at rest, but rather always moving albeit extremely slowly.
Who knows? I guess time will tell.