Chronons are the discrete quantum of time. In other words they are the smallest (or indivisible) length of time. Naturally, if we think chronons exist, then we must hold that time is discrete.
Admittedly, if we say chronons exist we have the following weird result: Two balls, each with a 10cm diameter, are moving in opposite directions each at the speed of 10cm per chronon.
It’s possible, then, that the two balls pass each other without ever being next to each other.
Because the balls moved between these two positions at the speed of a chronon, there wasn’t point between t1 and t2 at which A and B were next to each other. We’ll call this the “strangeness argument” for later reference.
Consider the following argument in favour of the existence of chronons based off the following 2 premises:
- Time is continuous, not discrete. In other words, time is infinitely divisible (there isn’t any minimum span of time that cannot be further divided).
- Let t0, t1 and t2 be points in time with t0 before t1 before t2. If we were a time t0 and are now at time t2, then at some point we were at time t1
Now assume we’re at some point in time, tn. Let tm be some point in time after tn. Since time is continuous (by 1. above) there exists some time tk with tm after tk after tn. By 2. we need to pass tk before we get to tm. But since tm was some arbitrary point after tn, it follows that we can never move forward in time past tn, since we’d always have to pass another point in time first. In other words, there isn’t any next point in time, so we can’t move to it in order to move forward in time.
Now of the 2 premises I think the first is the least likely to be true. Either way, if we deny the second premise, we keep time continuous, but it may as well not be. Let me explain.
Assume 1. is true and 2. is false. So we skip points in time when moving through it. In fact, we must always skip some range of points every time we move through time, because if we didn’t, 2. would be true for that range and then we wouldn’t be able to move through that range. Let’s even assume, for generality sake, that we don’t always skip by the same amount every time we move. But now, assuming 1 and not-2, time is almost indistinguishable from discrete time isn’t it? To see this we can note that the strangeness argument still applies. Say the balls are diagonally next to each other (like in the first picture above) at tn and the next point (the point we skip to) in time is tm. Now assume that the balls travel at 10cm per tm-tn moments of time. Then we have the same strange outcome we did when time was discrete. So rejecting 2. hasn’t done anything to remove the strangeness of discrete time.
It might be said that if we exist at ranges of time instead of points in time we might remove the problem. However, when the range is moving we still need to know how to move it’s boundaries which raises exactly the same problem (with a single point) we originally had. So that won’t help.