Here’s a little thought experiment about the nature of the universe.
As some background, we’ve all heard the little mathematical trick by Zeno of Elea: the paradox of the tortoise and Achilles. The two agree to a race in which the tortoise gets a head start, let’s call it 10 meters. Achilles is quicker but we allow Achilles to travel only half the distance to catch the tortoise, then half the remaining distance, then half again, and so on. So Achilles is first at 5m, then 7.5m, then 8.75m, etc. We can keep halving the distances forever and so it looks like Achilles can never catch the tortoise!
The flaw in the paradox is that since the time it takes to cross each successive half-distance is also halved, the time for the race is limited, since the formula never passes 2x time where x is the time it took to move the first 5 meters. If Achilles moves at 5 meters per second then we are only allowing 1.99999… seconds for the race and that is why the tortoise is never caught. We are limiting both distance traveled and time traveled, which explains away the apparent paradox.
So far so good, but let’s take a step back. Please allow me to present a different perspective.
If distance between A and B can be split into an infinite number of smaller points and an object takes a finite amount of time to pass through each point then it can never reach point B. This is not a trick question, it’s a statement that must be true: one cannot pass through infinite points if one has to spend a finite amount of time at each point because it would take an infinite amount of time to get anywhere. This is different to Zeno’s paradox because I’m not limiting time, I’m allowing infinite time but point B is still never reached because I must pass through each one of the infinite points.
There are only two solutions to this. Either there are a finite number of points, meaning that we cannot split distance into smaller and smaller points, or there are infinite points but I do not have to spend a finite amount of time on each of them. However, these two solutions turn out to be the same thing.
If there are a finite number of points then that means there is a smallest possible distance (distance quanta), therefore all movement is literally an object disappearing from one point in space and appearing in another point in space, i.e. teleportation.
Or if the object does not spend a finite amount of time passing through all points then it is spending 0 amount of time passing through some points, also meaning that the object is teleporting because to spend 0 amount of time on a point is to not pass through it, and therefore also implying that there is a smallest possible distance.
This should prove that:
- On the quantum level there is a minimum possible distance in this universe.
- All objects must ‘teleport’ between these minimum distances when they move.
The next question is: if all movement on the quantum level is actually teleportation then why does an object only teleport to the next distance-point? What is the difference between teleporting from point A to point C via point B, instead of just going straight from A to C?
That’s an interesting enough thought, but I’ll leave you with one more. If there is a minimum quanta of distance that must be teleported through on the quantum level then what is speed? Is higher speed teleporting through each successive distance-point within less time, or is higher speed teleporting across multiple distance-points within the same time? Is there a difference?