I can understand discrete space and time and if it’s really how universe works than this paradox is quickly resolved, but there is another solution which my brain can’t understand. How does continuous spacetime work and solve this paradox?
In: Physics
The Zeno paradox, or Achilles and Tortoise of you prefer, has nothing to do with continuous space and time. It is a faulty representation of the problem. There is no paradox if you don’t take this ridiculous infinite fraction representation. What you should conclude is that this representation isn’t correct, not that Achilles can’t pass the Tortoise.
Consider the time that it takes for Achilles to get to where the Tortoise started. This is some time T. Rather than step forward in smaller and smaller time steps, step forward by T again. Achilles passes the Tortoise, problem over. Yes, there are summations of fractional times that can’t ever reach 2T, but that’s no evidence that 2T is longer than the race might reasonably last. Simply that those representations are wrong.
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