How Zeno’s Paradox was resolved: by physics, not math alone

How Zeno’s Paradox was resolved: by physics, not math alone

Zeno’s Paradox: before you can ever reach your destination, you must travel halfway there, always leaving another half. Despite Zeno’s Paradox, you always arrive right on time. Travel half the distance to your destination and there’s always another half to go.

Zeno’s paradox: motion is impossible

The fastest human in the world, according to legend, was Atalanta

Zeno’s paradox at the quantum level

Certain physical phenomena only happen due to the quantum properties of matter and energy, like quantum tunneling through a barrier or radioactive decays.

How to inhibit this: observe/measure the system before the wavefunction can sufficiently spread out

If you make a measurement too close in time to the prior measurement, there is an infinitesimal probability of the system tunneling into the desired state. If you keep the system interacting with the environment, you suppress the inherently quantum effects, leaving you with only the classical outcomes as possibilities.

Zeno’s Paradox

This mathematical line of reasoning is only good enough to show that the total distance you must travel converges to a finite value.

The takeaway is this: motion from one place to another is possible, and because of the explicit physical relationship between distance, velocity and time, we can learn exactly how motion occurs in a quantitative sense.

Motion over a finite distance always takes a finite amount of time. Thanks to physics, we at last understand how.

The Zen Paradox

There’s no guarantee that each of the infinite number of jumps you need to take – even to cover a finite distance – occurs in a finite amount of time.

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