Zeno's Paradox

star field

2  Digitizing Speed

The minimum length and minimum time set the boundaries for maximum and minimum speed. Dividing the minimum length in a quantized spacetime by the minimum time gives a characteristic speed, c. In the stadium, c was 100 fps and was the maximum speed possible there.

Why? Imagine a pumped-up Achilles trying to go faster. To do so, he must cover more than the minimum length in the minimum time. Maybe he tries to steal two minimum lengths in the minimum time. Forbidden! He runs into the same problem as Magnifico. He would be trying to move one minimum length in half the minimum time. There is no half of the minimum time. The minimum time is indivisible. That is why it is the minimum. So, the characteristic speed, c, is an upper bound that cannot be exceeded.

In our universe, light moves at the maximum possible speed. No matter how much power we put into particle accelerators to make components of atoms move faster, they never reach the speed of light, which is defined as exactly 299,792,458 meters per second (real scientists use the metric system). Treating this as the universe’s upper bound to speed provides the basis for estimates of our spacetime minimum length (1.1616229 x 10-35 meter) and our minimum time interval (5.39116 x 10-44 second). Divide the first by the second and you get the speed of light. That's why it is logical to consider them as the minimum possible dimensions we can give the spacetime quantum.

Significantly, there is also a lower bound for speed in our universe. A particle transferring from one quantum to another at less than the maximum speed is also forbidden. Now this is really weird. But suppose a particle tried to move at half of the maximum speed by jumping between quanta in twice the minimum time. This means moving half a minimum length in each minimum time interval. Alas, there is no half of a minimum length. The quantum is indivisible. For transfer between two quanta, no speed less than the upper bound is allowed. The lower bound and the upper bound are the same!

This really affects elementary particles of matter more than us. They are following these quantum rules for their speed from quantum to quantum, down at infinitesimally small lengths and times. We experience the average movement of huge populations of these particles and don't notice the effects of quantization.

Neverthless, individual particle speeds slower than the maximum (light speed) can only be achieved by a particle pausing in quanta between transfers at the maximum speed. The speed we measure is the average gained by summing the pauses and transfers over a sufficient number of particles.

What this really means is that when you quantize space and time you quantize speed. So what? So you've found the physical basis for a theory that predicts time slows if you move fast enough. And if time slows as you travel in your spacecraft you age less quickly than planet-bound folk. And there are other implications. But let's return to the stadium and confirm that race-winner Achilles has aged less than the spectators.

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. . .the mind where thought's seine catches within  . . .