Xeno Meets Planck

Ok, so lets see if I can say this properly because I even only have the most tenuous grasp of this material. So Zeno (Xeno?) said that if you arrive at a crossing, but can only cross in measurements half the distance. So first 10 meters then 5 meters then 2.5 meters and so on into infinity thus hitting an infinite number of points along the line but never crossing. I mean the math works on that, you can divide by 2 forever. BUT! (I so wanted to say it like that too) If we have established that the Planck length is the smallest unit of measure and that it approximates the distance an electron travels during a quantum leap. And there is nothing in between, electrons don't slide between those points, they are there or they are not. And when we measure we see where they are but never see them moving to or from. (get to the point you hack theoretical physicist!) So in practical terms, you could say there are a finite number of points on a line since we can't put any kind of measurable point between the Planck Length.
- Jason e Johnson (age 33)
United States

Most physicists don't really think of Xeno's argument as being a paradox. So you can divide up a length into an infinite number of parts- so what? The length doesn't change. You can divide up the time it takes to travel that length into an infinite number of parts. That doesn't change the time either. 

Anyway, let's say that for some reason, Xeno-related or not, one worries about what happens when things are divided down to a Planck length.  We actually don't know what happens on that scale. Maybe the string theorists will figure it out. 

One thing we don't think is that "it approximates the distance an electron travels during a quantum leap". Quantum leaps aren't actual processes in modern quantum mechanics; they're just words left from Bohr's semi-quantum model. Back in that model, the distances involved in the alleged leaps were far bigger than a Planck length.

Mike W.

(published on 06/04/2013)