A Supertask Shows How Particles Can Spontaneously Start Moving

A particle, traveling at a meter per second, knocks into the square. Because the particle’s speed is a meter per second, and the square is a meter wide, within a second, all the motion that was introduced into the square is gone. But there is no particle ejected. The infinite amount of collisions means there is no final particle. The motion just stops.

The problem with thought experiments is that if they lack rigor, it’s easy to argue into something that is contrary to the laws of physics. With a verbal description, you can get something like Zeno’s paradox, which seems like a contradiction until mathematical rigor is applied.

I think the above is such an example. Somebody has taken a liberty with infinities or made a hand-wavy argument somewhere in the middle of all this. The conclusion violates conservation of momentum and energy, so there’s a flaw somewhere. I’d like to hear more about how the motion ceases after one second. There’s a dodgy assumption in there, I’m sure. There may be an infinite number of particles but they are also infinitely small, so how do you determine their cross-section and the resulting collision rate?

The paper isn’t even that subtle.

What happens at t = 1? By that time, every particle Pi has collided with its immediate left-hand neighbor and so is stationary. Therefore, all the particles are stationary.

Um, what? At that point I confess I stopped reading. This sounds like a technicality of math that doesn’t apply to a real system, i.e. there is no “last particle” that’s moving. If you assume something that is physically impossible, you can come to just about any conclusion you want.