When does the ball stop bouncing?

[Philosophy Explorer]

No units. That's why Planck's length is irrelevant.

PhilX

What do you mean no units? You are proposing a physical thought experiment. A ball falls through a distance. After some number of bounces, the distance ceases to be physically meaningful. You need to explain how the laws of physics become irrelevant in a thought experiment about physical law!

It's physical as I proposed it based on time, not length.

PhilX

[wtf]

It's physical as I proposed it based on time, not length.

So you hit the Planck time then. Same analysis with different numbers. The first bounce takes one second, one year, one trillion years, one age of the universe. After a finite number of bounces, a number easily calculated using high school math, your time interval is not physically meaningful.

The Planck time is around 5.3 x 10^(-44) seconds. Same analysis as before. After some relatively small number of bounces, your scenario is not physically meaningful.

I'm done here unless you say something sensible. You're playing games now.

[Philosophy Explorer]

It's physical as I proposed it based on time, not length.

So you hit the Planck time then. Same analysis with different numbers. The first bounce takes one second, one year, one trillion years, one age of the universe. After a finite number of bounces, a number easily calculated using high school math, your time interval is not physically meaningful.

The Planck time is around 5.3 x 10^(-44) seconds. Same analysis as before. After some relatively small number of bounces, your scenario is not physically meaningful.

I'm done here unless you say something sensible. You're playing games now.

Who's playing games? As we know, r x t = d. No r offered in this problem, therefore no d nor l. So Planck's length is irrelevant.

PhilX

[Science Fan]

Well, the mathematical pattern is easy enough to see. It's the summation of 1/2raised to the power of X, where the summation starts with X = 0. If you were to just run through a few summations, you'll see that for whatever number N we go up to, the summation will total (2N - 1)/N. So, if we go to infinity, we get the limit of (2N-1)/N as N approaches infinity, which gives us a limit of 2, since 1/N reduces to 0 as N approaches infinity. This does not mean the sum ever actually equals 2, but that it can never be greater than 2, even if we go out to infinity.

Math is non-empirical, so the trick is taking the non-empirical result that math gives us and making a sensible physical interpretation out of it.