Do you have a source on that? My back-of-the-envelope says 7 is not enough. For 1 kg located 1 m away from 60 kg, gravitional force is on the order of 10^-9 N. IIRC, angular uncertainty in a billiards system roughly doubles with each head-on collision, so the exponential growth would only kick in around a factor of 128, which still wouldn’t be large enough to notice most of the time. (Though I believe the uncertainty grows faster for off-center hits, so that might be what I’m missing.)
I heard it a long long time ago in a physics lecture, but I since verified it. The variation in where a ball is struck is magnified by the ratio of (distance to the next collision) / (radius of a ball), which could be a factor of 30. Seven collisions gives you a factor of about 22 billion.
I also tried the same calculation with the motion of gas molecules. If the ambient gravitational field is varied by an amount corresponding to the displacement of one electron by one Planck length at a distance equal to the radius of the observable universe, I think I got about 30 or 40 collisions before the extrapolation breaks down.
Do you have a source on that? My back-of-the-envelope says 7 is not enough. For 1 kg located 1 m away from 60 kg, gravitional force is on the order of 10^-9 N. IIRC, angular uncertainty in a billiards system roughly doubles with each head-on collision, so the exponential growth would only kick in around a factor of 128, which still wouldn’t be large enough to notice most of the time. (Though I believe the uncertainty grows faster for off-center hits, so that might be what I’m missing.)
I heard it a long long time ago in a physics lecture, but I since verified it. The variation in where a ball is struck is magnified by the ratio of (distance to the next collision) / (radius of a ball), which could be a factor of 30. Seven collisions gives you a factor of about 22 billion.
I also tried the same calculation with the motion of gas molecules. If the ambient gravitational field is varied by an amount corresponding to the displacement of one electron by one Planck length at a distance equal to the radius of the observable universe, I think I got about 30 or 40 collisions before the extrapolation breaks down.
Awesome. Thanks for the spot-check, I’ll probably use this as a dramatic example going forward.