2 ms·
Extreme sensitivity to initial conditions occurs at the level of interactions of molecules in a gas. Errors in position or velocity accumulate exponentially ov
by pfdietz 2y ago
Extreme sensitivity to initial conditions occurs at the level of interactions of molecules in a gas. Errors in position or velocity accumulate exponentially over very short time scales. It's so sensitive that moving a single atom on the other side of the universe would, by the small change in its gravity, cause O(1) changes in the position of molecules in less than a millisecond.
- kennysoona 2y ago> It's so sensitive that moving a single atom on the other side of the universe would, by the small change in its gravity, cause O(1) changes in the position of molecules in less than a millisecond. Could you expand on how this is possible?
- pfdietz 2y agoSmall errors in position/velocity are amplified exponentially at each collision. Air molecules collide on average about once every 200 picoseconds. So, an error of one part in 10^1000 will build up to an O(1) difference in about O(log 10^1000) collisions, or maybe ~1 microsecond (the "less than a millisecond" claim was being very conservative.) It's a testament to the power of exponential growth.
- Sharlin 2y agoOf course it could not. As is well known, the speed of causality has a hard upper limit.
- pfdietz 2y agoWhat I meant wasn't that moving the atom causes a FTL propagation of an effect, but that in two situations that differ just by the position of said atom, the changes become visible that quickly (after any imagined classical propagation delay).
- mitthrowaway2 2y agoAh, but does relativity count as classical physics?