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The physical limit of trick shots in billiards

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For anyone who has ever had their ass handed to them in a game of pool, take comfort knowing that in the end, physics beats everything. A physicist has calculated how many collisions it takes for billiards to be impossible without a supercomputer. It's less than you think!

Beginning pool players (or the hopelessly incompetent) know the despair of trying to do a seemingly simple mechanical thing — make one ball hit another so the second ball goes into a pocket — and failing entirely. It's generally due to lack of skill and practice. Lack of practice translates into a large amount of uncertainty as to how the ball will move when it's hit a certain way. However, as our practical certainty of the laws of motion specific to billiard balls increases, the range of motion that the second ball takes decreases. It will go where we want it to go. We know and control the variables that affect its motion.


Professor Michael Berry, a physicist, tracked how those variables increase as the number of billiard ball collisions increases. He had started studying such things on a larger scale, determining how the uncertainty of the position of a single electron could affect our certainty of the outcome of later molecular collisions. As the possibilities increased, how long before we knew, practically speaking, nothing about how a system of molecules would move? Berry calculated that, after 60 collisions with other molecules, uncertainty about a single electron will result in an inability to predict an entire molecular system. This would happen in milliseconds. Then Berry put aside the light work and got down to the serious business of examining the physics involved in a game of professional pool. How many collisions can a billiard ball make before we have no way of knowing its eventual trajectory?

The joker in the deck is gravity, a force that no one can entirely "screen out," no matter where they are in the universe. It makes a difference in the path of molecules and the path of billiard balls. For the first collision of a billiard ball, we can control the variable so well that we don't really have to think of gravity as anything other than the force holding the ball on the table. We control all the variables that matter: the placement and force of the hit. After a couple of collisions, we're less able to determine where the balls go. Even on an idealized surface, there are many options depending on the exact force with which the balls meet, and the forces acting upon them. After six or seven collisions, you don't just have to worry about the gravity of the Earth, but of the gravity of the people walking around the table. Exactly where these people are, and the gravitational pull their mass exerts on the balls, will determine whether the balls go one way or another. This means that, unless a pool player can carefully weight the people around the table, determine where they stand, there's no possible way for anyone to be certain of the trajectory of a ball after six or more collisions.


So if you see someone doing a trick shot that involves six or more collisions, you've crossed over to the X-Men universe and found yourself a mutant.

[Via A Passion for Science, Regular and Irregular Motion]