Question

the question is not about classical mechanics but it's in 8.01, heisenberg uncertainty principle lecture. dp*dx >= h/2pi so if we take billiard ball in to triangle, it's velocity increase and my question is, how universe conserve the energy? kinetic energy increasing, what is decreasing?

Answer 1

heisebergs uncertainity priciple is not applicable to billiards ball i think...only for really small particles like the electrons which are moving at very high velocities. Also KE of a ball increases then the energy stored in our body (which pushes the ball) decreases and the ball looses its KE afterwards due to production of heat due to friction.

Answer 2

yes i know heisenbergs uncertainty principle doesnt really works for macro world. it is not that important. lets take electron free in space and not moving. you captured it in atom, and it should goes like 10^6 m/s. its KE increase. what is the energy stored in our body? we are not touching the ball or electron, we just decrease dx and make its momentum uncertain.

Answer 3

A bound electron is not in any way like a moving particle. Its existence is a smeared-out probability density described by its wavefunction. It has energy (which can be found using the Schroedinger equation) but not kinetic energy per se. But the neat thing is that the energy predicted by Bohr, based on classical physics (electrostatic centripetal force, electron in circular motion, total static PE) gives exactly the same ionization energies as predicted by Schroedinger and verified experimentally. The Bohr radius and the most probable radius in the electron cloud are also the same, for Hydrogen at least. So we can often use the classical analogy if we don't take it too far. I'm guessing mixing the classical analogy with the uncertainty principle may be taking it too far.