Thursday, January 11, 2007
Over the holidays I was reading about entropy and what it means to quantum mechanics. Apparently all the formulas of quantum mechanics are time-symmetric, meaning they have no time-directionality. The question was, how do we get a time arrow and things like directionality of entropy if these principles are not present in the underlying quantum physical laws. In other words, in quatum mechanics you can find the equations that govern a glass reassembling itself from fragments on the ground, and filling itself with the water spilled on the carpet and jump back on the counter next to you playing wii tennis. Entropy on the surface seems a very anthropic principle, since we are needed to judge what is disordered and what the direction of time is. Of course there are good explanations involving phase space that kind of explain entropy but it still seems odd that quantum mechanics is symmetric. On this topic, I also recently stumbled across some great lectures by non other than Hans Bethe entitled quantum physics made relatively simple, and a personal entropy calculator, perhaps armed with these you can make sense of this connundrum. It's never too late, even the reverse-sprinkler problem of Feynman was recently elucidated.... "We discuss the reverse sprinkler problem: How does a sprinkler turn when submerged and made to suck in water? We propose a solution that requires only a knowledge of mechanics and fluid dynamics at the introductory university level. We argue that as the flow of water starts, the sprinkler briefly experiences a torque that would make it turn toward the incoming water, while as the flow of water ceases it briefly experiences a torque in the opposite direction. No torque is expected when water is flowing steadily into it unless dissipative effects, such as viscosity, are considered. Dissipative effects result in a small torque that would cause the sprinkler arm to accelerate toward the steadily incoming water. Our conclusions are discussed in light of an analysis of forces, conservation of angular momentum, and the experimental results reported by others. We review the conflicting published treatments of this problem, some of which have been incorrect and many of which have introduced complications that obscure the basic physics involved."