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Poincare’s “Return”

2nd January 2015 By Anthony Peake

As we will recall from our school-day physics Newton’s second law of thermodynamics states that heat flows from something that is hot to something that is cold. This is only a one-way process. In the 19th century there was a need to explain how this worked at a molecular level. The Austrian physicist Ludwig Boltzmann envisaged trillions of microscopic molecules enclosed in a box. He considered this assemblage of molecules to be a gas. The temperature of the gas would be determined by the speed of the molecules. Soon the high speed molecules would collide with the slower ones and in doing so they would give up some of their kinetic energy. Over time the heat would diffuse across all the all the molecules and the gas would reach a uniform temperature. However this model was attacked by Henri Poincare who proved that all the molecules would eventually, according to Newton’s law of motion, must return back to their initial state. In other words the circumstances reoccur. However the length of these “cycles” are mind-bogglingly huge. Roughly 10 to the n seconds where n is the number of molecules in the system (there are a trillion trillion in 40 litres of air) So that would be 10 to a trillion trillion. The age of the universe is only 10 to the 17 seconds so these cycles are huge, even for a small number of molecules. However huge these cycles are they are finite so in a universe with infinite time these cycles will happen innumerable times. Of course we know that time dilates at the speed of light and we also know that time is a subjective construct. So could subjective time dilate within the brain to such an extent that all the molecules creating somebody’s life could also be repeated?

 

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