pretendy

On the 5th of September 1906, while his family were taking an afternoon walk, the scientist and mathematician Ludwig Boltzmann hanged himself. Inscribed on his tombstone is this equation which marks his tremendous contribution to 20th century physics. His theories were well ahead of their time and were largely rejected by his contemporaries. Unfortunately he never lived to see the true impact of his work.

This is this Boltzmann Entropy Formula and it is one of the most fundamental equations in modern physics. It provides a theoretical basis for the 2nd Law of Thermodynamics – that the entropy (or disorder) of the universe is always increasing. It is a direct consequence of this that buildings decay and become decrepit when abandoned; that wine glasses shatter into shards of glass; and that the universe will one day evaporate into heat.

If you put ten coins in a row on a desk, there is only one way you can arrange them so they all show heads. In this case we would say the coins are well ordered (or in thermo language, have a low entropy). On the other hand, there are a couple of hundred ways of arranging the coins such that half of them are heads and half are tails, where we would say they were disordered.

Boltzmann formulated this relationship between S (the entropy), and W which counts the number of ways of microscopically arranging a system to give it the same overall state.

Though there are only 252 ways you can achieve full disorder with 10 coins, imagine a beaker of water and ink containing billions of billions (of billions) of molecules. When all the ink molecules are arranged together as a drop, the system is well ordered. However the number of ways of arranging all the molecules to be well mixed is astronomically larger! It is this reason, coupled with the law that entropy must always increase over time, that a drop of ink will dissipate and mix when placed in a beaker of water.

It is strangely appropriate that this equation appears on the tombstone of its creator as it acts as a constant reminder that everything dies, decays, and turns to dust.

(photo credit: illpadrino)