Transcript from Brian Cox, ‘Sandcastle’ (Click above to watch)

‘Back in the 19th century engineers were concerned with the efficiency of steam engines. How hot should the fire be? What substance should you boil in the steam engine? Should it be water or should it be something else? These were profound questions and out of those questions came the science of thermodynamics. It’s when concepts like heat, temperature and energy enter the scientific vocabulary for the first time.

Now along with that deeper understanding emerged what is probably the most important law of physics for understanding the evolution of the universe and the passage of time. It’s called the second law of thermodynamics.

The reason why the second law of thermodynamics was so profound was because at its heart it contains a radically new concept, something physicists call entropy.

Entropy explains why, left to the mercy of the elements, mortar crumbles, glass shatters and buildings collapse. And a good way to understand how is to think of objects not as single things but as being made up of many constituent parts, like the individual grains that make up this pile of sand.

Now entropy is the measure of how many ways I can re-arrange those grains and still keep the sand pile the same and there are trillions and trillions and trillions of ways of doing that. Pretty much anything I do to this sand pile and as I mess the sand around, it doesn’t change the shape or the structure at all. In the language of entropy this sand pile has high entropy because there are many, many ways that I can re-arrange its constituents and not change it.

NOW LET ME CREATE SOME ORDER IN THE UNIVERSE!

Now there are approximately as many grains of sand in this sandcastle as there are in the sand pile. But now virtually anything I do to it will mess it up, will remove the beautiful order of this structure. Because of that, the sandcastle has a low entropy. It’s a much more ordered state. So, many ways of re-arranging the sand grains without changing the structure, high entropy; very few ways of re-arranging the sand grains without changing the structure, without disordering it, low entropy.

Now imagine I was to leave this castle in the desert all day then it’s obvious what is going to happen. Desert winds are going to blow the sand around and this sandcastle is going to disintegrate, it is going to become less ordered. It’s going to fall to bits.

But think what’s happening on the  fundamental level. The wind is taking the sand off the castle and blowing it over there somewhere and making a sand pile. There is nothing fundamental in the laws of physics that says that the wind could not pick up some sand from over here, deposit it here and deposit it precisely the shape of a sandcastle. In principle the wind could spontaneously build a sandcastle out of a pile of sand. There is no reason why that couldn’t happen it’s just that it is extremely, extremely unlikely because there are very few ways of organizing this sand so that it looks like a castle. It’s overwhelmingly more likely that when the wind blows the sand around it will take the low entropy structure of the castle and turn it into a high entropy structure of a sand pile.

So entropy always increases. Why is that? Because it’s overwhelmingly more likely that it will.

It seems incredible that a law that says that sandcastles don’t spontaneously form on the wind could solve one of the deepest mysteries in physics. But by saying that entropy always increases, the second law of thermodynamics is able to explain why time only runs in one direction.