Monday, July 19, 2010

From Eternity to Here: More Booknotes

Sean Carroll has set himself the very difficult task of explaining entropy in non-technical terms. I was with him for a while, but he loses me when he tries to explain unmixing of water and oil:

...water molecules tend to stick to oil molecules - and due to the chemical properities of oil and water, they stick in very particular combinations. So when the oil and water (or vinegar) are thoroughly mixed, the water molecules cling to the oil molecules in specific arrangements, corresponding to a relatively low entropy state.

Not true and total bullshit quite right. Water and oil molecules are unmixed by two effects, and the more fundamental one is the effective mutual repulsion of oil and water molecules. Less important is gravity - oil has a lower specific gravity. The real problem, though, is that Sean doesn't want to acknowledge that we need to count energy states - simply coarse graining over spatial volumes is not enough here. The mixed state has higher energy (due to the two kinds of forces mentioned above, and that's why it has lower entropy.

It's an uncharacteristic mistake, so far as I can tell. He's usually quite careful - but it is a freshman chemistry mistake.