Q & A: entropy of light and messy rooms

Q:
I learned about randomness is class today. My teacher says it's called entropy. She says it's why I have to keep picking up my room. We also learned about light. My question is - when light travels through space, like from a star, is the beam of light entropic (sp?)
- Bo Fox (age 12)
Vancouver, WA, USA
A:

That's a very nice question. I'll give a beginning answer, but it's one of those questions where if you keep following it up, there are deeper layers.

Entropy is sort of connected to randomness. The problem is, we don't really have a clear meaning for "randomness", or how to put some number on it, so it's better just to explain what entropy is. Entropy does have a definition, and we can give a precise number saying how much there is.

Here's  a "starter" definition of entropy. It's the logarithm* of the number of different quantum states something might be in. In other words, the more different possible microscopic states something might be in, the bigger the entropy. So for example if you have a rubber ball (or anything else) and heat it up, it gains entropy, because the extra energy can make more ways for the little rubber molecules to shake around.

What would that have to do with your room? There are many more ways of leaving it messy than there are of having it orderly. So if things get moved around without much attention, you're more likely to find it messy. I know that by sad experience. It's not really the same as the actual entropy in physics, but it's sort of a nice picture to help get you started.

As for starlight, yes, it is entropic. There are all sorts of slightly different wave patterns it can have. There is a very precise way of calculating the entropy of the light, which depends on the total amount of energy, the distribution of different frequencies, and the range of different directions it's traveling.

When light from the nearest star (the sun) hits the earth, it warms the earth. The same energy then leaves the earth in the form of lower-frequency (mostly infrared) light. Both the incoming light and the outgoing light have entropy, but the outgoing light has more even though it has the same amount of energy. That's the way things always go- the total entropy just keeps going up. The fancy name for that is the Second Law of Thermodynamics.

Mike W.

*Rather than just give the count of the states, we use the logarithm so that the combined entropy of two things is the sum of their entropies. That's because if you have two things, the total number of ways they can be arranged is the product of the number of ways each can be arranged. For example, with two dice, you have 6x6 different possibilities. The logarithm of a product is the sum of the logarithms of the factors.

(published on 06/29/2013)