Entropy and the Arrow of Time

Somebody I talked to yesterday about what should the topic of my post be suggested that I should write something about cosmology, in particular the Big Bang and the ultimate fate of the universe. Being mostly interested in condensed matter, I am by no means an expert in cosmology (I’ll leave that to Corky). However, I will not abandon the request, but instead, spin it in a more condensed matter direction, by talking about Entropy.

Entropy is a quantity that measures disorder. The more ordered your system is, i.e. the less ways you can arrange the constituents of your system, the less entropy you have and vice versa. I like to use the example of how messy my room is to visualize this. When I clean my room, I would pick up the random articles of clothing, books, etc and put them in the places where they belong. Now imagine, I stopped cleaning my room for a couple of weeks. This would result in clothes on the ground, books on my bed, empty bottles on my desk, etc. anything can be anywhere. This means that there are more ways for my personal belongings to be arranged when my room is messy than when my room is clean (when everything would be at its place), so the entropy increases as the messiness of my room increases. Now, notice that left on its own (i.e. if I don’t put the conscious effort to put some order in my room once in a while) the entropy of the system that is my room increases with time. This is, in fact, the essence of one of the most fundamental (if not the most fundamental) laws of nature – The Second Law of Thermodynamics, which states that left on its own, the entropy of any system increases with time.

I know what you are thinking, “What does this talk about the messiness of your room and the law of increasing entropy has to do with the universe, the Big Bang and the universe’s ultimate fate?” Ok, here you go, read this short story by the greatest sci-fi writer Isaac Asimov: The Last Question.

Now that you’ve read this story (if you haven’t, please do), we can discuss some physics (or actually, some philosophy, but you know, sometimes there isn’t that much difference between the two). Einstein, with his Theory of Relativity, showed that the concept of time is not absolute, and time can be treated simply as another coordinate, much like the three spatial coordinates that define the three dimensional space we are used to. (A more in-depth explanation of the Theory of Relativity will be the topic of one of the next posts.) However, despite the relativity of time, the arrow of time is always well-defined. We can always tell future from past by measuring the entropy and applying the Second Law of Thermodynamics. At the instance of the Big Bang, the entropy was zero. Since then (about 13.8 billion years ago) the entropy of the universe has been increasing until it will eventually reach its maximum value, at which point all the matter of the universe would be evenly distributed and no physical process would be possible. Time eventually stops, resulting in the “heat death” of the universe.

I believe that one of the most unsettling parts of the Bing Bang theory is the question of what caused the Big Bang, and what was there before the Bing Bang. Having the arrow of time defined with regards to entropy, however, makes this question nonsensical… unless, of course, a Cosmic AC (or God) has managed to find the answer of how the entropy can be reversed.