Credit: Peter MacDonald, Edmonds UK.
While I don’t plan on giving a complete rundown of every sentence in my new Symmetry book every now and again, I figured I’d run some ideas by you and see if you have any followup questions. At the moment, I’m working on Chapter 2, with the working title, “Does Entropy Increase with Time or does it Make Time?” (Rest assured, there’s a lot of material that wasn’t in the original io9 article, but I like the title.)
Apropos of this, I’ve spent the weekend reading fellow Pennsbury High School alum and Dutton author Sean Carroll’s book, “From Eternity to Here,” who addresses this very question is a fair amount of detail. It’s a very well-reasoned book and has a very good tone, but in the end, I remain unconvinced. I still fall in the “time makes entropy” camp (which, to be fair, is the orthodox view, which is presumably one of the reasons why Sean wrote his book).
As you may know, the 2nd law of thermodynamics says, colloquially, that entropy always increases with time. Practically speaking, this means that energy will flow from hot materials to cooler ones in the form of heat.
Is there any loophole that could allow us to get around the Second Law? In the 19th century, James Clerk Maxwell devised a cool thought experiment to cheat entropy. Maxwell was no slouch. He unified all of electromagnetism into a single theory, combining a number of very disparate looking ideas into “Maxwell’s Equations,” which served as the principle inspiration for Einstein’s theory of Special Relativity.
Maxwell imagined a box filled with air molecules, some moving faster, and some moving slower than one another, but thoroughly mixed. In the middle of the box was a partition, separation the left from the right with a little hole and a trap door in front of it.
Maxwell’s idea was that whenever a “cold” molecule (one moving slower than average) approached the trapdoor from the left side of the box, a very clever demon would open the door and let the molecule through to the right side of the box. Likewise, whenever a “hot” molecule approached from the right, the demon would open the door and let the molecule go into the left side of the box. Otherwise, the door would remain closed.
That’s it, but it this has profound implications. Assuming the trapdoor is one of those no friction, the demon is basically making the left side of the box hot and the right side of the box cold. And he’s doing it without breaking a sweat.
Image Credit Science Photo Library
This is exactly the opposite of what’s supposed to happen in thermodynamics. Remember how it’s supposed to work. The takeaway about how the 2nd Law works is that heat should generally flow from hot regions to cooler ones. It’s probably not too much of a stretch to suppose that you didn’t even need a popular physics book to tell you that.
What gives? I admit that I first saw this problem when I was an undergraduate and was profoundly unimpressed with it. Who cares about a few atoms here and there? Besides, if the 2nd law is really only statistical in nature, does it really matter if we can circumvent it?
Yes, younger me. It does.
The 2nd law is supposed to be a hard and fast law of the universe, and a back door would be amazing. Why do we need to continuously burn coal, petroleum, or natural gas? Because most of the energy used by our machinery gets wasted as heat. If we could somehow employ a few million of Maxwell’s demons to recover the heat into useful energy, we’d be pretty much set.
It was until nearly a century after Maxwell came up with his demon that we really understood why the 2nd law remained inviolate. In 1948, Claude Shannon, a research scientist at Bell Labs, founded a branch of research known as “Information Theory.” Just as quantum mechanics made all of modern computing physically possible, information theory revolutionized cryptography, communication, and made innovations like the Internet possible.
One of the major results of information theory is that information and entropy are more or less the same thing. Suppose I send a message that is exactly two characters long. How many different messages can I send? I could in principle send you 26×26=676 different “words,” but most of those letter combinations are completely meaningless. Only a few (the Scrabble dictionary lists 101) are actual words.
To the computer scientists among you, this means that while in principle it would require about 10 bits (the 1’s and 0’s that are used to store data) to differentiate between every possible 2 letter combination, if you know that you’re transmitting a word, you only need about 7 bits. What a savings!
Communications can be significantly compressed by noticing that certain letters are used less frequently than others. E’s, for example, show up way more often than Z’s in the English language. This is why the former is worth only 1 point in Scrabble and the latter is worth 10. It also explains why “E” in Morse code is:
while Z is:
— — ••
Z takes far longer to tap out, but that’s okay, because you’re going to do it far less frequently. Another way of thinking about this is that the more complicated (or unlikely) a message is, the more information it carries, and the more bytes of data you’d need to store it on a computer.
What does all of this have to do with Maxwell’s Demon? Every time the demon has to decide whether or not to let an atom through his trap door, he takes a measurement and makes a recording of the speed of the atom. The very existence of that recording (whether in the brain of the demon, on a pad of paper, or in a computer) adds information to the universe, and information and entropy are the same thing.
The demon doesn’t really decrease entropy by playing his gas games; it’s just that the increased entropy goes in large part to creating his measurements and memories.
Your own memories, then, are in some sense a testament to the fact that the entropy of your brain is increasing with time. The fact that you remember the past and not the future really does just seem to be a testament to the increasing entropy of your brain.
Followup questions are appreciated.