Time Flies Like an Arrow

The current issue of Scientific American has an interesting article by Craig Callender. It’s called Is Time an Illusion? (it’s behind a paywall here). The article is about the fact that most of the fundamental equations of physics don’t contain any term which looks like what we think of as time. Most people find this kind of surprising. Time seems so fundamental to the world we live in. You would expect it to underlie all of physics. But the heart of modern physics doesn’t seem to think that time is very important at all. At least it doesn’t think that time is much like the way we think about it.

We think of time using a model which is known as the Arrow of Time. A key part of the arrow of time is its directionality. The future and the past are very different sorts of things and you can always tell them apart. If you follow this link, you’ll find a list of 7 types of time asymmetry. It turns out that none of these appear to be very fundamental to how the world in which we live works when you get down to fine scales.

Here’s a video which displays a related phenomena. Watch it now.

Did the ending surprise you? It’s completely real. There’s no trick photography. You can find a good explanation here.

It has to do with something called Reynold’s number. This is basically the speed at which the fluid is flowing divided by its viscosity. Below a critical Reynold’s number, fluid flows in a manner which is called laminar. Laminar flow is reversible. Above the critical Reynold’s number, fluid flows in a manner which is called turbulent. Turbulent flow is not reversible. We’re not used to seeing low Reynold’s number flow. It’s uncommon in the world we live in. Therefore we’re surprised by what happens in the video. If you were a paramecium, you would not be surprised by the video. In a lot of domains fluid flow is reversible, in the same way that in a lot of domains time doesn’t have the same character we expect it to have.

You probably already know that the key to all of these puzzles is something called entropy. Entropy is a measure of how the macrostate of a system is distributed over a set of microstates. Big, complex entities like us are used to interacting with a world which is made of macrostates which are each composed of very large numbers of microstates. Therefore entropy is very important in our world. But if you shift to a world which doesn’t have a large difference between the microstates and the macrostates, then entropy becomes much less important. We find that sort of world surprising, even though it’s actually much simpler than the world we live in.

BTW, the title of this post actually hasn’t got much to do with the subject. It comes from linguistics. Consider this Groucho Marx quote:

Time flies like an arrow. Fruit flies like a banana.

For each sentence, identify what part of speech each word is. Isn’t that odd? It is used to illustrate syntactic ambiguity.

Maybe language is even weirder than time.

Of course Groucho also said:

Outside of a dog, a book is a man’s best friend. Inside of a dog, it is too dark to read.

But that’s a story for a different day.