Fun fact of the day: physics has a word that can mean either “slow” or “fast”!
Some of the book I’m writing has to do with how the meaning of specific words in physics (like mass or energy, for instance) have changed over time. Sometimes, a word started out meaning one thing and then split into several meanings. Other times, it started out meaning several things and then merged into a single meaning. Often, none of the meanings are exactly what the word started out meaning before it was introduced into physics. Such is the case for the word mass, a subsection of a bit on the Higgs boson I’ve been working on this week.
But today while answering a question on Stack Exchange I happened to run across the word adiabatic again and it reminded me that, like mass, this is another great example of a word that has drastically changed meaning over time. In some cases, it has ended up meaning exactly the opposite of what it started out meaning.
There’s a word for words like this: auto-antonyms. For example, the word nonplussed started out meaning: so surprised or confused by something that you aren’t even sure how to react. But in North America, it has informally come to mean: unphased by or undistrubed by something. The word is its own antonym in that it can now mean either surprised or unsurprised, depending on who’s using it and how.
And incidentally, there are also words that sound like they would be opposites (like flammable and inflammable) but happen to be synonyms. Language is a funny thing!
As one might expect, scientists — and especially physicists — try to be more precise with language when writing academic papers and communicating with each other than the average person is accustomed to being. But I think many people would be very surprised to find how dynamic and flexible the language of physics is. It’s not that a word enters the physics lexicon and then gets a fixed meaning that everyone uses and it never changes. As the state of our knowledge about the universe evolves, so does the language along with it — often in ways that are unpredictable and very counterintuitive. Sometimes, viewed in hindsight, it seems like it would have been better to just scratch a word and come up with an entirely new one, or several — make a clean break. But there is no way to enforce top-down rules about how everyone should be using words. Usage just gradually evolves over time as different intersecting communities use it in slightly different ways. And sometimes they surprise each other when they run into contradictory interpretations.
In my book, I recently wrote about the much longer history of the evolution of the word mass. But since it’s a lot simpler and easier to explain in a single blog post, I’d like to just briefly go through what happened with the word adiabatic to illustrate how language in physics can shift.
The word was first introduced in the 19th century to mean something like “thermally isolated”. It came from the Greek word adiabatos meaning “impassable”. Some physical processes happen through exchanging heat with their environment. And others — the ones called adiabatic — happen without any heat getting exchanged. It seemed simple enough: if there is heat flowing in or out of a system during the process, it wasn’t called adiabatic. If the system was isolated somehow, preventing the flow of heat, then it was adiabatic.
The simplest way to prevent heat from flowing in or out of something is to create a barrier, for example to use thermal insulation. Most homes have insulation to prevent heat from flowing in or out as the seasons change. This still allows a little bit of heat in or out, but it’s good enough to save on an electric bill. If you want better insulation and had enough money to spend, you could add a layer including a sealed vacuum chamber. Heat needs some kind of material in order to transfer, it won’t go through a vacuum. So this would be about as close to perfectly adiabatic as you can get. This fits pretty well with the Greek root of the word, which referred to an impassable barrier.
But what if there is an easier way to prevent heat transfer, that doesn’t involve using any barriers? One of the key examples of an adiabatic process which emerged during the development of thermodynamics was the heat engine. This may sound surprising, because if you’ve ever touched an actual running engine, like the one in your automobile, you’ve probably noticed that it gets pretty hot. And if you’re able to feel that at all, then it means it’s not thermally insulated!
In abstract discussions of thermodynamics, this was usually described in terms of a more idealized heat engine. A heat engine is a device (either real or hypothetical) that uses a temperature difference between a hot and cold reservoir as a power source in order to efficiently perform useful work. It passes through a series of stages during which the work is performed, and then the whole thing repeats in a cycle. Even though heat engines don’t necessarily require any kind of thermal insulation, some of the stages of heat engines happen so rapidly that there is no time for heat to transfer in or out during that stage. Hence, these stages also started being referred to as adiabatic. One example is when gas in a cylinder gets rapidly compressed by a piston: this is called adiabatic compression. The heat engine only works if this stage happens fast enough that no heat is transferred. A similar thing happens when the piston comes back up and the gas in the cylinder expands again. This is called adiabatic expansion because it also happens faster than any heat can flow in or out.
Some of the stages in this process are adiabatic in the sense that no heat is exchanged with the surrounding environment, but none of them need be adiabatic in the sense of being insulated by an impassable barrier. It’s sort of like that trick when you whirl a bucket of water over your head very quickly in a circle — if you do it fast enough, centrifugal force will keep the water from falling out, even if there is no lid on it. If you do it more slowly, you’ll get soaking wet! The centrifugal force creates the equivalent of an invisible barrier, but it’s a barrier that is only impassable as long as the process is happening rapidly enough.
This already represents a slight shift in what the word means. It went from originally meaning isolated to meaning no-heat-transferred, and then in certain contexts such as when referring to the expansion of a gas it came to mean “fast”. Adiabatic expansion is essentially another way of saying “fast expansion”.
But what’s really ironic is that — through further developments in the progression of physics it has become a lot more common today to see the word adiabatic being used to mean “slow”.
Gradually, the idea of an adiabatic process started intermingled with the idea of an isentropic process. An isentropic process is one where there is no entropy change. The 2nd law of thermodynamics says that the entropy in any physical system never decreases (unless there is a greater increase in the entropy of the environment to offset it). So the overall entropy can only ever remain the same or increase. The condition for the entropy to remain the same is that any changes to it have to happen in a way that started frequently being referred to as “slow and adiabatic”.
Slow because rapid changes tend to be associated with the internal entropy of a system increasing, and adiabatic because if the system loses heat to the environment, entropy will leak out as well.
If the system is thermally isolated, then the changes just have to be slow enough for the system to remain in equilibrium while the process is happening. If the changes happen too fast, then the system may depart from equilibrium and instead of the nice neat linear equations of classical thermodynamics governing it, you start to need more sophisticated physics like chaos theory, turbulence, and non-linear dynamics to understand what’s going on. If you’ve ever driven a boat (or ridden in one), you may have noticed that when you drive slow enough the water remains calm. But if you speed up you’ll see big frothy waves behind the boat. The water is no longer in a state of equilibrium. These sorts of changes are much harder to predict and describe using equations. Turbulence like this also happens in any kind of fluid when things start happening too fast, including during the free (adiabatic) expansion of a gas.
The words isentropic and adiabatic became closely associated via the phrase “slow and adiabatic”, because both were linked to the idea of a reversible process — one where the amount of information in the final state of a system is enough to entirely reconstruct what the initial state was. When changes happen too fast, entropy increases, the changes become irreversible, and there is no longer any way to reconstruct the initial state from the final state. Information has been lost, or at least —it’s forever mixed up with the rest of the complexity in the environment. Gathering all of that information back together again and assembling it would be equivalent to putting Humpty Dumpty back together again after he’s fallen off the wall! That is to say, thermodynamically irreversible.
But in the 1920’s, during the development of quantum mechanics, Max Born and Vladimir Fock proved a theorem which became known as the adiabatic theorem. Even before this, the term had probably already started to mean “slow” in many contexts. But the publication of this theorem cemented the word adiabatic even further as meaning specifically “slow” (at least in quantum mechanics) rather than “isolated”.
In explaining the adiabatic theorem, they distinguished between two types of processes. An adiabatic process they defined as one that happens slowly enough that there will be no sudden change to the quantum state of a system. This meant, for instance, that if a quantum system starts in its ground state (lowest energy level), it will remain in its ground state. The state at the end may look very different, but at least it got there through a process of gradual change that didn’t involve any sudden jumps. This kind of process is reversible. In opposition to this, they defined a diabatic process as one where changes happen so fast that the quantum state doesn’t have enough time to adapt. Depending on the environment a system is in, these changes may mean that at the end the system will have some probability to have jumped to a completely different energy level. This is because the environment helps to define what the “energy eigenstates” of the system are — the different possible values of energy that can be observed when the system is measured, or interacts with its environment. If there was no time to slowly adapt to the new energy eigenstates, then measuring it after the process is done can result in a sudden change in energy. (Somewhat analogous to the change in heat during a non-adiabatic process in thermodynamics.)
This gave rise to the related phrase adiabatic approximation which refers to an approximation that applies only if the changes to a system happen sufficiently slowly. It doesn’t matter whether the system is isolated or not (usually the words open and closed are used for this now). As long as it is changing slowly enough it’s considered an adiabatic process and therefore the adiabatic approximation applies. These kinds of slow changes, in quantum mechanics, are also associated with reversibility. So long as things change slowly enough, the process is reversible and there is no entropy increase.
Hence, the word has come full circle and now means almost exactly the opposite of what it once meant. Of course, the old “no heat exchange” sense of the word is still used often in thermodynamics, so this could potentially create a lot of confusion if a quantum physicist sat down with a physicist who specializes in some kind of classical thermodynamics. But thankfully, the word is long enough that it’s not used in many science news articles. So it hasn’t created as much confusion as the use of the word “mass” has for the general public.
And that, my friends, is the story of how a word that once meant “fast” came to mean “slow”!