# The Attraction of Low Energy

One of the tricky things about learning, science or other topics, is that so many things are interconnected. You can take separate courses on literature and history, and maybe separating those two things is a reasonable way to categorize information, but really you might have understood the literature better with the historical context, or you might have learned historical motivations better by reading some relevant literature. Until the day comes when we can learn everything at once, we have to learn topics separately and then later on, look back for connections. I mention this because what I am about to talk about is relevant to huge swathes of physics, chemistry, and biology, and can be discussed in a wide variety of ways, and is difficult to really get to the bottom of. But it’s a really useful thing to have in the back of your mind while looking at a lot of scientific ideas.

I am talking about energy minimization.

When we discussed the forces due to electromagnetic and gravitational fields earlier, forces that draw oppositely charged objects together or two objects with mass together, we were talking about energy minimization. This is because, in each of those fields, there is a potential energy associated with sitting at a high field value. Imagine a rock perched on a high precipice, feeling a large gravitational force pulling it downward. Unless it is being supported in a way to counteract that force, it will fall, because it is seeking to minimize its energetic state. Oppositely charged objects drawing together are minimizing their electromagnetic potential energy with respect to each other, by moving toward each other.

At the atomic scale, energy minimization is also a factor, but in a different way. Within a single atom, electrons can be in many states, the equivalent of the rock choosing different positions on the precipice. If there is only one electron, it will go to the lowest energy state. But in atoms with many electrons, additional electrons are required to take higher energy states because the lowest ones are occupied; you can imagine a pile of rocks growing up the side of the precipice. And if an atom had no electrons at all, free electrons nearby would see that atom as very attractive, because atomic states are lower energy than free states.

If you consider multiple atoms coming together, the electrons are still looking to minimize their energy. In some cases this may mean sharing an electron with a neighbor, lowering the energy of both atoms and forming a chemical bond. But for other configurations of electrons, bonds do not lower overall energy, and so these atoms are unlikely to form bonds. In other words, for some atoms, bonding is energetically favorable, and for some atoms it isn’t. We’ll get more into the nuts and bolts of this later on, but you can imagine a whole energy landscape that determines what things bond or don’t, what chemical reactions happen or never start, and thus what macroscopic phenomena are commonplace.

Processes that are more energetically favorable are the ones we see in nature, also called “naturally occuring”. Energy minimization is at the heart of many of these processes, but in such a wide variety of ways that the more you learn, the more you see it around you.