We are now going to delve into the notion of spontaneous symmetry breaking. The reason it is called “spontaneous” is that the starting point is a symmetric situation, yet the solution inexorably forces us to an asymmetric outcome. Let us return to the above example, which places us at the center of a circle, with food (say loaves of bread) evenly distributed about the perimeter. We could, of course, have broken symmetry by hand, for instance, by putting more food on one side of the circle than the other. In that case it would be clear as to what the preferred direction of motion would be–namely towards the point on the circle where more food is clustered. That would not be an example of spontaneous symmetry breaking, because the starting point was already asymmetric to begin with.
There are many other examples of symmetry breaking in nature. Evolution has shaped us, just as our environment has shaped evolution. We live on a planet where up and down are different due to gravity, which points in one direction, namely down. There is not an “up/down exchange symmetry,” in other words, here on Earth things fall down; they do not fall up! Given that there is no symmetry between up and down, it therefore makes sense that our feet do not look anything like our head.
On the other hand, if we are standing on flat ground, everything in the plane is rotationally symmetric, yet evolution has broken that symmetry when it comes to human anatomy: our body does not enjoy horizontal circular symmetry. Our eyes, for example, point in specific directions rather than all around our heads. Nature has somehow found it to be more efficient, less wasteful of energy and other resources, to have eyes on one side of our bodies–facing “forward,” as we put it. In the context of Aristotle’s example, our eyes are in the front, so we can go towards the food! Even though our eyes are left-right symmetric, that is not the case for all of our body. For example, the human heart, for some reason, is located towards the left side of the thoracic cavity. The stomach too is more to the left, while the liver is mainly on the right.
