The Beauty in Physics
The concept of symmetry is ever present in physics. In nature, physical symmetry is represented by naturally occurring patterns that can be seen in animals, plants, and non-living entities. In fact, the demand for symmetry in nature has resulted in some of physics' most successful theories. In this context, symmetry in physics is described as the ability of a law to be applied to multiple instances. For example, saying the laws of physics are rotationally invariant implies that they do not offer preference towards a certain direction. In this same way, a circle can have rotational symmetry where all of the points are indistinguishable from each other.
In nature, circles are seen as organically occurring features. For these perfectly symmetrical shapes to arise from processes amongst other asymmetric things is incredible. The symmetry in flowers has always been of interest to me. The fact that something can grow from a non-uniformly shaped seed, receive a varying amount of nutrients, and yet still bloom into a circle with a perfectly shaped and balanced number of petals is crazy. I think this speaks to the way that physics can be used to describe the symmetries in the world, as nature is a lot more symmetrical than one would think.
Similarly, waves are examples of symmetry in nature that can be described by physics. Waves propagate through a medium (i.e., water) and oscillate as they travel, creating a pattern. Like a wave crashing on a beach, there is a symmetry that can be seen as a result of the traveling wave and the traveling break that it experiences. The break moves symmetrically with the waves as it rolls to the edge of the beach, causing a perfect relationship between the shape of the wave and the equation for the break.
Symmetry from physics is not only present in nature, but are as well. The physicist Anthony Zee has a romantic view of this, claiming, “let us worry about beauty first, and truth will take care of itself.” Bilateral symmetry (lobsters, humans) can be translated into spatial inversion by replacing the coordinates. Discrete transformations, such as rotation of a snowflake’s spikes, can be extrapolated and turned into complex transformations. This being said, symmetry in physics can be used to describe the symmetries seen in nature. Simple processes such as water flowing through a small crevice to the intricate complexities of the snowflake patterning can be described by mathematical equations derived from physics.