When one considers the term ‘symmetry,’ an image of regular polygons with dotted lines traced across their centers usually comes to mind. When one is asked to cite instances of symmetry in nature, mentions of human faces, starfish, and sunflowers usually tumble from their lips. What seldom arises in such conversations is the concept of symmetry as a measure of invariance, as well as its role in explaining the universe.
In physics, symmetry is not casually thrown around as a colloquial term for a mirror-image. Instead, symmetry describes the ability of a physical state or measurement to remain constant under a physical transformation. A common example of this idea is the tendency of most laws of physics to be resistant to time-reversal. The use of kinematics formulas to learn about an object’s future and past motion relies on the belief that Newton’s Laws hold true for any arbitrary period of time.
While physical symmetry is integral to understanding physical phenomena, it is just as important to understand how symmetries are broken. Faraday isolators break time-reversal symmetry by promoting the transmission of light in one direction, while blocking its transmission in the other. These devices function using a rotating axis that interacts with a plane of polarization. Regardless of the plane’s direction, the light is always directed the same way. In this case, forward and backward processes are not identical, and time-reversal invariance does not apply.
Symmetry describes the ability of a physical state or measurement to remain constant under a physical transformation.
In biology, broken symmetries are known as being responsible for cell polarity, as well as for the shapes cells must obtain in order to participate in cellular division and cellular fusion. It has also been discovered that symmetries (and/or the breaking of these symmetries) present in small-scale biological processes translate to larger-scale biological phenomena.
At extremely low temperatures, physical symmetries are known to break. Therefore, when the universe was young and temperatures were high, physical symmetries held true. As time went on, changes in the universe have resulted in the subsequent breaking and re-forming of physical symmetries. When these changes in the universe occur, energy is freed, and the physical world changes further.
The beauty in the invariance of the laws of physics is that it implies that there is potential for integrative discoveries. The universe is inherently invariant, and therefore observing symmetries in atomic-scale situations opens doors to understanding the larger physical world and its constant changes.
