DOE Explains...Symmetry in Physics | Department of Energy
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DOE Explains...Symmetry in Physics
A clock face is an example of parity transformation. The clock face’s appearance and behavior if the coordinate system is reversed is a test of symmetry. This image shows how the clock looks and works if it is reflected in a mirror.
Image courtesy of Nathan Clarke, Department of Energy Office of Science.
In physics, symmetry refers to how particles behave when space, time, or quantum numbers are reversed. We’re used to seeing simple types of symmetry in everyday life. For example, a human face is very nearly symmetrical when reflected left to right. But a face is completely asymmetric when reflected top to bottom—the top half of a face doesn’t look the same as the bottom. Small changes can break symmetry. For example, a face with a mole on one cheek would break left right symmetry.<br>Symmetry in physics is about more than just appearance and form. This is in contrast to symmetry in biology, which often refers to symmetry when discussing how organisms look and how their bodies are arranged.<br>Symmetry in physics can refer to the laws of nature being immune to changes in the identity or properties of certain elementary particles. Symmetry can also mean changes in what may seem to be abstract mathematical descriptions of nature.<br>Symmetry often refers instead to how nature behaves when particles are swapped with their anti-particles (called “charge conjugation”), when coordinates are reversed as in a mirror (called “parity inversion”), or when time is reversed (running the “movie” backwards). Physicists call these three symmetries C (for charge), P (for parity), and T (for time). So-called CPT symmetry is discrete—it happens in steps.<br>Physicists contrast discrete symmetry with continuous symmetry, where there are no steps between changes in symmetry. One example is rotational symmetry such as turning a circle. Unlike the case of rotating a square, there are no points where rotating a circle breaks the symmetry.<br>For scientists, translational symmetry in time and space are especially important. Translational symmetry means the laws of nature measured by one person at one time and in one place will not change if measured by another person at another time and another place. Without this symmetry, the physical sciences and the universal laws of nature wouldn’t work. In other words, symmetry in time and space is what makes experiments reproducible and science possible.<br>Understanding symmetries and broken symmetries is important for understanding the physical properties of matter and our universe.<br>Many of the advances in physics over the past several hundred years have been based on an increasing recognition of the importance of symmetry in generating theories of nature. If...