APPENDIX B - Symmetry in physics

Summary

Symmetries are features which are preserved after a specified operation. For instance, two figures are mirror-symmetrical when we can turn one of them over the other and check by transparency that it coincides with the original. We call this property an invariance of the mirror reflection.

In this case, there is invariance in the drawing when it is turned over. Circular symmetry arises from the invariance of the length used as the circle radius. Symmetry of the equilateral triangle comes from the invariance of the length chosen for the three sides.

It is possible to extend the idea of symmetry to time. An invariance in time is called a ‘conservation’. A mass that remains the same in the future as in the past comes from mass conservation, which expresses a time invariance, that is a symmetry when time flows. All conservation laws (of mass, energy, angular momentum, electric charge, etc.) are thus time symmetries.

An antisymmetry is also an invariance in absolute value, but with a change of sign. For example, a negative electric charge is antisymmetric to the same positive charge.

The symmetry properties of elementary particles, as well as those of the four distinct forces of nature, appear through particle interactions. These numerous symmetries are usually described as if they were geometrical symmetries in an abstract space of multiple dimensions.

A symmetry group is a set of properties that remain symmetric or antisymmetric over a specified type of operation.