Subatomic Physics

Part III
Symmetries and Conservation Laws
If the laws of the subatomic world were fully known, there would no longer be a
need for investigating symmetries and conservation laws. The state of any part of
the world could be calculated from a master equation that would contain all symmetries
and conservation laws. In classical electrodynamics, for example, the Maxwell
equations already contain the symmetries and the conservation laws. In subatomic
physics, however, the fundamental equations are not yet established, as we shall
see in Part IV. The exploration of the various symmetries and conservation laws,
and of their consequences, therefore provides essential clues for the construction of
the missing equations. One particular consequence of a symmetry is of the utmost
importance: Whenever a law is invariant under a certain symmetry operation there
usually exists a corresponding conservation principle. Invariance under translation
in time, for instance, leads to conservation of energy; invariance under spatial rotation
leads to conservation of angular momentum. This profound connection is
used both ways: If a symmetry is found or suspected, the corresponding conserved
quantity is searched for until it is discovered. If a conserved quantity turns up, the
search is on for the corresponding symmetry principle. One word of warning is in
place here: Intuitive feelings can be misleading. Often a certain symmetry principle
looks attractive but turns out to be partially or completely wrong. Experiment is
the only judge as to whether a symmetry principle holds.
Conserved quantities can be used to label states. A particle can be characterized
by its mass or rest energy because energy is conserved. Or consider the electric
charge, q. It is conserved and comes only in units of the elementary quantum e.
The value of q/e can thus be used to distinguish particles of the same mass. Positive,
neutral, and negative pions can be christened; pion is the family and positive the
first name.
In the next three chapters we shall discuss a number of symmetries and conservation
laws. Additional symmetries exist, and we shall encounter some later on.
Some of the symmetries are perfect even under closest scrutiny, and no breakdown
in the corresponding conservation law has ever been found. Rotational symmetry
and conservation of angular momentum are one example of this “perfect” class.