Symmetries as fundamental principles of Physics

Im SangHui

Physical laws are a kind of “restriction” governing the motion or dynamics of physical entities, and symmetry refers to the invariant property of a physical system under some transformation. Modern physics has found that almost all of the fundamental physical laws, discovered up to now, can be seen as consequences of certain symmetries. In addition physicists are now using symmetries in order to pioneer new fundamental laws or principles of nature. In this seminar, we will clarify what this means and review how the principal laws of physics can be implied by their corresponding symmetries. First we will introduce the “action principle” which plays important role with symmetries in determining the equations of motion in physics, which states that a physical system moves in a path where its “action” is minimized. We will then define what symmetry means mathematically in the context of the action principle. Then we will firstly see that the famous Newton’s laws of motion have rotation, (Galilean) boosting, and translation symmetries and we will show that some of these laws can be viewed conversely as a consequence of those symmetries with the action principle. Secondly we will examine the symmetries in classical electromagnetism which was another realm of classical physics with Newton’s laws, and we will show that it has (Lorentz) boosting symmetry with other symmetries in Newton’s laws. We will note that actually the finding of this new symmetry gave birth to the Einstein’s special theory of relativity. Generalizing the Lorentz symmetry to be local, we will also see that the Einstein’s general relativity, which modifies Newton’s gravity, can be derived. After this, we are going to smaller world where quantum mechanics is applied. There, we’ll see that the particle physics called Standard model including three fundamental forces other than gravity is described by (internal) gauge symmetries and its spontaneous breaking. Finally, we will mention Supersymmetry and its spontaneous breaking currently studied as being expected to be new physics beyond the established Standard model.