Explicit vs Spontaneous Symmetry Breaking

Explicit symmetry breaking occurs when a theory's fundamental laws inherently lack a certain symmetry, while spontaneous symmetry breaking happens when the laws possess a symmetry, but the system's particular state or environment obscures it.

• Explicit symmetry breaking means a theory's fundamental laws inherently lack symmetry.

• Spontaneous symmetry breaking means fundamental laws are symmetric, but the environment or state hides it.

• The universe's perceived asymmetry often results from spontaneous symmetry breaking.

The distinction between explicit and spontaneous symmetry breaking lies in whether the lack of symmetry is intrinsic to a theory's fundamental laws or emerges from the system's specific conditions, despite underlying symmetrical laws. Explicit breaking means the laws themselves are not invariant under a transformation, such as Newtonian physics near Earth's surface lacking 3D rotation invariance. Spontaneous breaking, however, describes a situation where fundamental laws are symmetric, but a particular instantiation of the universe or a system's environment makes the symmetry appear absent.

Explicit Symmetry Breaking

• 00:00:03 Explicit symmetry breaking occurs when the basic laws formulating a theory fundamentally fail to possess a certain symmetry. For example, if the universe is described by Newtonian physics near Earth's surface, the laws include gravity pointing in a specific direction, making them non-invariant under rotations not parallel to the ground. This means the theory itself inherently lacks three-dimensional rotation invariance from the outset.

Spontaneous Symmetry Breaking

• 00:01:27 Spontaneous symmetry breaking happens when the fundamental laws of physics are symmetric, but a particular state or environment of the universe makes that symmetry appear hidden or absent. For instance, while the actual Earth's presence gives a preferred 'down' direction, in empty space, full 3D rotation invariance would be evident. The universe's observed asymmetry, despite symmetrical fundamental laws, is largely attributed to numerous instances of spontaneous symmetry breaking, sometimes referred to as 'spontaneous symmetry hiding'.