One last prime principle or universal property, whether on the quantum level or on the very largest of scales is the universal property of symmetry. Here follows a definition of symmetry taken from the American Heritage Dictionary:
Def.: Symmetry – Exact correspondence of form and constituent configuration on opposite sides of a dividing line or plane or about a center or an axis.
There are many different kinds of symmetry but the most apparent or thought of kind of symmetry is visual or physical symmetry. This is when you look at a picture, film or object where both sides which are divided by a central line, plane or axis appear to correspond or mirror each other in a symmetrical manner. The dividing line, plane or axis is generally termed the line of symmetry. There are also two main aspects of symmetry: type and order. Three examples of type are mirror, rotational and point. Mirror symmetry is the simplest. Mirror symmetry means that each side on either side of the line of symmetry “mirrors” or reflects the other. Rotational and point symmetry are usually more complex for they take into account order also. Order means simply how many matches each side makes symmetrically to the other in a complete 360° revolution. Rotational symmetry is defined as being a symmetry around a central point with an order of (2) or greater. Point symmetry is a type of rotational symmetry, equivalent to rotational symmetry with an order of (2) (S(2)) where each part or point has a matching symmetrical partner the same distance from a central point yet in the opposite direction. In some cases mirror symmetry may also be or have rotational symmetry.
There are other kinds of symmetry other than purely visible or even physical. Even time itself has been proven to display a symmetrical property. Quantum particles have “anti-particles” with which they share a certain symmetry. Physical space and space-time curvatures may display symmetrical properties and at the proposed early instances of the Big Bang even the four fundamental forces (with perhaps the exception of gravity) are considered to have had and shared an intimate symmetrical quality. Even M-theory leaves open the door to higher extra-dimensional symmetry.
TCP theory (or TCP symmetry as it is alternately called) supposes a theoretical symmetry of time, charge and “handed-ness” in our universe with that of a “mirror” universe, thus suggesting symmetry on a universal scale. (There are subtle difficulties in this theory which I shall not delve into here). Thus time, space, energy/matter and space-time all exhibit certain symmetrical qualities and properties of one nature or another. As Einstein proposed, everything is relative.