Mathematical intuition says that a relation between two formulations A and B is a condition that is either true or false. Moreover, it is important to consider the order of priority. For example, the relation “greater than” of integers A=1 and B=2 makes A > B false but B > A true. However, any relation giving the idea of equality is an equivalence relation. Equivalence seems to disregard the order of priority with 3 distinctive properties: (1) reflexive, A=B or B=B. Both describe absolute identity, (2) symmetric: A=B or B=A, (3) transitive: if A=B and B=C then A=C. Physical formulation having these properties become equivalence principles.

For examples: (1) the principle of equivalence for inertial mass and gravitational mass of general relativity, (2) the mass and energy equivalence of special relativity, (3) the spatiotemporal equivalence of electric and magnetic field, and (4) the thermal equivalence of thermodynamic systems in equilibrium known as the zeroth law of thermodynamics. The first implies that the ratio of inertial acceleration to the gravitational constant is time independence. The second implies that mass is identical to energy if and only if the vacuum speed of light is normalized to unity. The 3rd implies the existence of displacement current of spacetime as in local infinitesimal motion. The 4th implies that at temperature T=0 the universe is determined by an infinite number of zero points energy.