As physical units, the squares of mass first appear in Newton’s law of universal gravitation. It was the first inverse square law of force given by its scalar form: ��=����₁��₂/��². If ��₁=��₂=�� then ��=����²/��². Here, the term ��² represents the square of gravitational mass for the attracting force between two identical bodies. On the other hand, Newton’s second law of motion states that the inertial force is proportional to the inertial mass with the inertial acceleration being the constant of proportionality: ��=����. By the principle of equivalence, it was experimentally proven conclusively that the gravitational mass is exactly equal to the inertial mass. Therefore, it is physically logical to equate the gravitational force to the inertial force: ����²/��²=���� and by rearranging both sides of the equation: ��²/��=����²/��. For unit mass ��=1 and ����=��² such that the remaining �� defines a quantum of length: ��=��/��² approximately 2x10¯² meter.

Since the Planck length is already established as √(��ℏ/��), the ratio of the quantum of length to the Planck length is of the order of 10. If the Planck length is scaled up to one meter then the quantum of length is equivalent to the distance that light travels in one second of time. Furthermore, if the speed of light is scaled down to dimensionless unity: ��=1 then by the hyperbolic non-Euclidean Lorentzian geometry of the space-time continuum the square of mass is equal to the difference of the square of energy and the square of the linear momentum: ��²=��²-��². Moreover, the square of mass can be used to define a rationalized quantum of mass such that the first condition is if the quantum of mass is exactly zero then the corresponding mass of the universe is also exactly zero. The second condition is if the quantum of mass approaches unity from zero then the corresponding mass of the universe approaches positive infinity. The third condition is if the quantum of mass approaches unity from infinity then the corresponding mass of the universe approaches negative infinity. The fourth condition is if the quantum of mass is exactly two units then the corresponding mass of the universe is exactly negative two units. Nevertheless, analogous to the existential probability, absolute certainty of unit mass happens only at absolute infinity of the space-time continuum.