Another form of the uncertainty principle is given by ∆��∙∆��≥ℏ (see L. I. Schiff, Quantum Mechanics, 2nd ed., Page 7, 1955) where ∆�� is the uncertainty of measured time and ∆�� is the uncertainty of measured energy, and ℏ is Planck’s constant of action divided by 2��. To reduce the uncertainty of this inequality is simply to square both sides giving (∆��∙∆��)²≥ℏ². Since the same form can be applied to any given physical dimension, the equivalent form is ∆��²∙∆��²≥ℏ². This indicates that both ∆�� and ∆�� are scalar quantities whose powers are more meaningful than the powers of vector quantities such as positions and linear momenta.

The factor ∆��² by itself represents the change in total relativistic energy as indicated by relativistic quantum mechanics (QM) for example in QED. However, since the total relativistic energy is a constant this change can only implies changes for the addend ∆(��²��²) or the addend ∆(��²��⁴) such that the total relativistic energy ��²=��²��²+��²��⁴ is always a constant. The factor ∆��² represents the square of measured uncertainty of time. However, in the limit of ∆��→0 ∆�� becomes the infinitesimal ���� or the partial differential �� or even the exact differential ����. The square of the last denotes always the changes acceleration respects to, whether it is linear or angular, such that ²��/��² or ��²��/����² is always an absolute physical quantity. Furthermore, the inner scalar dot product ��·��=��² where �� is the absolute acceleration and �� is the local spacetime metric is always a constant the square of light speed.