If a wavefunction (��, ��) in one dimension satisfies the Schrödinger equation then its conjugate ��*(��, ��) will also satisfies the Schrödinger equation. The product of these conjugate functions is defined in quantum mechanics as the probability density: (��, ��)= ��*(��, ��) ��(��, ��). If these are real then ��*(��, ��)= ��(��, ��) and ��(��, ��)=|��(��, ��)|². Moreover, for time independence (��)=|��(��)|². This implies that the probability density is topologically equivalent to the area of arbitrary surfaces. Since the area is a gauge invariance, the time derivative of the probability density is zero: ��(��)/����=0. On the other hand, if ��(��, ��) is space independence or mass independence then ��(��) is not identically zero and ��(��)≠0 defines the positive or negative direction or any arbitrary direction of time and ��(��)=|��(��)| defines a probability current such that its time integral is normalized: ∫|��(��)|����=1, and since probability and direction both satisfy a principle of equivalence hence ∫|��(��)|����=0 defines the directional invariance of the quantum vacuum fluctuations at all times. Therefore, the space derivative of (��) is identically zero: ����(��)/����=0. In generalized three dimensions, ����(��, ��)/����+ div[��(��, ��)]=0 or equivalently this signifies that the sum of the time derivative of the probability density plus the divergence of the probability current is identically zero and this continuity equation indicates that both are probability density and current are gauge invariance. Gauge invariance of the probability current implies that at the infinitesimal domain of space-time the direction of time is indeterminate or simply means that the reality of quantum vacuum fluctuations is time independence. However, this independence is magnified if and only if these quantum vacuum fluctuations represent the square integrable functions of zero-point energies of space-time quantization of the space-time continuum.