Change of state can be effected by the multiplication of a local infinitesimal phase factor. On the other hand, the multiplication of an overall global phase factor, generally speaking, will not alter the predicted probability measurements in terms of the square of the complex modulus of every wavefunction at the subquantum domain. In other words, the rule for subquantum superposition is such that there exists an asymmetry where and when integral of squares and square of integrals are not mathematically equivalent. For example: x+y is not equal to (x+y). The latter can be expanded to x+2xy+y. The additive difference is the product factor 2xy.

These are clearly understandable and make more sense if and only the wavefunctions are now replaced by symmetric Hadamard matrices. Consequently, the infinite sums of Hadamard matrices can only affect the states of physical charge while the infinite products of symmetric Hadamard matrices can only affect the states of physical mass or the first power of energy. This new rule implies that the scalar coefficients of Hadamard matrices of varying orders can be added. However, only Hadamard matrices of the same orders can be multiplied. The true nature is inherent in their representations as squares of energy. Since the elements of each symmetric Hadamard matrix are composed of equal numbers of 1’s and -1’s, there must be mathematical connections between them and the usual phase factors of quantum mechanics in terms of the imaginary irrational exponents of the base of natural logarithms. Fortunately, this precise connection has already been established by Euler in the 18th century. Euler’s equation for some other mathematical investigators is really a formula or an identity since it contains no algebraic variables. But in fact, it can contain six of the most fundamental numbers of all mathematical investigations: base of natural logarithms, p, i, 0, 1, or -1 and four operations: addition, multiplication, exponentiation, and equality all of which occur only once. Unfortunately, it cannot contain the infinity of global natural continuity but it implicitly indicated its subquantum superposition continuity of infinite series.