Mass is defined in physics as the product of density and volume. Although mass and volume are both considered as extensive variables, density, on the other hand is a good example of intensive variables. For any macroscopic system such as the whole universe an intensive variable is a quantity that has a well defined value at every point of space-time and that remains (nearly) constant when the size of the system is increased. Examples of intensive variables are the pressure, temperature, density, viscosity, and specific heat capacity at constant volume. An intensive variable results when any extensive variable is divided by an arbitrary extensive variable such as the volume. Therefore, the universe itself as a macroscopic system can be described by an extensive variable and a set of intensive variables. Besides mass and volume, one other example of an extensive variable is the total energy of an arbitrary system. The commonly accepted definition of an extensive variable is a quantity in a macroscopic system that is proportional to the size of the system.
Unfortunately, since energy is equivalent to mass (=²), the total energy of the universe cannot be derived from the pre-existence or preorigin state of the universe composed completely of zero masses: gluons, photons, and gravitons. This list would certainly include the three generations of neutrinos if ever they are proved to be massless as well. Although the physical asymmetry of the electroweak coupling does provide nonzero masses to the SU(2) gauge invariance bosons by the application of the Higgs mechanism, it does not provide or serve as an all inclusive mechanism for deriving all zero masses of high-energy elementary particles. Fortunately, if density is defined as a square symmetric singular Hadamard matrix and the volume is defined as a positive unit or negative unit (all elements are positive unity or negative unity) square matrix then the product of the same order density and volume matrices gives the zero mass matrix.


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