even power

[AntonioLao]

One of Planck’s defenses for the objective reality of mechanical reversible processes is the requirement that the differential of the equations must be even powers. Reversibility implies temporal independence. In turn, it implies uniformity of state variables like pressure, temperature, density, and viscosity. Furthermore, independence suggests inherent invariance, conservation, and symmetry. At the infinitesimal level, evenly powered physical quantities possess all eight space-time properties of directional invariance. A complete set of these also leads to mass independence as intensive state variables. On the other hand, mass dependence or incomplete set can only lead to extensive state variables like length, volume, and energy. But the ratios of extensive state variables remain intensive.

However, the intensive state variable of fluid viscosity is derived statistically by assuming the existence of infinitely many fluid particles assembled then emerged as a macroscopic system comprising a set of extensive state variables with at least one other intensive state variable. Therefore, viscosity becomes irrelevant at the infinitesimal region, for example, zero-point energy of quantum vacuum fluctuation. Hence, vacuum resistivity is exactly zero, although vacuum’s electric permittivity and magnetic permeability are both minutely finite, whose reciprocal product is equal to the square of lightspeed. This becomes the proportionality constant for mass and energy equivalence in special relativity, E = mc. Since c is transposed as the ratio of two extensive state variables namely mass and energy: c = E/m, it is essentially intensive. In general, the squares of extensive state variables must also become intensive. By inductive reasoning, it can be seen that the 2nd power of length (area), of speed (Lorentz invariance), of time (absolute acceleration), of mass (its quantization), and of energy (space-time quantum) are all intensives which are suitable for describing natural invariance and symmetry.

If the universal expansion of space-time is considered as one’s of a dispersive medium then c becomes the product of distinctive high frequency phase velocity (p) and low frequency envelope modulating group velocity (g) such that pg = c. Moreover, If p and g are rational numbers then p – g = pg = c, where p ≥ g. Phase velocity and group velocity are equal if and only if both are identically zero.

[mkirkpatrick]

Thanks Antonio,even power is I feel the perfect circle which is squared by the one power
that is the ONLY power!



warm regards michael.