Essentially, the quantity of Leibniz’s vis viva is twice the modern physical quantity of kinetic energy. It is translated into English as the ‘living force’. Without sufficient knowledge of variational principles of modern analytical mechanics, why the living force double the kinetic energy absolutely presents a physical mystery that is very hard to swallow.
Same kind of puzzle lingers around the kinetic energy (T) formulation of said mechanics against the mass (m) and energy equivalence of special relativity: T = ˝ mv versus E = mc, where c is the constant for the speed of light in vacuum and v is the subluminal speed of an object with mass m. However, without enough understanding of variational principles, these contrasting similarities could be shown to have an intimately, fundamentally unshakable and indivisible relationship. This relationship promises the complete elucidation of an absolute natural invariance. It is local as well as global invariant gauge symmetry. This is the square of energy, the product of two dissimilar vis vivas or two distinct living forces: yin-yang, male-female, up-down, left-right, front-back, plus-minus, positive-negative, east-west, or north-south. Furthermore, as Planck pointed out in his book on a survey of physical theory which clearly implies that in the consideration of the differential equations of reversible processes the differential must always occurs in even powers in order for an analysis to proceed along directed paths of time independence.


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