In physics, force is best defined as the agent of change and energy is best defined as the measure of this change. In general, change is synonymous with the universal concept of motion. Since there are different forms of motion, energy is measured also in many different ways. Some these measures are given as heat, potential, kinetic, electric, magnetic, electromagnetic, gravitational, nuclear, atomic, molecular, frictional, chemical, wind, geothermal, hydrostatic, radiative, conductive, and convective. That is to say for every defined agent of force, there is a corresponding measure of energy. Although each distinct measure of energy must be given as a scalar quantity of the same dimensional unit and basically convertible between themselves, if the measured energy is derived from the quantum vacuum of space-time charges as the interactions of infinitesimal primary forces then this measurement is properly defined as the measure of directed energy, which at the fundamental level of physical reality can be both positive and negative. As already mentioned earlier, positive energy is useful energy, while negative energy is useless energy. This useless energy is disguised as the quantum vacuum fluctuations of zero-point energies, whose quanta are defined as virtual particles of the different types of quantum fields.
Mathematically speaking, a directional quantity is equivalent to a vector quantity, a physical quantity having both attributes of magnitude and direction. Consequentially, the computational methodology of directed physical quantities is equivalent to the mathematics of wave interference as clearly described in The Feynman Lectures on Physics, Chapter I, Volume III, CIT, Addison Wesley, 1965. This mathematical formalism relies on the triangular inequality and the cosine law of circular functions, which are applicable to complex imaginary analysis, points in the infinitely dimensional Euclidean geometry, as well as multi-dimensional linear vector spaces similar to the Hilbert spaces used in quantum mechanics. Obviously, the mathematics of quantized wave interference is also equivalent to the mathematics of squares of energy: ²=₁×₁×₂×₂ such that ²≤₁²+₂² where ₁ and ₂ are defined primary thermal forces and ₁ and ₂ are the local infinitesimal metrics.


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