In some standard physics textbooks, energy is best defined as the measure of change while force is the agent of change. The dot product of an agent and its displacement in space-time is defined as work. Its unit is the same as that of energy. Furthermore, there exists a cross product of an agent and its space-time displacement defined as torque, and again, its unit is the same as that of energy. Hence, both work and torque are equivalent to energy in measuring the magnitude of change. However, they differ only in measuring the direction of change. Work measures parallel and anti-parallel changes while torque measures orthogonal changes. Parallel changes are responsible for normal central agents while orthogonal changes could explain the mysterious non-central tangential agents of change.
Moreover, since there are eight degrees of freedom as resulted from eight directional properties in a 4-dimension space-time, the measured dispersion or absolute variance of change must be square integrable. This expression of integrability is similar in form to the statistical variance of mathematical sciences with a factor of 1/n and the variance is d²=(1/n)S(Ei-E0)², i=1,2,3, to n. In this context, a degree of freedom (absolute range) is defined as the absolute difference of two magnitudes neglecting their directional properties. The value of this 1/n factor differs in classical mechanics, statistical thermodynamics, and quantum mechanics. For 1-particle systems, the factor is unity, n=1. For 2-particle systems, the factor is ½, n=2. For 3-particle systems, the factor is 1/3, n=3, so on and so forth. For systems of infinite number of particles, the factor is zero. All these systems assumed identical particles: the same mass, the same volume, saying the same internal parameters. Nevertheless, for quantum vacuum, the factor becomes infinite, which implies a system of no particles and that variance with a measured value of infinity is the same as a system of total and complete randomness.


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