The Formulation of a Comprehensive Mass and Energy Balance Equation
Authors: Khan M. M. , Zatzman G. , Islam M. R. 
Published: August 2009

Nanotechnologies are considered to be the driver of the Information-Age engineering. Recent discoveries in practically all aspects of engineering developments indicate that properties at nano-levels are starkly different from properties at bulk levels. These discoveries signal great potentials for nanotechnologies that can revolutionize all technologies, ranging from medicine to energy. However, the same discoveries also point to the fact that conventional laws and theories that have enjoyed long-standing confidence of the scientific community do not apply to nanotechnologies. In absence of such laws that describe nano-scale phenomena, it is difficult if not impossible to predict long-term impacts of nanotechnologies. This paper presents a comprehensive formulation of mass and energy balance equations. This formulation gives rise to a unique set of equations that apply to both nano- and bulk scale natural phenomena. The formulation is based on momentum balance, which is preserved at all scales, ranging from cosmic to nano- and even the inter-atomic level. Although Newton posited gravitation as a universally acting force, we now know that electromagnetic forces predominate in matter at the nano or inter-atomic level. Electromagnetic forces, like frictional forces, however, can exist and persist without ever having been externally applied. Reasoning thus “by exhaustion”, Newton’s Three Laws of Motion plus the principle of universal gravitation are actually special cases of “something else”. That “something else” is far more general, viz., the universal preservation of mass-energy balance and conservation of momentum. The connecting element of this universal balance is that motion is the mode of existence of all matter. This renders time a characteristic of matter itself within the overall context of mass-energy-momentum conservation. In other words, time ceases to be mainly or only a derivative of some spatial displacement of matter. In this way, it becomes possible at last to treat time, consistently, as a true fourth dimension — and no longer as merely the independent variable. This description is consistent with Einstein’s revolutionary relativity theory, but does not rely on Maxwell’s equations as the starting point. The resulting equation is shown to be continuous in time, thereby allowing transition from mass to energy. As a result a single governing equation emerges. This equation is solved for a number of cases and is shown to be successful in discerning between various natural and artificial sources of mass and energy. With this equation, the difference between chemical and organic fertilizers, microwave and wood stove heating, and sunlight and fluorescent light can be made with unprecedented clarity. By applying this equation, a complete pathway analysis of nanomaterials is made and it is shown that engineering at nano-scale will have long-term impacts. This analysis would not be possible with conventional techniques. Finally, analysis results are shown for a number of energy- and material-related prospects.