Dialogue on the Principle of Mass-Energy Equivalence

This paper is directed to the readers who are familiar with the earlier papers by the author on the topic of mass-energy equivalence. A number of important questions about the total energy equation H = mv and its implications are answered qualitatively. The relationship between the equation H = mv and the 4-vector (Minkowski) representation of Special Relativity is discussed in detail. Other issues, such as de Broglie’s original formulation of wave mechanics, are also discussed. Introduction: This paper is a compilation of a number of important questions received by the author from several colleagues. It is organized as follows: Sec.1 contains a rather informal discussion about the implications of the total energy equation H = mv (see ref.[1]), presented in the form of questions and answers. The most important question asked was how a total energy equation such as H = mv can possibly fit with the 4-vector (Minkowski) representation of special relativity, in which H = mc is a cornerstone. This issue is addressed in detail in Sec.2. Sec.3 discusses some mathematical issues related to the concepts of the phase velocity and the group velocity, as well as de Broglie’s original arguments that led to the development of wave mechanics. In Sec.4, derivations are presented for a modified KleinGordon equation and a de Broglie dispersion relation. 1. Questions and answers: Q1. According to the total energy equation H = mv, the rest energy is equal to zero. How nuclear fusion can be possible without rest energy? Two fusing particles (e.g., a deuteron and a triton) usually require little kinetic energy to start the fusion process, yet the energy released from fusion is huge! A. In the fusion process, kinetic energy (usually on the order of 100Kev) is required to bring the electrostatic centers of the two fusing particles to a distance of a few fm apart, where the strong nuclear force takes over. Once the strong nuclear force takes over, the two particles move toward each other very rapidly. This relative velocity is the important parameter. The energy released in the reaction will be then equal to ∆mv, not ∆mc. That is why a wide distribution of energies is obtained, rather than the precise quantity ∆mc. A de-