The energy that would be carried by a wave produced by the superposition of two small amplitude mechanical waves of the same type would generally differ from the sum of the energies of the component waves in the superposition. Thus energy conservation appears to be violated. In this paper we address the question of the compatibility of the principles of superposition and energy conservation for small amplitude mechanical waves. We show that in the course of producing a pair of waves that interfere constructively, a second pair of waves that interfere destructively is naturally and unavoidably produced. Moreover, we show that the combination of constructive and destructive intereference is just that necessary for energy conservation. Thus we conclude that the principles of superposition and energy conservation are fully compatible.
All measurable phenomena in physics are irreducibly particle like and the wave picture of physical systems only arises when explaining a statistically relevant set of measurements of individual systems as an average. The wave picture arises in the effects of interference which can always be explained in the context of the state description of the interfering system, interference necessitates that the measurement outcomes be calculated by squaring the amplitudes after adding and non-interference is calculated by squaring before adding. Even though the calculation for each is independently valid, the change in the statistics when one modulates between interference and noninterference, as in the quantum eraser, requires a violation of the law of conservation of energy. There is no “driving force ” in the change of statistics. It is always a change in preparation that leads to the change of interference statistics, whilst in the calculation there is only a change in the state description. The irreducibly particle like nature of the quanta requires that there be a causal “driving force ” in the change in statistics and a mere change in description is an insufficient explanation by the standards of energy conservation. We present the argument that indeed this has already all been proven in the historic 1991 study of the ZWM papers of quantum coherence. Wave Particle Duality by Statistical Correspondence The first conceptual argument to arise in the history of quantum mechanics is that which questions how the