Principle of Superposition of Waves and Energy Conservation Law

N. V. Lunin

A. Lees

W. N. Mathews

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.

J.P. MATHIEU

Shuang-Ren Zhao

In electromagnetic theory and quantum theory, there are superposition principle. Traditionally there are only one kind superposition principle. However, in this author's theory the retarded wave and advanced wave are all involved, the superposition become multiple. For example this author need to deal the problem how to superpose the retarded wave and the advanced wave. This author found that there are 5 different kinds of superpositions. The superposition principles have some differences. The research about these differences is a key to open the door of many physical difficulties. For example the particle and wave duality problem, and to judge which interpretation of the quantum mechanics is a correct one. The first two superposition principles are the superpositions with and without the test charges. The slight different superposition principles are the superposition with a retarded wave alone and the superposition with the advanced wave alone. According to theory of this author, the emitter sends the retarded wave, the absorber sends the advance wave. Hence, normal electromagnetic field actually is consist of retarded wave and advanced wave. This two waves together become the traditional electromagnetic fields. This kind of electromagnetic fields can be seen approximately as retarded wave only, this kind wave also has its own superposition. This kind of superposition is also different with the superposition when we consider the retarded waves alone and also the advanced waves alone. In this article this author will discuss the differences of these different superpositions. This author will also discuss the different physical result with a few different superposition principles. In this article this author will prove the superposition with test charge and the superposition with retarded waves alone or advance wave alone can be see one kind of superposition. This superposition is correct and can be derived from the mutual energy principle. This will be referred as first kind of superposition. The superposition without test charge and the superposition with the retarded waves and advanced waves can be seen as one kind of superposition. For this kind of superpositions are not correct naturally. This kind of super position are applied to N-charge's Poynting theorem. In order to make this superposition work, the self-energy principle have to be applied. Without self-energy principle this kind of superpositions will violate the energy conservation law. Considering the self-energy conservation this kind of superposition become the superposition of first kind. This is referred as second kind of superposition. The third kind of superposition is for the traditional electromagnetic field. Here the traditional electromagnetic field means the electromagnetic field where the advanced waves are omit. When the advanced waves are omit doesn't mean the advanced waves do not exist, that is only means the retarded wave and the advanced wave are with nearly same intensity and can be treated together in some situation, for example, in wave guide, or in the free space where the absorber are uniformly distributed at infinite big sphere. Abstract Only when the self-energy principle is accept, all kinds of superposition can be accept. However different superposition has different physical meanings. Otherwise only the superposition with test charge or the superposition with only one kind wave either retarded waves or advanced waves can be accepted. Hence, the discussion about the superposition also support the concept of the self-energy principle which means there must exist the time reversal waves. That also means the waves do not collapse but collapse back. Wave collapse means collapse to its target, for example, the retarded wave will collapse to an absorber and the advanced wave will collapse to an emitter. Wave collapse back means the retarded wave sent from emitter will collapse back to an emitter; The advanced wave sent from the absorber will collapse back to an absorber. Hence, one purpose of this article is to clarify the superposition principles, and another purpose is to support this author's electromagnetic field theory which is started from two new axioms the self-energy principle and the mutual energy principle.

Phil Attard

The probability operator is derived from first principles for an equilibrium quantum system. It is also shown that the superposition states collapse into a mixture of states giving the conventional von Neumann trace form for the quantum average. The mechanism for the collapse is found to be quite general: it results from the conservation law for a conserved, exchangeable variable (such as energy) and the entanglement of the total system wave function that necessarily follows. The relevance of the present results to the einselection mechanism for decoherence, to the quantum measurement problem, and to the classical nature of the macroscopic world are discussed.