Authors: Shuang-Ren Zhao
The particle and wave duality is solved through the self-energy and the mutual energy principles. Welch has introduced the time-domain reciprocity theorem in 1960. This author have introduced the mutual energy theorem in 1987. It has been proved that the above two theorems are same theorem in time-domain or in Fourier domain. This author believe there is an energy flow from transmitting antenna to the receiving antenna. Hence this theorem is a energy theorem instead of a mathematical theorem i.e. the reciprocity theorem. This author found that the mutual energy is the additional energy when the two waves are superposed comparing to the situation when the two waves alone stayed in the space. It is often asked that if the two waves are identical what is the energy after the two waves are superposed, 4 or 2 times? this author's answer are 2 or 4 depending whether the sources of the waves are involved or not. However this author noticed that a more important situation, which is the superposition of two waves: one is retarded wave sent from the emitter, another is the advanced wave sent from the absorber. This situation actually described the photon. This author have found that, instead there are two photons the retarded photon and the advanced photon like some author believed, there is only one photon. The reason is that the two waves the retarded wave and the advanced wave they both bring one photon energy, which are sent to the space, but these energy are returned with the time-reversed waves. The additional energy because of the superpose process of the two waves is just with 1 photon's energy instead of 2 photon's energy. This energy is sent from the emitter to the absorber. These build this author's photon model. This photon model is proved by this author through the notice of the conflict between the energy conservation and both the superposition principle and the Maxwell equations for single charge. This conflict force this author introduced the mutual energy principle and the self-energy principle. Self-energy principle tell us the self-energy (the wave's energy before superposed) time-reversal return to its source and hence do not transfer any energy from emitter to the absorber. The mutual energy principle tell us that transferring the energy from the emitter to the absorber is only done by the mutual energy flow. This author also proved that the mutual energy flow theorem, which says that the energy transferred by mutual energy flow is equal in any surface between the emitter to the absorber. The wave function collapse process is explained by the two processes together the first is the self-energy time-reversal return to their sources (instead of the targets), the second is that the mutual energy flow brings a photon's energy package from emitter to the absorber. The wave's probability property is also explained that because only when a retarded wave synchronized with an advanced wave the energy can be transferred. The photon energy is transferred only when the retarded wave (one of solution of Maxwell equations) and the advanced wave (another solution of the Maxwell equations) are synchronized, otherwise the two waves are returned by two time-reversal waves. Time-reversal wave are not satisfy Maxwell equations but satisfy the time-reversal Maxwell equations. Hence, 4 time-reversal Maxwell equations which describe the two additional time-reversal waves are added to Maxwell equations. Hence, the photon's package wave is consist of 4 waves which are corresponding to 4 self-energy flows. There are two additional energy flows, which are the mutual energy flows that is responsible for transferring the energy from emitter to the absorber. The time-reversal mutual energy flow which is responsible to bring the energy back from the absorber to the emitter if the absorber only obtained a half photon or a part of photon.
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