**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. The 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. The 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. The author found that the mutual energy is the part of additional energy when the two waves are superposed comparing to the situation if 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? The author's answer are 2 or 4 depending whether the sources of the waves are involved or not. However the 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. The 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 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 the author's photon model. This photon model is proved by the 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 the 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) is 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 it is only the mutual energy flow which is responsible to transfer the energy from the emitter to the absorber. The author also proved that the mutual energy flow theorem, there is a mutual energy flow go through the emitter to the absorber. 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-revesal-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 is because the Maxwell equations are only partially correct or correct with some probabilities. 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 which are not satisfy Maxwell equations but satisfy the time-reversal Maxwell equations. Hence 4 additional equations are added to Maxwell equations which describe the two additional time-reversal-return waves. Hence, the photon's package wave is consist of 4 waves which have 4 corresponding self-energy flows. There are two additional energy flows, which are the mutual energy flow that is responsible for transferring the energy from emitter to the absorber, the time-reversal-return energy flow which is responsible to bring the energy back from the emitter to the absorber if the absorber only obtained a part of photon.

**Comments:** 88 Pages.

**Download:** **PDF**

[v1] 2018-04-07 09:50:29

**Unique-IP document downloads:** 18 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful. *