**Authors:** Shuang-ren Zhao

The solutions of Maxwell equations includes the restarted and the advanced waves. There are a few famous scientists supported the concept of advanced wave. Wheeler and Feynman have introduced the absorber theory in1945 which told us the absorbers can send the advanced wave. The absorber theory is based on the action-at-a-distance of Schwarzschild, Tetrode and Fokker, which told us the electric current sends a half retarded wave and a half advanced wave. John Cramer has introduced transactional interpretation in quantum mechanics, which said the retarded wave and the advanced wave have a handshake. What is the advanced wave in electromagnetic field theory? In 1960, Welch introduced the reciprocity theorem in arbitrary time domain which involved the advanced wave. In 1963 V.H. Rumsey mentioned a method to transform the Lorentz reciprocity theorem to a new formula. In early of 1987 Shuang-ren Zhao (this author) introduced the mutual energy theorem in frequency domain. In the end of 1987 de Hoop introduced the time-domain cross-correlation reciprocity theorem. All these theories can be seen a same theorem in different domain: Fourier domain or in time domain. This theorem can be applied to prove the directivity diagram of a receiving antenna are equal to the directivity diagram when the receiving antenna are used as a transmitting antenna. According to this theory, the receiving antenna sends the advanced wave. As a reciprocity theorem the two fields in it do not need to be real for all. Hence, for the reciprocity theorem of Welch, Rumsey and Hoop do not need to claim that the advanced wave is a physical wave. However, when Shuang-ren Zhao said it is a energy theorem that means the two waves the retarded wave and the advanced wave in the theorem must be all real physical waves. After the mutual energy theorems has been published 30 years, Shuang-ren Zhao re-enter this field. First, the mutual energy flow theorem is derived. The mutual energy flow produced by the superposition of the retarded wave and the advanced wave. The mutual energy flow can carry the energy from the transmitting antenna to the receiving antenna. Our textbook of electromagnetic field tell us the energy is carried by the energy flow of the Poynting vector which is the self-energy flow. Hence, there is a question that the energy of electromagnetic field is transferred by the mutual energy or self-energy or by both? This author found that only the former can offer a self-consistency theory. This author also proved that the energy is transferred by the self-energy or both all conflict with the energy conservation law and hence cannot be accept. If the energy is transferred by the mutual energy, the axioms of the electromagnetic field needs to be modified. Hence, the mutual energy principle is introduced to replace the Maxwell equations as axioms. The mutual energy principle can be derived from the Maxwell equations. The Maxwell equations can also be derived from the mutual energy principle. However, the mutual energy principle does not equivalent to the Maxwell's equations. Starting from the mutual energy principle, the solution needs to be two groups of Maxwell equations existing together. One group of the Maxwell equation is corresponding to the retarded wave, another is corresponding to the advanced wave. The two waves must be synchronized to produce the mutual energy flow. The conflict of Maxwell equations with the energy conservation law further suggest that there exist a time-reversal wave and self-energy principle. Self energy principle tells us that self-energy flow or the energy flow corresponding to Poynting vector does not carry or transfer the energy, because there exist 2 time-reversal waves corresponding to the retarded wave and the advanced wave. The energy flow of the time-reversal waves cancels the energy flows of the self-energy flows of the retarded wave and the advanced wave. This also tell us there are 4 waves for electromagnetic fields, the retarded wave, the advanced wave, the 2 time-reversal waves corresponding to the retarded wave and the advanced wave. The self-energy flow of these 4 waves are all canceled. However the mutual energy flow of the retarded wave and the advanced wave does not disappear. The energy of electromagnetic field is transferred by the mutual energy flow. Photons can be explained by the mutual energy flows. There is also the time-reversal mutual energy flow which can wipe out the half-photon or partial photon. Anti-particle can also be explained by the time-reversal mutual energy flow. This theory has been widen to the quantum mechanics. That means all particles for example electron is also consist of 4 waves and 6 energy flows. There is the mutual energy principle and self-energy principle corresponding to the Schrödinger equation. In this article 3 modes of radiation are introduced which are photon, anti-photon, ant unsuccessful radiation. Photon is consist of one mutual energy flow, self-energy flow for the retarded wave and advanced wave, self-energy flow of the time-reversal waves. All self-energy flows are canceled. Hence only the mutual energy flow survive. Anti-photon is consist of the time-reversal mutual energy flow; Time-reversal self-energy flow and self-energy flows. All the self-energy flow canceled. Only the time-reversal mutual energy survived. The last mode is the unsuccessful radiation. The retarded wave is sent out but it did not meat any advanced wave to handshake/synchronized. Hence, the energy is returned, the radiation is unsuccessful. Photon is transfer the radiation energy. Anti-photon is responsible to eliminate the half-photon or partial photon. The unsuccessful radiation is the necessary result that the source and sink both send the waves, one is the retarded wave and the other is the advanced wave.

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[v1] 2019-08-25 08:08:46

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