**Authors:** Shuang-Ren Zhao

It is found that the Poynting theorem is conflict with the energy conservation principle. It is a bug of the Poynting theorem. The Poynting theorem is derived from Maxwell equations by using the superimposition principle of the fields. Hence, this bug also existed at either in superimposition principle or in the Maxwell equations. The Poynting theorem is corrected in this article. After the correction the energy is not quadratic and hence the field is also not linear. The concept of the superposition of fields need also to be corrected. Hence the new definitions for the inner product and cross product are proposed. The corrected Poynting theorem become the mutual energy formula, it is strongly related to the mutual energy theorems. It is shown that starting from the mutual energy formula, the whole electromagnetic theory can be reconstructed. The Poynting theorem can be proved from the mutual energy formula by adding pseudo items. The Maxwell equations can be derived from Poynting theorem as sufficient conditions. Hence if the mutual energy formula is corrected, the Maxwell equations still can be applied with knowing its problem. Most the problems originally caused by Maxwell equations are solved. Examples of this problems are: (1) electric field infinity which need to be re-normalized in quantum physics; (2) collapse of the electromagnetic field, the waves has to be collapsed to its absorber, otherwise the energy is not conserved; (3) the emitter can send energy without absorber, this is conflict to the direct interaction principle and absorber theory; (4) if our universe is not completely opaque, the charges will continually send energy to the outside of our universe, our universe will have a continual loss of energy. However there is no testimony supporting that our universe is opaque. The new theory supports the existence of advanced wave, hence also strongly support the absorber theory and transactional interpretation of quantum physics. It can offer an equation for photon and a good explanation for the duality of the photon. If photon and electromagnetic field obeys the mutual energy formula, it is very possible that all other quanta also obey their similar mutual energy formula. Hence the mutual energy formula can be applied as a principle or axiom for the electromagnetic theory and quantum physics. According to this theory the asychronous retarded wave and the asychronous advanced wave of electromagnetic fields both are an ability or probability waves, which is also partly agree with Copenhagen interpretation.

**Comments:** 41 Pages. In this version English is corrected, and the summation used in Action-at-a-distance of Tetrode and Fokker is added.

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