**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 ether in superimposition principle or in the Maxwell equations. Assume it is wrong with the field superimposition, even the Maxwell equations is correct with singular charge, we can still not prove it still correct for many charges. Hence, at least something also wrong with 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 is the mutual energy theorem. It is shown that starting from the mutual energy theorem, the whole electromagnetic theory can be reconstructed. The Maxwell equations can be proved from the mutual energy theorem by adding pseudo items. Hence if the mutual energy theorem 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) zero 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, a electron can continually send energy to the outside of our universe, however there is no testimony supporting that our universe is opaque. The new theory supports the exist of advanced wave, hence also strongly support the absorber theory and transactional interpretation of quantum physics. It can offer a equation for photon and a good explanation for the duality of the photon. If photon and electromagnetic field obeys the mutual energy theorem, it is very possible that all other quanta also obey their similar mutual energy theorem. Hence the mutual energy theorem can be applied as a principle for the electromagnetic theory and quantum physics. According to this theory the retarded wave and advanced wave of electromagnetic fields both are a ability or probability wave, which is also partly agree with Copenhagen interpretation.

**Comments:** 25 Pages. Could you accept that there is a bug in Poynting theorem and Maxwell's equations?

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[v1] 2017-04-10 23:20:47

[v2] 2017-04-11 06:30:33

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