Why Maxwell's Electromagnetic Theory, Despite Serious Errors, Often Yields Correct Results

Abstract

Shuang-Ren Zhao

In 1987, the author proposed the Mutual Energy Theorem and the concept of the electromagnetic inner product. Although initially met with skepticism from the academic community regarding its nomenclature and distinction from the reciprocity theorem, by 2017, it was further elevated to the Mutual Energy Flow Theorem (Law) and the Law of Energy Conservation. The author argues that energy is transferred via mutual energy flow, while the conventional view that self-energy flow (Poynting vector) transfers energy suffers from theoretical flaws. Research has revealed that the limitation of Maxwell's electromagnetic theory lies in defining the magnetic field as the curl of the vector potential function, which holds only under quasi-static conditions. In reality, the curl of the vector potential reflects the average magnetic field around a small loop. Despite this deviation, the theory has effectively solved numerous engineering problems for 160 years due to two main reasons: First, the quasi-static electromagnetic theories contributed by pioneers like Ampère and Faraday remain correct, ensuring the validity of basic calculations. Second, in radiation fields, Maxwell's theory mistakenly attributes energy transfer to self-energy flow instead of mutual energy flow; furthermore, Maxwell's theory erroneously calculates the phase of the magnetic field by 90 degrees. Remarkably, these two errors partially cancel each other out, leading to a calculated self-energy flow that numerically equals the mutual energy flow. This numerical coincidence allows Maxwell's theory to still yield correct results in engineering calculations such as antenna radiation patterns and power output. However, self-energy flow lacks the desirable physical property of mutual energy flow, which "starts from the source and extinguishes at the sink," and fails to fully satisfy Poynting's theorem in cases like dipole antennas. This theoretical discrepancy extends to the physics community, manifesting as the wave- particle duality paradox: Maxwell's theory attributes energy transfer to electromagnetic waves, while experiments prove energy is carried by photons. Although quantum mechanics introduces concepts like probability waves and collapse, fundamentally, electromagnetic waves are probabilistic, which aligns with the author's proposition that electromagnetic waves represent reactive power. The author finds that the energy transfer process described by the Schrödinger equation should also be represented by mutual energy flow, not self-energy flow (probability current). The complete calculation of mutual energy flow cannot be derived solely from the original Schrödinger equation but requires establishing and revising the theory of the magnetic field within the quantum framework.

PDF