作为狄拉克粒子磁相互作用的量子波动力学
Quantum Wave Mechanics as the Magnetic Interaction of Dirac Particles
AI总结：
本研究从相对论经典电动力学出发，将狄拉克粒子建模为相对论循环点电荷，通过其磁相互作用的调制效应推导薛定谔方程，结合Osiak静能公式与修正的吸收体理论得到完整复波函数，为量子波力学提供经典电磁学起源解释。
摘要：
研究表明，波动力学量子理论可从相对论性经典电动力学中推导出来，这是被建模为相对论性循环运动点电荷的狄拉克粒子的磁相互作用的一个特征。两个经典点电荷各自做半径远小于其循环中心间距的相对论性循环运动，且假设电磁相互作用是时间对称的，它们之间的磁力会被一个行为与薛定谔波函数相似的因子调制。此前已有研究证明，相对论性循环运动电荷之间的磁力存在一个径向指向的平方反比分量，其强度与库仑力相近，且会随电荷循环运动的相位差呈正弦调制。当电荷循环中心发生相对运动时，磁力的调制满足一个形式上与含时自由粒子薛定谔方程完全相同的方程，仅偏时间导数项相差一个因子2。考虑在不含时势场中的运动时，该调制量也满足一个形式上与定态薛定谔方程相似的方程。利用Osiak提出的相对论静能公式，得到的调制函数可精确求解定态薛定谔方程。量子力学波函数的意义可直接从这些观测结果中得出。在考虑了采用Minkowski-Osiak相对论所需的Wheeler-Feynman吸收体理论修正后，该模型得到扩展，可获得完整的复薛定谔波函数。
英文摘要：
It is shown that a wave mechanical quantum theory can be derived from relativistic classical electrodynamics, as a feature of the magnetic interaction of Dirac particles modeled as relativistically circulating point charges. The magnetic force between two classical point charges, each undergoing relativistic circulatory motion of small radius compared to the separation between their centers of circulation, and assuming a time-symmetric electromagnetic interaction, is modulated by a factor that behaves similarly to the Schrödinger wavefunction. The magnetic force between relativistically-circulating charges has been shown previously to have a radially-directed inverse-square part of similar strength to the Coulomb force, and sinusoidally modulated by the phase difference of the charges' circulatory motions. The magnetic force modulation in the case of relatively moving centers of charge circulation solves an equation formally identical to the time-dependent free-particle Schrödinger equation, apart from a factor of two on the partial time derivative term. Considering motion in a time-independent potential obtains that the modulation also satisfies an equation formally similar to the time-independent Schrodinger equation. Using a formula for relativistic rest energy advanced by Osiak, the time-independent Schrödinger equation is solved exactly by the resulting modulation function. The significance of the quantum mechanical wavefunction follows straightforwardly from these observations. After considering the modification of Wheeler-Feynman absorber theory required by the adoption of Minkowski-Osiak relativity, the model is extended to obtain the full complex Schrödinger wavefunction.
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