论文标题
麦克斯韦方程中的洛伦兹转换，以缓慢移动的介质
Lorentz transformation in Maxwell equations for slowly moving media
论文作者
论文摘要
我们使用现场分解的方法，这是一种广泛用于相对论磁性水力动力学的技术，用于研究麦克斯韦方程中洛伦兹转化的小速度近似（SVA），以缓慢移动介质。实验室框架中SVA下得出的“变形”麦克斯韦方程可以在介质的comoving框架中放入麦克斯韦方程的常规形式中。我们的结果表明，SVA中的Lorentz转换最高为$ O（v/c）$（$ v $是培养基的速度，$ c $是真空中的光速）对于得出这些方程式至关重要：即使在SVA中转换为另一个位置和当前密度，时间和电荷密度也必须变化，而不仅仅是在SVA中转换为另一个位置和当前密度。这标志着洛伦兹（Lorentz）与加利利（Galilean）的转变的本质差异。我们表明，缓慢移动表面的法拉第和安培方程的积分形式与麦克斯韦方程一致。我们还提出了法拉第方程的协变形式，其中电动力可以定义为独立于观察者框架的Lorentz标量。没有证据支持麦克斯韦方程的扩展或修改。
We use the method of field decomposition, a technique widely used in relativistic magnetohydrodynamics, to study the small velocity approximation (SVA) of the Lorentz transformation in Maxwell equations for slowly moving media. The "deformed" Maxwell equations derived under the SVA in the lab frame can be put into the conventional form of Maxwell equations in the medium's comoving frame. Our results show that the Lorentz transformation in the SVA up to $O(v/c)$ ($v$ is the speed of the medium and $c$ is the speed of light in vacuum) is essential to derive these equations: the time and charge density must also change when transforming to a different frame even in the SVA, not just the position and current density as in the Galilean transformation. This marks the essential difference of the Lorentz transformation from the Galilean one. We show that the integral forms of Faraday and Ampere equations for slowly moving surfaces are consistent with Maxwell equations. We also present Faraday equation the covariant integral form in which the electromotive force can be defined as a Lorentz scalar independent of the observer's frame. No evidences exist to support an extension or modification of Maxwell equations.
