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首页> 外文期刊>Physica Scripta: An International Journal for Experimental and Theoretical Physics >Making the relativistic dynamics equation covariant: Explicit solutions for motion under a constant force
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Making the relativistic dynamics equation covariant: Explicit solutions for motion under a constant force

机译：使相对论动力学方程协变：恒定力下运动的显式解

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摘要

We derive a four-dimensional (4D) covariant relativistic dynamics equation. This equation canonically extends the 3D relativistic dynamics equation F = dp/dt, where F = is the 3D force and p = m_0γv is the 3D relativistic momentum. The standard 4D equation F = dp/dt is only partially covariant. To achieve full Lorentz covariance, we replace the four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By taking this tensor to be constant, we obtain a covariant definition of uniformly accelerated motion. This solves a problem of Einstein and Planck. We compute explicit solutions for uniformly accelerated motion. The solutions are divided into four Lorentz-invariant types: null, linear, rotational and general. For null acceleration, the worldline is cubic in time. Linear acceleration covariantly extends 1D hyperbolic motion, while rotational acceleration covariantly extends pure rotational motion.
机译：我们推导了一个四维（4D）协变相对论动力学方程。该方程式规范地扩展了3D相对论动力学方程F = dp / dt，其中F =是3D力，p =m_0γv是3D相对论动量。标准4D方程F = dp / dt仅是部分协变量。为了获得完整的洛伦兹协方差，我们用作用在四速度上的2级反对称张量代替了四作用力F。通过使该张量恒定，我们获得了均匀加速运动的协变定义。这解决了爱因斯坦和普朗克的问题。我们为均匀加速运动计算显式解。解分为四种Lorentz不变类型：零值，线性，旋转和一般。对于零加速度，世界线在时间上是立方的。线性加速度协变地扩展一维双曲线运动，而旋转加速度协变地扩展纯旋转运动。

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