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arXiv physics/0302065physics.class-phphysics.gen-ph
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论狭义相对论中的运动定律

On the law of motion in Special Relativity

Gonzalo E. Reyes, Antoine Royer

摘要:

牛顿相对于惯性系的运动定律(“实验室”)对于一个粒子在某一时刻受到一个力的作用,可以用两种方式来解释:(1)在无限小的时间内作用在粒子上的力给实验室带来了推动力。(冲量除以质量),同时粒子保持相对于新帧的原始速度,以及(2)在无限小的时间内作用在粒子上的力,相对于粒子的固有坐标系,赋予粒子相同的推动力,该粒子以相对于实验室的原始速度运动。我们表明,相对论运动定律承认两种解释,其中第一个是事实上相当于运动定律。因此,我们表明,相对论运动定律也可以重新表述为“力等于质量乘以加速度”,类似于牛顿定律,但相对论质量和相对论加速度定义在相对论速度加法定律,而不是普通的质量和普通的矢量速度加法,导致经典的加速度和牛顿定律。

英文摘要:

Newton's law of motion relative to an inertial frame ("the laboratory") for a particle subject to a force acting at a certain time may be interpreted in either of two ways: (1) The force acting on the particle during an infinitesimal time imparts to the laboratory a boost (impulse divided by the mass) while the particle maintains the original velocity relative to the new frame and (2) The force acting on the particle during an infinitesimal time imparts to the particle the same boost relative to the proper frame of the particle which moves with the original velocity with respect to the laboratory. We show that the relativistic law of motion admits both interpretations, the first of which is in fact equivalent to the law of motion. As a consequence, we show that the relativistic law of motion may also be reformulated as "force equals mass times acceleration" in analogy with Newton's law, but with a relativistic mass and a relativistic acceleration defined in terms of the relativistic addition law of velocities, rather than ordinary mass and ordinary vectorial addition of velocities that lead to the classical acceleration and to Newton's law.

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