相对性原理与惯性系的时空变换

Principle of relativity and space-time transformations for inertial reference frames

依据相对性原理,要求粒子动量和能量对于粒子速度的依赖关系在不同惯性系中具有相同的函数形式,由此可证明惯性系之间的时空变换必须是线性变换,并建立了线性变换系数与粒子无量纲质速关系之间的联系。由相对性原理普遍证明了相对论能量必须正比于动质量而不依赖于具体的时空变换关系。无须利用光速不变假设和相互作用守恒定律求解粒子质速关系,确定了惯性系之间时空线性变换的广义洛伦兹变换公式;证明了光速不变假设以及动量守恒和能量守恒定律实际上都不是建立相对论的必要条件。

It follows from the principle of relativity that particle's momentum and energy depend on its velocity must take the same functional form in different inertial reference frames. For this reasoning, the space-time transformation between inertial reference frames must be linear. We also relate the coefficients of space-time linear transformation to the dimensionless mass-velocity relation. By applying the principle of relativity, we prove that the relativistic energy proportional to the moving mass is independent of the specific space-time transformation, the mass-velocity relation of massive particle is obtained and the generalized Lorentz transformations are then derived without relying on the assumption of constant speed of light and the conservation laws. It is proved that neither the assumption of constant speed of light nor the conservation laws of momentum and energy is a necessary condition for establishing theory of relativity.