Acta Scientiarum Naturalium Universitatis Pekinensis

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Universal Mass-Velocity Relation and Special Relativity

DAI Youshan1, DAI Liang2   

  1. 1. Zhejiang University City College, Hangzhou 310015; 2. Department of Physics and Astronomy, Johns Hopkins University, Baltimore 21218;
  • Received:2012-12-21 Online:2014-05-20 Published:2014-05-20



  1. 1. 浙江大学城市学院, 杭州 310015; 2. Department of Physics and Astronomy, Johns Hopkins University, Baltimore 21218;

Abstract: Based on the principle of relativity and conservations of momentum and energy, the authors present a proof that the relativistic energy has to be proportional to the relativistic mass. The proof is new in that it is not built upon the assumption of constant speed of light, nor it requires any specific form of space-time transformation. A differential equation for the mass-velocity relation is derived and solved, from which an universal relativistic mass-velocity relation can be obtained and a speed limit vm automatically arises. The mass-velocity relation applies to tardyons which motion are slower than the speed limit and have a rest mass, to tachyons which motion are faster than the speed limit and do not have rest mass, and to constons which always travel at the speed limit and also do not have rest mass. Furthermore, the generalized Lorentz transformation for kinematics, as well as the mass-energy and energy-momentum relations for dynamics can be determined, and thus a more general theory of special relativity is developed. Such new theory of relativity holds consistently regardless of whether any tachyons or constons exist, or whether any superluminal phenomenon is observed. The value for the speed limit can be measured by experiments. In the case vm= c, the conventional relativity is recovered, and the constant speed of light becomes a corollary of the relativity theory.

Key words: special relativity, mass-velocity relation, generalized Lorentz transformation, principle of constant speed of light, tardyon, tachyon, conston

摘要: 依据相对性原理以及动量守恒和能量守恒定律, 无需利用光速不变假设和具体的时空变换关系证明相对论能量必须正比于相对论质量。通过建立和求解质速关系的微分方程, 自动给出极限速度vm, 并得到一种普遍适用的相对论质速关系。该质速关系既适用于具有静质量且运动速度小于极限速度的“慢子”, 又适用于不具有静质量且运动速度大于极限速度的“快子”以及运动速度等于极限速度的“常子”。在此基础上可确定运动学时空变换的广义洛伦兹变换公式以及动力学的质能关系和能量-动量关系, 从而建立一种更为普遍的狭义相对论理论。无论是否存在无静质量的“快子”和“常子”, 无论是否发现超光速现象, 新的相对论理论都是成立并自洽的。极限速度的具体取值可由实验测量确定, 若取vm=c , 就回到传统相对论的公式, 光速不变则成为相对论的一个推论。

关键词: 狭义相对论, 质速关系, 广义洛伦兹变换, 光速不变原理, 慢子, 快子, 常子

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