用相对论群代替相对论群
Relativity grupoid insted of relativity group
摘要：
闵可夫斯基在1908年使用了介质相对于观测者的类空二元速度场。Hestenes在1974年引入了Clifford代数中的一个公理化的二元相对速度作为Minkowski双向量。我们提出把二元相对速度看作是算子代数中的无迹幂零自同态。任何二元公理相对速度的概念都可以用相对论广群代替洛伦兹相对论群。相对论广群是一类相互相对运动的大质量物体，其中二元相对速度被解释为带有结合加法的范畴态射。这种结合加法与等距狭义相对论中（三元）相对速度的非结合加法（环结构）形成对比。我们考虑一个多时空分裂的代数，作为一个由幂等元生成的算子代数。相对论广群的运动学由结合Frobenius算子代数控制，而范畴相对论的动力学则需要非结合的Frölicher-Richardson算子代数.洛仑兹协变性是物理学理论的基石。相对论广群内的观测者依赖性和洛伦兹协方差（在洛伦兹相对论群内）是不同的概念。物理定律可以是无偏的，而不是洛伦兹不变的。
英文摘要：
Minkowski in 1908 used space-like binary velocity-field of a medium, relative to an observer. Hestenes in 1974 introduced, within a Clifford algebra, an axiomatic binary relative velocity as a Minkowski bivector. We propose consider binary relative velocity as a traceless nilpotent endomorphism in an operator algebra. Any concept of a binary axiomatic relative velocity made possible the replacement of the Lorentz relativity group by the relativity groupoid. The relativity groupoid is a category of massive bodies in mutual relative motions, where a binary relative velocity is interpreted as a categorical morphism with the associative addition. This associative addition is to be contrasted with non-associative addition of (ternary) relative velocities in isometric special relativity (loop structure). We consider an algebra of many time-plus-space splits, as an operator algebra generated by idempotents. The kinematics of relativity groupoid is ruled by associative Frobenius operator algebra, whereas the dynamics of categorical relativity needs the non-associative Frölicher-Richardson operator algebra. The Lorentz covariance is the cornerstone of physical theory. Observer-dependence within relativity groupoid, and the Lorentz-covariance (within the Lorentz relativity group), are different concepts. Laws of Physics could be observer-free, rather than Lorentz-invariant.
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