Study on the average speed of particles from a particle swarm derived from a stationary particle swarm

Abstract

Abstract It has been more than 100 years since the advent of special relativity, but the reasons behind the related phenomena are still unknown. This article aims to inspire people to think about such problems. With the help of Mathematica software, I have proven the following problem by means of statistics: In 3-dimensional Euclidean space, for point particles whose speeds are c and whose directions are uniformly distributed in space (assuming these particles’ reference system is $$\mathcal {R}_{0}$$ R 0 , if their average velocity is 0), when some particles (assuming their reference system is $$\mathcal {R}_{u}$$ R u ), as a particle swarm, move in a certain direction with a group speed u (i.e., the norm of the average velocity) relative to $$\mathcal {R}_{0}$$ R 0 , their (or the sub-particle swarm’s) average speed relative to $$\mathcal {R}_{u}$$ R u is slower than that of particles (or the same scale sub-particle swarm) in $$\mathcal {R}_{0}$$ R 0 relative to $$\mathcal {R}_{0}$$ R 0 . The degree of slowing depends on the speed u of $$\mathcal {R}_{u}$$ R u and accords with the quantitative relationship described by the Lorentz factor $$\frac{c}{\sqrt{c^2-u^2}}$$ c c 2 - u 2 . Base on this conclusion, I have deduced the speed distribution of particles in $$\mathcal {R}_{u}$$ R u when observing from $$\mathcal {R}_{0}$$ R 0 .