Statistics

A Kinetic Route to the Lorentz Transform and Beyond

Authors: Jayanta Majumder
Comments: 9 Pages.

We model an elementary particle as a closed, lightlike intrinsic motion with rest-cycle period $tau$ that can undergo bodily translation without ever exceeding speed~$c$. A local triangle construction and cycle averaging yield the Pythagorean relation $T^{2}=tau^{2}+(x/c)^{2}$, where $x$ is the net spatial advance of the wavefront over one intrinsic cycle. Interpreting the exchange between intrinsic cycling ($T$) and bodily shift ($x/c$) as a symmetric two-channel kinetics with rate $k(t)$ integrates to a hyperbolic rotation (Lorentz boost) with rapidity $phi=int k,dt$ and $v/c=tanhphi$. In the small-signal limit this identifies $k=F/(mc)$, linking the kinetic picture to Newton's second law while the $tanh$ nonlinearity enforces the $c$ bound. We also give a physical reading of emph{relative rapidity} as the net logarithmic bias needed to map between motion states.
Category: Statistics