Special Relativity and Information
Francesco R. Ruggeri · Zenodo (CERN European Organization for Nuclear Research) · 2022
In a previous note (1) we attempted to derive Newton’s second law d/dt p = F(x) = -dV/dx for a conservative force using information ideas alone. In this derivation we implicitly treated mo, the rest mass, as a constant. In this note we focus on the situation of special relativity in the presence of a function V(x) which is independent of time, but changes the speeds of particles as they pass through space. In (1) we used the idea that d/dt → v(x) d/dx and assumed v(x)=dx/dt with dx being constant and dt(x) as representing information. We linked V(x) which changes particle velocities to v(x) which is variable and changes through d/dt v(x) which we equated with C dV/dx so that there was minimum information for an equilibrium result. Using d/dt → v(x)d/dx this leads to a form: .5v(x)v(x) + C V(x) = constant which is equivalent to Newton’s conservation law if the constant C and constant are chosen properly. To consider the special relativistic situation we consider a single particle with rest mass mo at x=0 at t=to and then view it from a moving frame with constant speed -v. We argue that a person in the frame sees x’,t’ such that x’/t’=v. We also argue that there should be an energy E and momentum defined by p=Ev/bb where b is constant which becomes as we argue c the speed of light. From these ideas we show that E=mocc in the rest frame and E= mocc/sqrt(1-vv/cc) in the moving frame. We note that in the limit of v/c> Eo-V yields the .5movv form.