414(9): Equations of Motion and Multiple Self Consistency Checks
This note gives a rigorous self consistency check for the free particle hamiltonian (6) using the ECE2 infinitesimal line element (1). This is a baseline calculation before embarking on m theory in UFT415. It is found that the relativistic equations (40) and (41) give r(phi) as in Eq (31), derived in two different ways giving the same results. This means that the numerical integration of Eqs. (40) and (41) must give the orbit (31). This provides a check for the numerical method. The orbit (31) is integrated to give Eq. (53) for the relativistic free particle in plane polar coordinates.The non relativistic free particle is described by Eq. (56). The m theory with m = 1 – r sub 0 / r gives the obsolete Einsteinian general relativity (EGR), and introduces additional terms in Eq. (17). Here r sub 0 is the obsolete Schwarzschild radius. It is known that m theory gives a shrinking orbit, so will be merged with the relativistic orbital theory of UFT414 in UFT415. So I will now proceed to writing up UFT414.