Quantized conic sections; quantum gravity.

摘要

Starting from free relativistic particles whose position and velocity can only be measured to a precision (equivalent to) (plus minus) k/2 meter(sup 2)sec(sup (minus)1) , we use the relativistic conservation laws to define the relative motion of the coordinate r = r(sub 1) (minus) r(sub 2) of two particles of mass m(sub 1), m(sub 2) and relative velocity v = (beta)c = (sub (k(sub 1) + k(sub 2)))/ (sup (k(sub 1) (minus) k(sub 2))) in terms of conic section equation v(sup 2) = (Gamma) (2/r (plus minus) 1/a) where ''+'' corresponds to hyperbolic and ''(minus)'' to elliptical trajectories. Equation is quantized by expressing Kepler's Second Law as conservation of angular niomentum per unit mass in units of k. Principal quantum number is n (equivalent to) j + (1/2) with''square'' (sub T(sup 2))/(sup A(sup 2)) = (n (minus)1)nk(sup 2) (equivalent to) (ell)(sub (circle dot))((ell)(sub (circle dot)) + 1)k(sup 2). Here (ell)(sub (circle dot)) = n (minus) 1 is the angular momentumquantum number for circular orbits. In a sense, we obtain ''spin'' from this quantization. Since (Gamma)/a cannot reach c(sup 2) without predicting either circular or asymptotic velocities equal to the limiting velocity for particulate motion, we can also quantize velocities in terms of the principle quantum number by defining (beta)(sub n)/(sup 2) = (sub c(sup 2))/(sup v(sub n(sup 2)) = (sub n(sup 2))/1((sub c(sup 2))a/(Gamma)) = ((sub nN(Gamma))/1)(sup 2). For the Z(sub 1)e,Z(sub 2)e of the same sign and (alpha) (triple bond) e(sup 2)/m(sub e)(kappa)c, we find that (Gamma)/c(sup 2)a = Z(sub 1)Z(sub 2)(alpha). The characteristic Coulomb parameter (eta)(n) (triple bond) Z(sub 1)Z(sub 2)(alpha)/(beta)(sub n) = Z(sub 1)Z(sub 2)nN(sub (Gamma)) then specifies the penetration factor C(sup 2)((eta)) = 2(pi)(eta)/(e(sup 2(pi)(eta)) (minus) 1)). For unlike charges, with (eta) still taken as positive, C(sup 2)((minus)(eta)) = 2(pi)(eta)/(1 (minus) e(sup (minus)2(pi)(eta))).