Common Description of Quantum Electromagnetism and Relativistic Gravitation
Jérémy Kerneis
We use 3 equations as postulates: Pem referring to electromagnetism, Pgrav referring to gravity, and Pqm referring to quantum mechanic and defining the wave function. Combining Pem with Sommerfeld's quantum rules corresponds to the original quantum theory of Hydrogen, which produces the correct relativistic energy levels of atoms (Sommerfeld's and Dirac's theories of matter produces the same energy levels, and Schrodinger's theory produces the approximation of those energy levels). Pqm implies that the wave function is solution of both Schrodinger's and Klein-Gordon's equations in the non interacting case while, in the interacting case it implies Sommerfeld's quantum rules: Pem and Pqm then produce the correct relativistic energy levels of atoms (the same as Dirac's energy levels). We check that the required degeneracy is justified by pure deduction, without any other assumption (Schrodinger's theory only justifies one half of the degeneracy). We observe the connection between Pqm, Quantum Field Theories and tunnel effect. From Pgrav we deduce an equation of motion very similar to general relativity (with accuracy 10^{-6} at the surface of the Sun), our postulate being explicitly an approximation. First of all, we discuss classical Kepler problems (Newtonian motion of the Earth around the Sun), explain the link between Kelpler's law of periods (1619) and Plank's law (1900) and observe the links between all historical models of atoms (Bohr, Sommerfeld, Pauli, Schrodinger, Dirac, Fock).
•Sep 1, 2017•0 citations