Quantum Mechanics as a Classical Theory V: The Quantum Schwartzchild Problem
In this continuation paper, we apply the general relativistic quantum theory for one particle systems, derived in paper II of this series, to a simple problem: the quantum Schwartzchild problem, where one particle of mass m gravitates around a massive body. The results thus obtained reveal that, in the realm of such a theory, the negative mass conjecture we made in paper IV of this series is, indeed, adequate. It is shown that gravitation is responsible for the loss of energy quantization. We relate this property with the ideas of irreversibility and time arrow. In the previous paper (hereafter IV), we conjectured that it is possible to describe Nature appealing to negative mass particles (antiparticles). All the experiments the ”orthodox” interpretation might explain can also be explained by our interpretation. The experiment where particle and antiparticle travel under the influence of a homogeneous magnetic field was one we explained in details. We saw that the electromagnetic interaction alone is not capable of deciding about mass sign, since it is concerned only with the ratio e/m and the velocity. We also argued that a theory that accounts for gravitational effects will be capable of such a decision. In paper II of this series[1, 2, 3], we developed a general relativistic quantum theory for ensembles composed of one particle systems. This theory can be considered an immediate generalization of Klein-Gordon’s and Dirac’s special relativistic theories. It includes Einstein’s equations as part of the system of equations one shall solve and, thus, takes into account gravitation. The application of this theory to a problem where only gravitational effects are present will decide unambiguously about the correctness of the conjecture made in IV.