Abstract

The energy-momentum relationship in the special theory of relativity (STR) holds in an isolated system in free space. However, this relationship is not applicable to an electron in a hydrogen atom where there is potential energy. Using three types of methods, the author has already derived an energy-momentum relationship applicable to an electron in a hydrogen atom. In the past, Dirac asserted that Einstein’s relationship has negative solutions. This paper too obtains negative solutions (energy) from the derived relationship using Dirac’s reasoning. However, the discontinuity peculiar to the micro world is not incorporated into that solution. Thus discontinuity is incorporated into the solution by using a new quantum condition already derived by the author. Next, the orbital radius of an electron with negative energy in an absolute sense is found, and that radius is compared with the orbital radius of an electron in an ordinary hydrogen atom. A search is conducted for experiments supporting the DM model advocated by this paper. A hydrogen atom at this ultra-low energy level is formed from an atomic nucleus (proton) with positive mass, and a single electron with negative mass existing near that. In this paper, this unknown type of matter will be called a dark hydrogen atom (DHA). This paper also points out that DHA accounts for part of the true nature of dark matter (DM), the mysterious material whose true nature is currently unknown. Although this differs from the conventional interpretation, this paper holds that the experiment which demonstrates the existence of DHA is triplet production. The paper points out that one of the two electrons produced in a triplet production experiment is the electron which forms a DHA. If the DM model advocated by this paper is correct, then DM has already been discovered.

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