Abstract
Einstein derived the energy-momentum relationship which holds in an isolated system in free space. However, this relationship is not applicable in the space inside a hydrogen atom where there is potential energy. Therefore, in 2011, the author derived an energy-momentum relationship applicable to the electron constituting a hydrogen atom. This paper derives that relationship in a simpler way using another method. From this relationship, it is possible to derive the formula for the energy levels of a hydrogen atom. The energy values obtained from this formula almost match the theoretical values of Bohr. However, the relationship derived by the author includes a state that cannot be predicted with Bohr’s theory. In the hydrogen atom, there is an energy level with n = 0. Also, there are energy levels where the relativistic energy of the electron becomes negative. An electron with this negative energy (mass) exists near the atomic nucleus (proton). The name “dark hydrogen atom” is given to matter formed from one electron with this negative mass and one proton with positive mass. Dark hydrogen atoms, dark hydrogen molecules, other types of dark atoms, and aggregates made up of dark molecules are plausible candidates for dark matter, the mysterious type of matter whose true nature is currently unknown.
Highlights
The energy-momentum relationship in the special theory of relativity (STR) holds in an isolated system in free space
We look to potential energy as the answer to that problem, but there is no substantiality to potential energy
If rn+ is the orbital radius in an ordinary hydrogen atom, and rn− is the orbital radius of an electron at a negative energy level, the ratio of the two is as follows [8]
Summary
The energy-momentum relationship in the special theory of relativity (STR) holds in an isolated system in free space. This relationship is not applicable to the electron in a hydrogen atom where there is potential energy. By all rights, this problem should have been investigated in the first half of the 20th century. In Equation (4), the energy (i.e., the sum of potential energy and kinetic energy) when the electron is separated from the atomic nucleus (proton) by an infinite distance and placed at rest there, is assumed to be zero. From the perspective of the theory of relativity, the relativistic energy mnc of the electron constituting a hydrogen atom must be defined as follows. Classical (nonrelativistic) kinetic energy, in contrast, is defined as follows
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