Limitation of Applicability of Einstein's Energy-Momentum Relationship
Koshun Suto
Keywords: Special Theory of Relativity, Einstein?fs energy-momentum relationship, Klein-Gordon equation, Dirac equation.
When a particle moves through macroscopic space, for an isolated system, as its velocity increases, the kinetic energy and hence total energy of the particle will increase. However, according to classical quantum theory, when the momentum and kinetic energy of an electron inside a hydrogen atom increases, total energy decreases. From this truth, it is evident that the equation for Einstein's energy-momentum relationship does not hold true inside a hydrogen atom.
