Lorentz Invariance in Relativistic Particle Mechanics

The notion of invariance under the Lorentz transformation is fundamental to special relativity and its continuation beyond the speed of light. Theories and solutions with this characteristic are stronger and more powerful than conventional theories or conventional solutions because the Lorentz-invariant approach automatically embodies the conventional approach. We propose a Lorentz-invariant extension of Newton’s second law, which includes both special relativistic mechanics and Schrödinger’s quantum wave theory. Here, we determine new general expressions for energy–momentum, which are Lorentz-invariant. We also examine the Lorentz-invariant power-law energy–momentum expressions, which include Einstein’s energy relation as a particular case.