Lorentz-invariance in quantum theory

Extract

The formal conditions of Lorentz-invariance apply to coordinates x₁, x₂, x₃, x₄ which form a 4-vector, and to expressions associated with them. In this paper attention is called to the frequent disregard in quantum investigations of the proviso that the coordinates form a 4-vector.

In most quantum investigations with a practical application the coordinates employed are relative space coordinates ξ, η, ζ coupled with a progressive time coordinate, so that (ξ, η, ζ, it) is not a 4-vector. Nevertheless, conditions of Lorentz-invariance are applied by many authors. Alternatively, they attempt to base the investigation on wave functions of non-relative coordinates x, y, z, t. It is here pointed out that such wave functions give no information about the eigenstates, and that there is no means of deriving wave functions of ξ, η, ζ from those of x, y, z.

Special attention is directed to the misapplication of Lorentz-invariance in Dirac's theory of the hydrogen atom, and in the calculation of degeneracy energy of ionized material.