## The Basis of Quantum Mechanics' Compatibility with Relativity Whose Impairment Gives Rise to the Klein-Gordon and Dirac Equations

**Authors:** Steven Kenneth Kauffmann

Solitary-particle quantum mechanics' inherent compatibility with special relativity is implicit in Schrödinger's
postulated wave-function rule for the operator quantization of the particle's canonical threemomentum,
taken together with his famed time-dependent wave-function equation that analogously treats
the operator quantization of its Hamiltonian. The resulting formally four-vector equation system assures
proper relativistic covariance for any solitary-particle Hamiltonian operator which, together with its canonical
three-momentum operator, is a Lorentz-covariant four-vector operator. This, of course, is always the
case for the quantization of the Hamiltonian of a properly relativistic classical theory, so the strong correspondence
principle definitely remains valid in the relativistic domain. Klein-Gordon theory impairs this
four-vector equation by iterating and contracting it, thereby injecting extraneous negative-energy solutions
that are not orthogonal to their positive-energy counterparts of the same momentum, thus destroying the
basis of the quantum probability interpretation. Klein-Gordon theory, which thus depends on the square
of the Hamiltonian operator, is as well thereby cut adrift from Heisenberg's equations of motion. Dirac
theory confuses the space-time symmetry of the four-vector equation system with such symmetry for its
time component alone, which it fatuously imposes, thereby breaching the strong correspondence principle
for the free particle and imposing the starkly unphysical momentum-independence of velocity. Physically
sensible alternatives, with external electromagnetic fields, to the Klein-Gordon and Dirac equations are
derived, and the simple, elegant symmetry-based approach to antiparticles is pointed out.

**Comments:** 14 pages, Also archived as arXiv:1005.2641 [physics.gen-ph].

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### Submission history

[v1] 18 May 2010

[v2] 23 May 2010

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