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We show that there is a manifestly covariant version of the Pauli Hamiltonianwith equations of motion quadratic on spin and field strength. Relativisticcovariance inevitably leads to noncommutative positions: classical brackets ofthe position variables are proportional to the spin. It is the spin-inducednoncommutativity that is responsible for transforming the covariant Hamiltonianinto the Pauli Hamiltonian, without any appeal to the Thomas precessionformula. The Pauli theory can be thought to be $1/c^2$ approximation of thecovariant theory written in special variables. These observations clarify thelong standing question on the discrepancy between the covariant and PauliHamiltonians. We also discuss the transformational properties of spin axis inthe passage from laboratory to comoving and instantaneous frames, and revealthe role of Thomas spin-vector in the covariant scheme.

Covariant version of Pauli Hamiltonian, spin-induced non commutativity, Thomas precession and precession of spin