The Dirac particle S_D is investigated by means of dynamic methods, i.e. without a use of the principles of quantum mechanics. It is shown that the Pauli particle S_P and the nonrelativistic approximation S_{nD} of the Dirac particle S_D are different dynamic systems. S_{nD} contains the high frequency degrees of freedom, which are absent in the dynamic system S_P. It means that the nonrelativistic Dirac particle S_{nD} is composite (i.e. it has internal degrees of freedom), whereas the Pauli particle S_P is a pointlike particle with the spin. In the absence of the electromagnetic field the world line of the classical Pauli particle S_{Pcl} is a timelike straight, whereas that of the classical nonrelativistic Dirac particle S_{nDcl} is a helix. The characteristic frequency $Ω=2mc^{2}/\hbar $ of this helix is the threshold frequency of the pair production. Using dynamic methods, one shows freely that the Copenhagen interpretation, when the wave function is a specific quantum object describing the state of individual particle, is incompatible with the quantum mechanics formalism. Besides, it is shown that the momentum distribution in quantum mechanics is in reality the mean momentum distribution. Effectiveness of different investigation strategies is discussed and compared.
It is shown that in the context of stochastic-phase-space formulations of quantum mechanics a nonlocal type of nonrelativistic as well as relativistic dynamics for a massive spin-zero particle moving in an external electromagnetic field can be formulated in ${L}^{2}(\ensuremath{\Gamma})$ space. In a sharp-point limit $s\ensuremath{\rightarrow}+0$ the nonrelativistic dynamics merges into the conventional local model. The relativistic dynamics is gauge invariant, it can be formulated covariantly in the relativistic phase space
Mm, it possesses a covariant propagator, it leaves the space of positive-energy solutions of the Klein-Gordon equation invariant, and it gives rise to a covariant and conserved probability current on stochastic phase space. Furthermore, for states describing a particle moving at nonrelativistic speeds in relation to a given inertial frame, the relativistic propagation contracts into its nonrelativistic counterpart. The sharp-point limit $s\ensuremath{\rightarrow}+0$ of the relativistic
S matrix also exists in each such inertial frame. The necessity of interactions acting at nonsharp configuration points for a consistent formulation of covariant relativistic one-particle dynamics is traced to the question of the nonexistence of covariant position operators in relativistic theories. The mandatory character of this feature is shown to be firmly rooted in the theory of quantum measurement.