# A dynamical time operator in Dirac's relativistic quantum mechanics - Quantum Physics

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Abstract: A self-adjoint dynamical time operator is introduced in Dirac-s relativisticformulation of quantum mechanics and shown to satisfy a commutation relationwith the Hamiltonian analogous to that of the position and momentum operators.The ensuing time-energy uncertainty relation involves the uncertainty in theinstant of time when the wave packet passes a particular spatial position andthe energy uncertainty associated with the wave packet at the same time, asenvisaged originally by Bohr. The instantaneous rate of change of the positionexpectation value with respect to the simultaneous expectation value of thedynamical time operator is shown to be the phase velocity, in agreement with deBroglie-s hypothesis of a particle associated wave whose phase velocity islarger than c. Thus, these two elements of the original basis andinterpretation of quantum mechanics are integrated into its formal mathematicalstructure. Pauli-s objection is shown to be resolved or circumvented. Possiblerelevance to current developments in interference in time, in Zitterbewegunglike effects in spintronics, grapheme and superconducting systems and incosmology is noted.

Author: ** Mariano Bauer**

Source: https://arxiv.org/