Harmonizing de Broglie-Bohm's Causal Interpretation with the Copenhagen Interpretation of Quantum Mechanics

The non-relativistic quantum theory has been interpreted causally by de Broglie, David Bohm, and others, where a quantum entity is viewed as a particle with a definite position and momentum. This interpretation opposes the Copenhagen orthodox interpretation, which expresses uncertainty through the commutator relationship between position and momentum operators. This is further exacerbated by the de Broglie-Bohm interpretation, which uses no operators corresponding to these observables. We reconcile these opposing viewpoints by introducing mathematical nonlinear operators for the momentum observable. While nonlinear non-Hermitian operators cannot be easily used as matrices in the Hilbert space, we show that they are implicitly embedded in de Broglie-Bohm's interpretation of quantum theory.