Smooth Quantum Mechanics

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Stoica, Ovidiu Cristinel
preprint description
I show that the contradiction between the unitary evolution and the condition to obtain, as a result of the measurement, an eigenstate of the observable, can be resolved without making use of discontinuities. The apparent state vector reduction can be replaced with a delayed initial condition, imposed to the unitary evolution of the observed system entangled with the measurement device used for the preparation. Since the quantum state of this device is not available entirely to the observer, its unknown degrees of freedom inject, by the means of entanglement, an apparent randomness in the observed system, leading to a probabilistic behavior. The condition imposed by the observable combined with the condition of minimal disturbance lead to the Born rule. Thus, we can construct a Smooth Quantum Mechanics, without the need of discontinuities in time evolution, and the probabilities appear from the lack of knowledge of the quantum states of all the systems involved. As a consequence, the evolution is deterministic, but there is no way for an observer to make complete use of this determinism. For such an observer, and for an open quantum system, the evolution will still be indeterministic. The possibility to choose the initial conditions with a delay makes the determinism to be compatible with the free will at the same extent as the indeterministic version of Quantum Mechanics is. The apparent indeterminism at the observer's level also leaves room for a smooth version of the Many Worlds Interpretation.