Early in the development of quantum theory Bohr introduced what came to be called the Copenhagen interpretation. Specifically, the square of the absolute value of the wave function was to be used as a probability density. There followed lengthy arguments about this ranging from alternative universes to Schrodinger's cat. Einstein famously remarked "I am convinced that He (God) does not play dice." The purpose of this paper is to present a mathematical model of the measuring process that shows that the Copenhagen interpretation can actually follow from the fact that the time development of quantum systems is governed by the usual one parameter group of unitary transformations exp-iHt and that probability enters into the theory in the way it usually does in physics, namely, by having a large number of deterministic equations that can only be handled probabilistically.
Blackman, Jerome and Hsiang, Wu Teh, "Why Probability Appears in Quantum Mechaincs" (2011). Mathematics Faculty Scholarship. 92.
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