Measurements and Amplitudes
We present a framework for quantum mechanics based on the concepts of measurements and amplitudes. The measurements are represented by functions and therefore commute. The interference effects characteristic of quantum mechanics are caused by the fact that probabilities are computed using am-plitude functions. Moreover, in order to consider inexact measurements we define fuzzy (or nonsharp) amplitudes. We also study measurements that satisfy a positivity condition and that axe covariant relative to a symmetry group. It is shown that the framework includes stochastic quantum mechanics which in turn includes traditional Hilbert space quantum mechanics.
KeywordsHilbert Space Stochastic Quantum Amplitude Density Additive Probability Measure Classical Statistical Theory
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