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We introduce a 'uniform tension-reduction' (UTR) model, which allows torepresent the probabilities associated with an arbitrary measurement situationand use it to explain the emergence of quantum probabilities (the Born rule) as'uniform' fluctuations on this measurement situation. The model exploits thegeometry of simplexes to represent the states, in a way that the measurementprobabilities can be derived as the 'Lebesgue measure' of suitably definedconvex subregions of the simplexes. We consider a very simple and evocativephysical realization of the abstract model, using a material point particlewhich is acted upon by elastic membranes, which by breaking and collapsingproduce the different possible outcomes. This easy to visualize mechanicalrealization allows one to gain considerable insight into the possible hiddenstructure of an arbitrary measurement process. We also show that the UTR-modelcan be further generalized into a 'general tension-reduction' (GTR) model,describing conditions of lack of knowledge generated by 'non-uniform'fluctuations. In this ampler framework, particularly suitable to describeexperiments in cognitive science, we define and motivate a notion of 'universalmeasurement', describing the most general possible condition of lack ofknowledge in a measurement, emphasizing that the uniform fluctuationscharacterizing quantum measurements can also be understood as an average overall possible forms of non-uniform fluctuations which can be actualized in ameasurement context. This means that the Born rule of quantum mechanics can beunderstood as a first order approximation of a more general non-uniform theory,thus explaining part of the great success of quantum probability in thedescription of different domains of reality. This is the first part of atwo-part article.

The Unreasonable Success of Quantum Probability I: Quantum Measurements as Uniform Fluctuations