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John Harding
New Mexico State University

Project Title

Events as Decompositions

Project Summary

The standard view of quantum mechanics is that a superposition of states corresponding to different outcomes of an event is given by the sum s = s1 + s2 of states of the alternatives. Since vectors are the natural setting to add physical quantities, Dirac viewed this as rational for his formulation of quantum mechanics with states as vectors in a Hilbert space. We take the view that events correspond to ways to decompose a system as a product of others A = A1 × A2. This is like choosing a coordinate axes to express points in the plane. The superposition of states s1 and s2 for different outcomes is given not by a sum, but by an ordered pair s = (s1, s2). The collection of ways to decompose a system as a product carries a structure similar to that carried by the projections that are used to model events in the standard Hilbert space setting. This allows development of alternative versions of quantum mechanics based in structures other than Hilbert spaces and motivated entirely by simple physical assumptions.

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