ABSTRACT
More generally, suppose that |ψ〉p = c1 |ψ1〉p + c2 |ψ2〉p is a superposition of proton spin-states. Then it seems reasonable to assume that the pair (|ψ〉p , |φ〉e) should describe a composite spin-state that is linearly related to those described by the pairs (|ψ1〉p , |φ〉e) and (|ψ2〉p , |φ〉e), and similarly if |φ〉e is a superposition. M agrees with this assumption, and offers the following construction as a simple way of satisfying this requirement. Begin by considering the complex vector space C {Wp ×We} with basis given by the set Wp ×We. This is a huge vector space, of uncountably infinite dimension equal to the cardinality ofWp×We. But we will construct a small quotient by imposing some equivalences coming from the previous remarks. So consider the subspace R ⊂ C {Wp ×We} defined as the span of all vectors of the form
(a, αb1 + βb2)− α(a,b1)− β(a,b2), (αa1 + βa2,b)− α(a1,b)− β(a2,b).
