 Gleason 's theorem implies the nonexistence of certain types of hidden variable theories for quantum mechanics , strengthening a previous argument of John von Neumann . Von Neumann had claimed to show that hidden variable theories were impossible , but ( as Grete Hermann pointed out ) his demonstration made an assumption that quantum systems obeyed a form of additivity of expectation for noncommuting operators that might not hold a priori . In 1966 , John Stewart Bell showed that Gleason 's theorem could be used to remove this extra assumption from von Neumann 's argument . 
