Study of Quantum Set Theory Aiming at an Interpretation of Elements of Reality in Quantum Theory

点击翻译按钮获取中文摘要

It is one of long-standing open problems in the field across physics and philosophy to give a realistic interpretation for values of quantum observables. In this research we proposed a new approach to this problem based on quantum set theory. We studied the relationship between quantum set theory and modal interpretation of quantum theory, and we showed the equivalence between the condition for a von Neumann algebra to be a beable algebra for a given state and the condition for a subuniverse of quantum set theory to satisfy all the theorems of ZFC set theory in that state. We also extended the conventional no collapse interpretation for projective measurements to a no collapse interpretation for arbitrary generalized measurements by using the equivalence between quantum perfect correlation for two observables and the quantum-set-theoretical equality for two real numbers in quantum set theory.