From: jimgoetz316@gmail.com   
      
   I am working on a thought experiment that assumes the certainty of   
   quantum set theory (QST). Below is my two paragraph summary. Are   
   there any quantum mechanics experts here who could check if I am   
   accurately summarizing QST?   
      
   Birkhoff and von Neumann [11] introduced quantum logic in response   
   to logical problems with the Copenhagen interpretation. Takeuti [8]   
   formed the quantum logic into an introduction of QST. Eventually,   
   Ozawa took the lead to develop QST into a feasible interpretation   
   of quantum mechanics (QM) that coheres with the classical law of   
   noncontradiction, predicate logic, and experimental physics [9, 10,   
   12, 13]. For example, QST defines quantum states with certainty   
   instead of classical uncertainty.   
      
   In short, QST begins with a prior probability distribution of   
   observables for a particular quantum state. This distribution looks   
   similar to a corresponding Copenhagen probability distribution of   
   observables for the quantum state, but QST assigns predicate logic   
   to each observable in the prior set for the quantum state. For example,   
   the existence of each observable in a particular quantum state is true   
   or false. This results in a set of existing observables that completely   
   defines the quantum state despite classically non-commuting observables   
   such as momentum and position. Additionally, QST can define entangled   
   states because it is a state-dependent theory instead of a   
   particle-dependent theory. Furthermore, QST preserves two points of   
   the Copenhagen interpretation. First, each quantum state endures for   
   1 Planck time. Second, there is a probability distribution for the   
   probabilistic causality during the transition from one quantum state to   
   the next. For instance, the transition from one quantum state to the   
   next is the only element of uncertainty in QST.   
      
   References   
   8. Takeuti, G.: Quantum set theory. In: Beltrametti, E.G., van Fraassen,   
   B.C. (eds.) Current Issues in Quantum Logic, pp. 303=E2=80=93322. Plenum,   
   New York (1981)   
      
   9. Ozawa, M. Quantum reality and measurement: A quantum logical approach.   
   Found. Phys. 41, 592=E2=80=93607 (2011)   
      
   10. Ozawa, M. Quantum set theory extending the standard probabilistic   
   interpretation of quantum theory. New Generat. Comput. 34, 125=E2=80=93152   
   (2016)   
      
   11. Birkhoff, G., von Neumann, J.: The logic of quantum mechanics. Ann.   
   Math. 37, 823=E2=80=93843 (1936)   
      
   12. Sulyok, G., Sponar, S., Demirel, B., Buscemi, F., Hall, M.J.W., Ozawa,   
   M., Hasegawa, Y.: Experimental test of entropic noise-disturbance   
   uncertainty relations for spin-1/2 measurements. Phys. Rev. Lett. 115,   
   030401 (2015)   
      
   13. Demirel, B., Sponar, S., Sulyok, G., Ozawa, M., Hasegawa, Y.:   
   Experimental test of residual error-disturbance uncertainty relations for   
   mixed spin-1/2 states. Phys. Rev. Lett. 117, 140402 (2016)   
      
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