There is long-held suspicion that self-reference and undecidability are the circumstances of quan... more There is long-held suspicion that self-reference and undecidability are the circumstances of quantum measurement. This paper offers concrete evidence for these in actual experiments. The famous arguments of Cantor, Russel, Tarski, Gödel and Turing and other classical paradoxes all employ Diagonal Arguments. And in 1969, F W Lawvere showed these are all special cases of the same Fixed-Point Theorem. Making use of Lawvere, Jochen Szangolies argues that there is no avoiding a class of physical measurements that result in Liar Paradox output, stemming from self-reference absent of fixed-point. Following up on Szangolies, in this paper I impose self-reference absent of fixed-point on the photon polarisation density matrix for experiments conducted by Tomasz Paterek et al. As result, in addition to revealing the expected Liar Paradox output behaviour, logically independent propositions are found to derive also, identical to those which Paterek et al identify as correlating directly with quantum randomness in their experiments. This direct connection is evidence supporting Szangolies, and by extension, completes a link between quantum randomness and self-reference absent of fixed-point-the common sub-structure beneath: Russell's Paradox, Turing's Halting Problem, and Gödel's Incompleteness theorems.
There is long-held suspicion that self-reference and undecidability are the circumstances of quan... more There is long-held suspicion that self-reference and undecidability are the circumstances of quantum measurement. This paper offers concrete evidence for these in actual experiments. The famous arguments of Cantor, Russel, Tarski, Gödel and Turing and other classical paradoxes all employ Diagonal Arguments. And in 1969, F W Lawvere showed these are all special cases of the same Fixed-Point Theorem. Making use of Lawvere, Jochen Szangolies argues that there is no avoiding a class of physical measurements that result in Liar Paradox output, stemming from self-reference absent of fixed-point. Following up on Szangolies, in this paper I impose self-reference absent of fixed-point on the photon polarisation density matrix for experiments conducted by Tomasz Paterek et al. As result, in addition to revealing the expected Liar Paradox output behaviour, logically independent propositions are found to derive also, identical to those which Paterek et al identify as correlating directly with quantum randomness in their experiments. This direct connection is evidence supporting Szangolies, and by extension, completes a link between quantum randomness and self-reference absent of fixed-point-the common sub-structure beneath: Russell's Paradox, Turing's Halting Problem, and Gödel's Incompleteness theorems.
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