Applications to Foundations of Quantum Theory
摘要
In this chapter we explain how the p-adic theory of causality developed in preceding chapters can be applied to the foundations of quantum theory in order to give rigorous mathematical reasoning to the so-called superdeterministic interpretations of quantum mechanics. We are aimed to show that superdeterministic models (e.g., the ones which are developing by S. Hossenfelder, T. Palmer, and others) are realistic models in the sense of the so-called model-dependent realism first coined in The Grand Design by S. Hawking and L. Mlodinow. We rigorously prove that since observational data (i.e., numerical values of physical quantities) are only rational numbers due to inevitably non-zero measurement errors, a conclusion whether Nature on the smallest of the scales is discrete or continuous, random/chaotic, or strictly deterministic solely depends on experimenter’s free choice of the metrics (real or p-adic) he chooses to process the observational data; that is, “free will” is consistent with superdeterminism. Moreover, the assumption of causality at the smallest of the scales inevitably implies superdeterminism.