Determinism in hidden variable interpretation and Turings halting problem

Abstract

Heisenberg deduced the famous uncertainty principle which shows that there exist several conjugated quantities that can never be measured precisely at the same time. Further, Copenhagen interpretation gives a new perspective about quantum mechanics, which claims that particles do not have properties like position or momentum until people measure it. Hence, the famous EPR paradox was proposed to question the realism and locality of Quantum mechanics, which leads to the Hidden Variable explanation. However, this theorem was proved wrong by John Bell in 1964 with Bell Inequality. In addition, Hidden Variable Interpretation was developed by De Broglie and Bohm, they came up with the Bohmian Mechanics, which can be considered as Non-local Hidden Variable theorem. This interpretation gives physical meaning to waves. Unlike Copenhagen Interpretation, this theorem claims that particles do have a determined position. Some people may argue that it can be proved contradicted by using the Turing method (self-reference). Because if the algorithm represented by physics law described Hidden Mechanics to determine particles state, then the future is determined and predictable. Therefore, another algorithm can be established based on that, which will lead to Liar Paradox. This article will briefly introduce the uncertainty principle and some interpretations about quantum mechanics. Furthermore, this article will combine some ideas in Alan Turings Halting Problem to the universe of non-local hidden variables as a thought experiment, which involve self-reference, to give an interesting result of locality and determinism.