Uncomputable UV-complete theory and hidden variables interpretations beyond Bohmian particle mechanics
William Icefield
When statistical models are used in social sciences, there is no presumption that actual reality is stochastic. Even if actual reality is deterministic, hidden and unobservable variables require a use of effective (in ordinary language, approximate) models, with number of variables potentially unrestricted. From the quantum reconstruction point of view, quantum mechanics can be interpreted as a statistical information-processing framework - therefore, the aforementioned view in social sciences can naturally be transported to quantum physics - this especially so given prevalent uses of effective theories. This naturally gives us the common framework behind hidden variables interpretations unconstrained by particular laws of deterministic motion. The measurement problem is cleanly identified as arising from missing hidden variables. However, hidden variables interpretations do not imply that a final UV-complete theory of physics has to be usable - the theory may be uncomputable, with inability to generate predictions. In such a case, an infinite sequence of effective quantum theories would have to be used. Therefore, even if hidden variables interpretations are correct, supremacy of the orthodox quantum mechanics framework may be upheld, which is supported by a combination of quantum reconstruction and computational complexity arguments. This allows us to bypass considerable difficulties of hidden variables interpretations in satisfying Lorentz invariance. Connections to entropic gravity are then explored.
•Jul 21, 2020•0 citations