On the hidden parameter in quantum and classical physics

I. I. Zinnes

The hidden variable theorem due to von Neumann is deduced in a physically transparent manner. As a result it is clear that the theorem is correct only if one requires that these hidden variables merely enlarge the set of observables employed at present in quantum mechanics. The theorem cannot be interpreted to mean that one cannot introduce such additional variables in order (1) to specify a state with classical completeness and (2) to define the usual observables as statistical parameters.

John Stewart Bell

Xiaoyu Li, Qin-Sheng Zhu, Yong Hu +4 more

The Hidden Quantum Markov Model (HQMM) has significant potential for analyzing time-series data and studying stochastic processes in the quantum domain as an upgrading option with potential advantages over classical Markov models. In this paper, we introduced the split HQMM (SHQMM) for implementing the hidden quantum Markov process, utilizing the conditional master equation with a fine balance condition to demonstrate the interconnections among the internal states of the quantum system. The experimental results suggest that our model outperforms previous models in terms of scope of applications and robustness. Additionally, we establish a new learning algorithm to solve parameters in HQMM by relating the quantum conditional master equation to the HQMM. Finally, our study provides clear evidence that the quantum transport system can be considered a physical representation of HQMM. The SHQMM with accompanying algorithms present a novel method to analyze quantum systems and time series grounded in physical implementation.

John Stewart Bell

Simon Kochen, Ernst P. Specker

Nicolas Gisin

Do scientific theories limit human knowledge? In other words, are there physical variables hidden by essence forever? We argue for negative answers and illustrate our point on chaotic classical dynamical systems. We emphasize parallels with quantum theory and conclude that the common real numbers are, de facto, the hidden variables of classical physics. Consequently, real numbers should not be considered as ``physically real" and classical mechanics, like quantum physics, is indeterministic.