The possibility that quantum mechanics is founded on non-metric space has been previously introduced as an alternative consequence of Bell inequalities violation. This work develops the concept further by an analysis ...The possibility that quantum mechanics is founded on non-metric space has been previously introduced as an alternative consequence of Bell inequalities violation. This work develops the concept further by an analysis of the iconic Heisenberg gedanken experiment. No lower bound is found in the gedanken uncertainly relation for a non-metric spatial background. This result has the fundamental consequence that the quantum particle trajectory is retained in non-metric space and time. Assignment of measurement number-values to unmeasured incompatible variables is found to be mathematically incorrect. The current disagreement between different formulations of the empirically verified error-disturbance relations can be explained as a consequence of the structure of space. Quantum contextuality can likewise be explained geometrically. An alternative analysis of the extendedEPRperfect anti-correlation configuration is given. The consensus that local causality is the sole assumption is found to be incorrect. There is also the additional assumption of orientation independence. Inequalities violation does not therefore mandate rejection of local causality. Violation of the assumption of orientation independence implies rejection of metric, non-contextual variables algebraically representing physical quantities.展开更多
In this paper,we propose a state-varying endogenous regime switching model(the SERS model),which includes the endogenous regime switching model by Chang et al.,the CCP model,as a special case.To estimate the unknown p...In this paper,we propose a state-varying endogenous regime switching model(the SERS model),which includes the endogenous regime switching model by Chang et al.,the CCP model,as a special case.To estimate the unknown parameters in the SERS model,we propose a maximum likelihood estimation method.Monte Carlo simulation results show that in the absence of state-varying endogeneity,the SERS model and the CCP model perform similarly,while in the presence of state-varying endogeneity,the SERS model performs much better than the CCP model.Finally,we use the SERS model to analyze Chinese stock market returns,and our empirical results show that there exists strongly state-varying endogeneity in volatility switching for the Shanghai Composite Index returns.Moreover,the SERS model can indeed produce a much more realistic assessment for the regime switching process than the one obtained by the CCP model.展开更多
文摘The possibility that quantum mechanics is founded on non-metric space has been previously introduced as an alternative consequence of Bell inequalities violation. This work develops the concept further by an analysis of the iconic Heisenberg gedanken experiment. No lower bound is found in the gedanken uncertainly relation for a non-metric spatial background. This result has the fundamental consequence that the quantum particle trajectory is retained in non-metric space and time. Assignment of measurement number-values to unmeasured incompatible variables is found to be mathematically incorrect. The current disagreement between different formulations of the empirically verified error-disturbance relations can be explained as a consequence of the structure of space. Quantum contextuality can likewise be explained geometrically. An alternative analysis of the extendedEPRperfect anti-correlation configuration is given. The consensus that local causality is the sole assumption is found to be incorrect. There is also the additional assumption of orientation independence. Inequalities violation does not therefore mandate rejection of local causality. Violation of the assumption of orientation independence implies rejection of metric, non-contextual variables algebraically representing physical quantities.
基金The authors extend their sincere thanks to the editor and two referees for their insightful comments that helped improve the article substantially.This research is supported by the National Natural Science Foundation of China(Project 71803091)by the MOE(Ministry of Education in China)Project of Humanities and Social Sciences(Project 18YJC790015).
文摘In this paper,we propose a state-varying endogenous regime switching model(the SERS model),which includes the endogenous regime switching model by Chang et al.,the CCP model,as a special case.To estimate the unknown parameters in the SERS model,we propose a maximum likelihood estimation method.Monte Carlo simulation results show that in the absence of state-varying endogeneity,the SERS model and the CCP model perform similarly,while in the presence of state-varying endogeneity,the SERS model performs much better than the CCP model.Finally,we use the SERS model to analyze Chinese stock market returns,and our empirical results show that there exists strongly state-varying endogeneity in volatility switching for the Shanghai Composite Index returns.Moreover,the SERS model can indeed produce a much more realistic assessment for the regime switching process than the one obtained by the CCP model.
