Quantum Foundations, Probability and Information

omposed of contributions from leading experts in quantum foundations, this volume presents viewpoints on a number of complex problems through informational, probabilistic, and mathematical perspectives and features novel mathematical models of quantum and subquantum phenomena. Rich with multi-disciplinary mathematical content, this book includes applications of partial differential equations in quantum field theory, differential geometry, oscillatory processes and vibrations, and Feynman integrals for quickly growing potential functions. 

Due to rapid growth in the field in recent years, this volume aims to promote interdisciplinary collaboration in the areas of quantum probability, information, communication and foundation, and mathematical physics. Many papers discuss complex yet novel problems that depart from the mainstream of quantum physical studies. Others devote explanation to fundamental problems of the conventional quantum theory, including its mathematical formalism. Overall, authors cover a diverse set of topics, including quantum and classical field theory and oscillatory processing, quantum mechanics from a Darwinian evolutionary perspective, and biological applications of quantum theory.

Together in one volume, these essays will be useful to experts in the corresponding areas of quantum theory. Theoreticians, experimenters, mathematicians, and even philosophers in quantum physics and quantum probability and information theory can consider this book a valuable resource. 

Table of Contents

1. The Dirac Equation as One Fourth-Order Equation for One Function: A General, Manifestly Covariant Form
2. At the Crossroads of Three Seemingly Divergent Approaches to Quantum Mechanics
3. Implications of Einstein-Wey! Causality on Quantum Mechanics
4. The Action Reaction Principle in Quantum Mechanics
5. Replacing Nothing with Something Special: Contextuality-by-Default and Dummy Measurements
6. A Computational Proof of Locality in Entanglement
7. Efficient Energy Transfer in Network Model of Photosynt hesis
8. Clockwork Rebooted: Is the Universe a Computer?
9. External Observer Reflections on QBism, Its Possible Modifications, and Novel Applications
10. Epistemic View of Quantum Communication
11. Quantum Decoherence Emulated in a Classical Device
12. Local Realism Without Hidden Variables
13. Underground Test of Quantum Mechanics: The VIP2 Experiment
14. Feynman Integrals for a New Class of Time-Dependent Exponentially Growing Potentials
15. Classical Field Theory of the Photoelectric Effect
16. Classification Problem in a Quantum Framework
17. On Complexity for Open System Dynamics
18. Bell Correlations and the Common Future
19. Temporal Vibrations in a Quantized Field

About the Authors

Professor Andrei Khrennikov is the author of roughly 380 papers published in physical and mathematical journals and 18 monographs. He is currently the director of the International Center for Math Modeling in PHysics and Cognitive Science and the head of research at the Mathematical Institute in Linnaeus University. Khrennikov also organizes Quantum and Beyond, a world-famous series of conferences on quantum foundations, quantum information and probability held in Växjö annually.

Bourama Toni is a Professor of Mathematics in the College of Engineering and Technology at Virginia State University. He received his PhD from the University of Montreal, and his research interests include bifurcation theory, abstract differential equations in Banach and Hilbert spaces, quasi-limit cycles, mathematical modeling in biosciences, and game & utility Theory.