The aim of this book is to show that the probabilistic formalisms of classical statistical mechanics and quantum mechanics can be unified on the basis of ageneral contextual probabilistic model (the Växjö model). By taking into account the dependence of (classical) probabilities on contexts (complexes of physical conditions) one can reproduce all distinguishing features of quantum probabilities, e.g. the interference of probabilities and violation of Bell’s inequality. Moreover, by starting with the formula for interference of probabilities (which generalizes the well known classical formula of total probability) one can construct the representation of contextual probabilities by complex probability amplitudes or in the abstract formalism by normalized vectors of the complex Hilbert space or its hyperbolic generalization. Thus the Hilbert spacerepresentation of probabilities can be derived from natural classical probabilistic assumptions. Clarifies the probabilistic structure of quantum theory Unifies probabilistic formalisms of classical statistical mechanics and quantum mechanics INDICE: From the contents Part I: Quantum and Classical Probability, 1: Quantum Mechanics: Postulates and Interpretations, Chapter 2: Classical Probability Theories; Part I I: Contextual Probability and Quantum-Like Models, 1: Contextual Probability and Interference, 2: Quantum-Like Representation of Contextual Probabilistic Model, 3: Ensemble Representation of Contextual StatisticalModel, 4: Latent Quantum-Like Structure in the Kolmogorov Model, 5: Interference of Probabilities from Law of Large Numbers; Part III: Bell's Inequality, 1: Probabilistic Analysis of Bell's Argument, 2 : Bell's Inequality for Conditional Probabilities, 3: Frequency Probabilistic Analysis of Bell-type Considerations, 4: Original EPR-Experiment: Local Realistic Model; Part IV: Interrelation between Classical and Quantum Probabilities, 1: Discrete Time Dynamics, 2: Noncommutative Probability in Classical Disordered Systems, 3: Derivation of Schrödinger's Equation in the Contextual Probabilistic Framework.
- ISBN: 978-1-4020-9592-4
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 375
- Fecha Publicación: 01/02/2009
- Nº Volúmenes: 1
- Idioma: Inglés