The debate on quantum mechanics and constructive mathematics: a review

Xiaoling Wang

The paper reviewed the construction and development of quantum mechanics,and analyzed the corresponding philosophical debate of some paradox and interpretation.It also investigated the dialectic determinism relationship between philosophy and the development of quantum mechanics from an epistemology and ontological point of view,and discussed the attribution and the essence of determinism from the achievements of quantum mechanics.It concluded that the determinism is recovered both in theoretical framework and substance validation.

Douglas Bridges, Karl Svozil

Manuel Gadella

We review the mathematical tools that are suitable for a formulation of time asymmetry in quantum mechanics. In particular, Hardy functions on a half plane and rigged Hilbert spaces constructed with a subclass of Hardy functions. This time asymmetry often appears in quantum scattering and, in particular, in resonance scattering. We review the construction of Gamow vectors, often considered Gamow states for resonances. A brief summary of the fundamental ideas of time asymmetric quantum mechanics is presented in a last section.

Walter Smilga

Douglas Bridges

Shan Gao

At the heart of quantum mechanics lies the wave function, a powerful but mysterious mathematical object which has been a hot topic of debate from its earliest stages. Covering much of the recent debate and providing a comprehensive and critical review of competing approaches, this ambitious text provides new, decisive proof of the reality of the wave function. Aiming to make sense of the wave function in quantum mechanics and to find the ontological content of the theory, this book explores new ontological interpretations of the wave function in terms of random discontinuous motion of particles. Finally, the book investigates whether the suggested quantum ontology is complete in solving the measurement problem and if it should be revised in the relativistic domain. A timely addition to the literature on the foundations of quantum mechanics, this book is of value to students and researchers with an interest in the philosophy of physics.