Towards a nonlinear quantum physics - Croca, J. R. (World Scientific Pub. Co., 2003)
Includes bibliographical references and indexes
1. Introduction -- 2. Complementarity principle and the nonlocal Fourier analysis. 2.1. Introduction. 2.2. Fourier nonlocal analysis. 2.3. The measurement and the collapse of the wave train. 2.4. Heisenberg uncertainty relations and the complementarity principle. 2.5. References -- 3. New generation of microscopes. 3.1. Introduction. 3.2 The common Fourier microscopes. 3.3 Tunneling super-resolution microscope. 3.4. Apertureless optical microscope. 3.5. References -- 4. Beyond Heisenberg's uncertainty relations. 4.1. Introduction. 4.2. Wavelet local analysis. 4.3. Some elements of the causal theory of de Broglie. 4.4. A nonlinear Schrodinger equation. 4.5. Local paradigm in place of the nonlocal Fourier paradigm. 4.6. Derivation of a more general set of uncertainty relations. 4.7. Experiments to test the general validity of the usual uncertainty relations. 4.8. An example of a concrete measurement that goes beyond Heisenberg's uncertainty relations. 4.9. References -- 5. The meaning of the wave function. 5.1. Introduction. 5.2. A causal interpretation for the two-slit experiment. 5.3. Experiments to test the nature of the wave function. 5.4. Experiments on the collapse of the wave function. 5.5. Experiments based on the complex interaction process of the causal quantum particles. 5.6. References -- 6. Interference without superposition of the wave packets. 6.1. Introduction. 6.2. Interferometric experiments without overlapping of the wavepackets. 6.3. Orthodox interpretation. 6.4. Causal explanation. 6.5. Experimental test for the two approaches. 6.6. Franson type experiments. 6.7. References
The author of this book presents conceptual and experimental evidence showing that Heisenberg's uncertainty relations are not valid in all cases. Furthermore, he derives a more general set of uncertainty relations. The new relations result from the replacement of the Fourier nonlocal and nontemporal paradigm by wavelet local analysis. These results lead to a coherent and beautiful causal synthesis unifying quantum and classical physics