Theoretical and Empirical Explorations of “Generalized Quantum Theory”

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Theoretical and Empirical Explorations of “Generalized Quantum Theory” Theoretical and empirical explorations of “Generalized Quantum Theory” Nikolaus von Stillfried Dissertation zur Erlangung der Doktorwürde Eingereicht an der Kulturwissenschaftlichen Fakultät der Europa-Universität Viadrina Frankfurt an der Oder 2010 Gutachter dieser Dissertation: Herr Prof. Dr. Dr. H. Walach Fakultät für Kulturwissenschaft der Europa-Universität Viadrina, Frankfurt an der Oder Herr Prof. Dr. H. Römer Fakultät für Mathematik und Physik der Albert-Ludwigs- Universität, Freiburg im Breisgau Herr Prof. Dr. H. Schröder Fakultät für Kulturwissenschaft der Europa-Universität Viadrina, Frankfurt an der Oder Datum der Disputation: 26. April 2010 Gewidmet Nicole Table of contents 1. Overview.....................................................................................................................................7 2. Some Aspects of Quantum Theory.......................................................................................11 2.1 Complementarity ...............................................................................................................11 2.1.1 The Wave-Particle Duality of light and the Double-Slit Experiment .................11 2.1.2 The Complementarity Principle ...............................................................................19 2.2 Observables........................................................................................................................25 2.3 Entanglement.....................................................................................................................29 2.3.1 The EPR-type experiments.......................................................................................31 2.3.2 How to explain these EPR correlations? ................................................................33 2.3.2.1 Bell Inequalities ...................................................................................................35 2.3.2.2 Summary...............................................................................................................40 2.3.2 Properties of entanglement.......................................................................................41 2.4 Probability and the “interpretation problem”................................................................47 2.5 Self-referentiality................................................................................................................53 3. Some Aspects of Generalized Quantum Theory (GQT)...................................................57 3.1 Introduction .......................................................................................................................57 3.2 Generalized probability.....................................................................................................61 3.3 Generalized observables ...................................................................................................65 3.4 Generalized complementarity ..........................................................................................69 3.4.1 Proposed examples of generalized complementarity ............................................69 3.4.2 Elements of a definition of complementarity.........................................................78 3.4.3 Analysis of the mind-body problem from the point of view of complementarity ................................................................................................................................................84 3.4.4 How to interpret this potential analogy?.................................................................92 3.4.5 How to interpret complementarity?.........................................................................93 3.5 Generalized entanglement................................................................................................99 3.5.1 Existing theories of generalized entanglement.....................................................100 3.5.1.1 Synchronicity .....................................................................................................100 3.5.1.2 Model of Pragmatic Information (MPI) ........................................................103 3.5.1.3 Holistic Correlations.........................................................................................105 3.5.1.4 Weak Quantum Theory (WQT)......................................................................106 3.5.2 Comparison with entanglement in quantum theory............................................107 3.5.3 Concise formulation.................................................................................................109 3.5.4 Possible examples of generalized entanglement...................................................110 3.5.4.1 Analysis of parapsychological phenomenology in the light of generalized entanglement ..................................................................................................................110 3.5.4.2 Speculative relevance in other fields...............................................................119 3.5.5 Implications for possible experimental designs ...................................................123 4. Experimental approaches to testing GQT with regard to entanglement.......................127 4.1 Entanglement through ‘indistinguishability’?...............................................................127 4.1.1 Introduction and rationale ......................................................................................127 4.1.2 Pilot experiments......................................................................................................128 4.1.2.1 Material and Methods.......................................................................................128 5 4.1.2.2 Analysis...............................................................................................................131 4.1.2.3 Results.................................................................................................................132 4.1.2.4 Discussion..........................................................................................................134 4.1.3 Main experiments.....................................................................................................135 4.1.3.1 Material and Methods.......................................................................................135 4.1.3.2 Results.................................................................................................................138 4.1.3.3 Discussion..........................................................................................................140 4.2 Entanglement through correlation-triggered feedback?.............................................143 4.2.1 Introduction and rationale ......................................................................................143 4.2.2 Material and Method................................................................................................147 4.2.2.1 Outline................................................................................................................147 4.2.2.2 Hardware............................................................................................................150 4.2.2.3 Experimental participants and conditions .....................................................150 4.2.2.4 Software, data processing and statistical analysis:.........................................151 4.2.3 Results........................................................................................................................153 4.2.4 Discussion .................................................................................................................155 5. Conclusion and Outlook.......................................................................................................165 6. Acknowledgements................................................................................................................169 7. Appendix.................................................................................................................................171 7.1 Appendix 1 (Calculations for Bell Inequality)..............................................................171 7.2 Appendix 2 (Entanglement overview)..........................................................................175 7.3 Appendix 3 (Data for indistinguishability experiment: pilot study)..........................177 7.3.1. Statistical analysis of ‘indistinguishability’ pilot study.........................................177 7.3.2. Post hoc statistical exploration..............................................................................181 7.3.2.1 Analysis of minimal complete dataset: ...........................................................181 7.3.2.2 Tests for equality of means using tests which are robust against differing sample sizes ....................................................................................................................184 7.4 Appendix 4 (Data for indistinguishability experiment: main study).........................185 7.4.1 Experiment 1 ............................................................................................................185 7.4.1.1 Experiment 1, Analysis ‘Placebo’....................................................................185 7.4.1.2 Experiment 1, Analysis ‘Verum’ .....................................................................186 7.4.2 Running Control 1 ...................................................................................................187
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