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