Description of Research
Our contemporary understanding of both non-relativistic and relativistic quantum theory is plagued by a variety of problems: While the non-relativistic theory of quantum mechanics has a rigorous mathematical foundation, its deep conceptual problems have been the subject of historical, still ongoing debates. In the relativistic domain, on the other hand, there is no universally agreed upon mathematical foundation. This typically forces the practicing physicist to work with models that lack internal mathematical consistency, so that - even within their domain of applicability - not every empirical prediction of those models is reliable.
Rather than viewing these two big problems in the foundations of physics as separate, my research aims to show that they are intimately related: Progress on one of the two can lead to progress on the other.
Publications
M. Reddiger, "On the applicability of Kolmogorov's theory of probability to the description of quantum phenomena. Part I", arXiv:2405.05710 [quant-ph] (2024). Submitted.
M. Reddiger and M. Scherfner, "Peer assessment as an exam prerequisite in undergraduate mathematics teaching: pilot study and practical advice" (2024). Submitted.
M. Reddiger and B. Poirier, "Towards a probabilistic foundation of relativistic quantum theory: the one-body Born rule in curved spacetime", arXiv:2012.05212 [math-ph] (2024). Submitted.
M. Reddiger and B. Poirier, "Towards a mathematical theory of the Madelung equations: Takabayasi's quantization condition, quantum quasi-irrotationality, weak formulations, and the Wallstrom phenomenon", J. Phys. A: Math. Theor. 56, 193001 (2023). DOI: 10.1088/1751-8121/acc7db. arXiv:2207.11367 [math-ph].
M. Reddiger and B. Poirier, "The Differentiation Lemma and the Reynolds Transport Theorem for submanifolds with corners", Int. J. Geom. Methods Mod. Phys. 20, 2350137 (2023). DOI: 10.1142/S0219887823501372. arXiv:1906.03330 [math-ph].
M. Reddiger, "The Madelung Picture as a Foundation of Geometric Quantum Theory", Found. Phys. 47, 1317–1367 (2017). DOI: 10.1007/s10701-017-0112-5. arXiv:1509.00467 [quant-ph].
M. Reddiger, "Towards a probabilistic Foundation for non-relativistic and relativistic quantum theory" (2022). Ph.D. thesis. URL: https://hdl.handle.net/2346/91876
M. Reddiger, “An observer’s view on relativity: space-time splitting and Newtonian limit”, arXiv:1802.04861 [math-ph] (2018). Master’s thesis.
Selected Presentations
03/2024 “On the applicability of Kolmogorov’s theory of probability for the description of quantum phenomena”, talk in the session Many-body Theory II of the meeting of the Theoretical and Mathematical Physics Division at the spring meeting of the German Physical Society (DPG), Berlin (Germany)
01/2024 “Towards a probabilistic foundation of relativistic quantum theory: the one-body Born rule in curved spacetime”, talk for the “Mathematical Physics” seminar, University of Regensburg (Germany)
10/2023 “On a probabilistic approach to the foundations of non-relativistic quantum theory”, talk for Max von Renesse’s stochastics research group, University of Leipzig (Germany)
08/2023 “Towards a probabilistic foundation of relativistic quantum theory: the one-body Born rule in curved spacetime”, poster presentation, "Quantum Effects in Gravitational Fields" conference, University of Leipzig, Germany
11/2022 ‘The One-Body Born Rule on curved Spacetime’, 2nd Mini-Symposium on Quantum Trajectories, Tech University, Lubbock, TX, USA
05/2022 ‘Towards a probabilistic Foundation of non-relativistic Quantum Theory’, Mini-Symposium on Quantum Trajectories, Tech University, Lubbock, TX, USA
04/2022 ‘The One-Body Born Rule on curved Spacetime’, contributed talk, AMS contributed paper session on quantum theory at the Virtual Joint Mathematics Meetings
11/2022 ‘The One-Body Born Rule on curved Spacetime’, contributed talk, Midwest Relativity Meeting
07/2021 ‘On a rigorous Framework for a Quantum N-Body Theory on curved Spacetime’, contributed talk, APS Meeting of the Division of Particles and Fields (DPF21)
03/2021 ‘On a rigorous Framework for a Quantum N-Body Theory on curved Spacetime’, contributed talk, AMS Eastern Sectional Meeting
10/2020 ‘Space-Time Splitting and the Newtonian Limit in General Relativity Theory’, contributed talk, Midwest Relativity Meeting
10/2020 ‘The Madelung Equations and Kolmogorovian Probability Theory’, invited talk, ‘Probability, Differential Geometry and Physics’ seminar, Texas Tech University, Lubbock, Texas, USA
04/2020 ‘Space-Time Splitting and the Newtonian Limit in General Relativity Theory’, contributed talk, APS Virtual April Meeting
11/2019 ‘On the Conservation of Charge in Special Relativity’, course talk, Texas Tech University, Lubbock, Texas, USA
10/2019 ‘Approaching relativistic Quantum Theory via Probability Conservation’, poster presentation, Texas Section APS Joint Fall Meeting in Lubbock, Texas, USA; Click for the poster and for the presentation
05/2019 ‘Addressing the Foundations of Quantum Mechanics via non-linear Analogue Systems’, course talk, Texas Tech University, Lubbock, Texas, USA
02/2017 ‘Space-Time Splitting and Newtonian Limit’, master thesis presentation, TU Berlin, Germany
10/2016 ‘Plane Wave Spacetimes’, seminar talk in German, TU Berlin, Germany
01/2016 ‘Elementary Geometry of dynamical Systems’, seminar talk, TU Berlin, Germany
01/2016 ‘Tetrad and Triad Formalism in General Relativity’, seminar talk in German, TU Berlin, Germany