Description of Research
Description of Research
As a mathematical physicist, I develop physical theories on an axiomatic basis using formal mathematical reasoning. The central hypothesis of my research is that quantum theory is to be adapted to accord with the laws of mathematical probability theory. I established that in certain instances this adaption, geometric quantum theory, reproduces central predictions of quantum mechanics, and that in other instances it also makes quantitatively different, novel predictions. The theory has shown itself viable in addressing long-standing conundrums in the foundations of quantum physics, such as the time of arrival problem and the measurement problem.
M. Reddiger, "A solution of the quantum time of arrival problem via mathematical probability theory", arXiv:2508.11368 [quant-ph] (2025). Submitted.
M. Reddiger, "On the applicability of Kolmogorov’s theory of probability to the description of quantum phenomena. Part I: foundations", Quantum Stud.: Math. Found. 13, 1 (2026). DOI: 10.1007/s40509-025-00375-6
M. Reddiger and M. Scherfner, "Peer assessment as an exam prerequisite in undergraduate mathematics teaching: experiment and practical advice", Teach. Math. Appl. 44, 226-239 (2025). DOI: 10.1093/teamat/hrae026
M. Reddiger and B. Poirier, "Towards a probabilistic foundation of relativistic quantum theory: the one-body Born rule in curved spacetime", Quantum Stud.: Math. Found. 12, article no. 5 (2025). DOI: 10.1007/s40509-024-00349-0.
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.
09/2025 "A solution of the quantum time of arrival problem via mathematical probability theory", contributed talk at the 2nd DPG Fall Meeting: 100 Years of Quantum Physics, University of Göttingen (Germany)
07/2025 "A heuristic solution to the time of arrival problem via mathematical probability theory", invited talk at the "Bohm in Brazil" Meeting, University of São Paulo (Brazil). RECORDING & SLIDES
04/2025 "On the applicability of Kolmogorov’s theory of probability to the description of quantum phenomena", contributed talk at the BRCP Annual Meeting 2025, Centre Inria de Paris (France)
03/2025 "On the applicability of Kolmogorov's theory of probability to the description of quantum phenomena'', contributed talk for the 88th Annual Conference of the DPG and DPG Spring Meeting, Bonn (Germany) SLIDES
02/2025 "On the mathematical theory of the Madelung equations'', contributed talk for the workshop "Mathematical Challenges in Quantum Mechanics'', Gran Sasso Science Institute (Italy)
11/2024 "Peer-Assessment als Prüfungsvorleistung mit dem Moodle-Plugin Gegenseitiges Beurteilen“, invited talk, eSALSA Jahrestagung, Anhalt University of Applied Sciences (Germany)
09/2024 “Towards a probabilistic foundation of relativistic quantum theory: the one-body Born rule in curved spacetime”, poster presentation, “Time in Quantum Theory” conference, Smolenice Castle (Slovakia)
09/2024 “Towards a probabilistic foundation of relativistic quantum theory: the one-body Born rule in curved spacetime”, poster presentation, “Time in Quantum Theory” conference, Smolenice Castle (Slovakia)
07/2024 “On the applicability of Kolmogorov’s theory of probability to the description of quantum phenomena”, contributed talk for the “Summer School on Current Topics in Mathematical Physics”, University of Zurich (Switzerland)
06/2024 “On the applicability of Kolmogorov’s theory of probability to the description of quantum phenomena”, invited talk for the “Theorie-Kolloquium”, Martin-Luther University Halle-Wittenberg (Germany)
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