Mathematics in Physics and Philosophy Group

Any proposed solution to the "screen problem" in quantum mechanics—the challenge of predicting the joint distribution of particle arrival times and impact positions—must align with the extensive data obtained from scattering experiments. In this paper, we conduct a direct consistency check of the Absorbing Boundary Condition (ABC) proposal, a prominent approach to address the screen problem, against the predictions derived from scattering theory (ST). Through a series of exactly solvable one- and two-dimensional examples, we demonstrate that the ABC proposal's predictions are in tension with the well-established results of ST. Specifically, it predicts sharp momentum- and screen-orientation-dependent detection probabilities, along with secondary reflections that contradict existing experimental data. We conclude that while it remains possible that physical detectors described by the ABC proposal could be found in the future, the proposal is empirically inadequate as a general solution to the screen problem, as it is inconsistent with the behavior of detectors in standard experimental settings. [To appear in Phys. Rev. A; arXiv:2509.07518.]

In recent years there has been quite some progress in understanding the effective descriptions of interacting many body systems. While finding analytical or numerical solutions for interacting systems of many particles is in many cases impossible with given techniques, physicists use effective, simplified descriptions to describe the main features of the systems. These effective descriptions significantly reduce the complexity of the system by considering only a selected limited number of the degrees of freedom of the system - the macro-variables of the system.

In the talk the most important steps in the derivation of some selected effective equations from microscopic principles will be given. A special emphasis will be the derivation of a time-irreversible macro-dynamics from time-reversible microscopic equations.

There is a lot of confusion about the entropy of gravitating systems. It is often said that the Boltzmann entropy of a classical gravitating system is infinite or not well-defined. In a different vein it is said, and this is presented as a puzzle, that, for a gas in a box, a state of high entropy should be a homogeneous state while, for a gravitating system, it should be the other way round, a homogeneous state being a state of low entropy. We show that both problems can be resolved if one is ready to adapt the notion of the Boltzmann entropy to the context of gravity. To motivate this step, we study the similarities and differences between the Newtonian gravitational N-body system (NBS) and an ideal gas in a box (GB). We explain why a sensible definition of ‘gravitational entropy’ involves an adaptation of the Boltzmannian macrovariables. This does not only lead to a well-defined, finite notion of entropy, but it also shows that entropy increases as the N-body system expands while clusters/galaxies form. This last result corroborates Penrose’s conjecture about the long-time behaviour of the entropy of gravitating systems.

Related Literature:

• Bell - How to Teach Special Relativity
• Strauch - On Bell's Dynamical Route to Special Relativity

Physicists and philosophers often allow themselves the luxury of contemplating the methodology of a sort of idealized physicist. One such tempting model of how physicists make predictions is provided by Laplace's (or more accurately Bošković's) demon: the complete physical state of the universe at a moment is fed into some fundamental dynamical equation and then one calculates what will or might happen. Of course, everyone knows that this is an idealization. The requisite initial condition cannot, in fact, be known. And even if it were, the calculation could not be done. So arriving at actual predictions must involve idealizations and simplifications. But the extent and nature of those idealizations and simplifications has not, I think, been properly acknowledged, especially in the context of quantum-mechanical predictions.

I will consider the problem at a somewhat abstract level, and then make specific remarks about predictions of arrival-place and arrival-time predictions that are based in quantum theory. There, the conceptual foundations of the predictive methods are more shaky and contestable than is generally recognized.

We warmly invite you to join our group for a small Christmas sit-in. There will be Glühwein, punch, and biscuits. Feel free to bring something of your own if you like.

• Time: 14:00 - 16:00
• Location: B448 Math Common Room (Theresienstraße 39)

Quantum mechanics is the most successful theory of the microscopic world; yet its foundations still pose deep questions. How is the wave function collapsing (the famous measurement problem)? Is the Pauli Exclusion Principle truly inviolable?

In this talk, I will present a series of precision underground experiments at the Gran Sasso National Laboratory (Italy) designed to explore possible deviations from standard quantum mechanics. Using state-of-the-art low-background radiation detectors, we search for two classes of rare signals:

• spontaneous radiation predicted by collapse models, proposed as solutions to the quantum measurement problem and potentially linked to gravity;
• Pauli-forbidden atomic transitions, which would indicate a violation of one of the cornerstones of quantum physics.

I will discuss our latest results and future plans for gravity-related collapse tests, as well as broader constraints on Continuous Spontaneous Localization (CSL) models. I will also present the VIP experiment, dedicated to high-sensitivity searches for Pauli Exclusion Principle violations, and highlight how these studies interface with emerging ideas in quantum gravity.

This seminar offers a journey to the deepest underground laboratory and to the frontiers of our understanding of Nature’s laws, and aims to stimulate discussion and foster synergies for future collaborations.

The classical radiation-reaction problem for point charges originated in the late 19th century, roughly coincident with the discovery of the electron and the ensuing attempts to formulate an electrodynamics with atomized charge and current densities. Approximately 125 years later a well-posed special-relativistic joint initial value problem of N point charges and their electromagnetic fields has finally been formulated.

In this talk I survey the problem, the many failed and sometimes misguided attempts at solving it, and then explain how the problem was overcome. I conclude with an outlook on the general-relativistic version of the problem, which is far from solved. This is joint work with Shadi Tahvildar-Zadeh and Annegret Burtscher.

This talk reviews the different ways in which the standard philosophical accounts of laws rely on spacetime. We then discuss the extent to which these conceptions can be adapted to a context where central spacetime features (or even spacetime itself) may not be fundamental but only emergent, such as within certain approaches to quantum gravity. Some of the difficulties at this level can be traced back to the tension between, on the one hand, central physical features of quantum theory and general relativity–the ingredient theories of most approaches to quantum gravity–and, on the other hand, the spacetime characterization underlying the standard analyses of laws.

For the description of quantum mechanical systems of many particles it is important to identify a small number of main variables that dominate the spatial or temporal behavior of the system. A good example for such a main variable is the one-particle density or the one-particle density matrix of the system. These main variables are retained and the equations determining the state of the system are truncated, so that only the main variables enter. This reduction yields an effective theory for the many-particle system under consideration.

Given a many-particle system and an effective theory for its description, two questions naturally arise:

• How much information is lost by the reduction? Is it possible to quantify the error when comparing the predictions made by the effective theory to the actual behavior of the many-particle system?
• What is the mathematical nature of the effective theory? What predictions are obtained from the effective theory, e.g., about the system's total energy, its energy differences, and its long-time behavior, to name a few?

Most such effective theories describe the low energy states of the system. The reduction process is often so singular, that it cannot be carried out in one step, but is split into several iterative steps of ever coarser effective theories with ever fewer variables that derive from its predecessor in the iteration. The renormalization group of theoretical physics is such a scheme.

In the talk I will describe the general process above and illustrate it with a variety of examples ranging from quantum chemistry to quantum field theory, which are seemingly very different, but follow the same guiding principle.

Wir wollen in diesem Vortrag in einer gemeinsamen, ausschnittweisen Lektüre Kurt Gödels historisches Paper "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I" aus dem Jahr 1931 betrachten, wobei wir uns auf den Beweis der Existenz formal unentscheidbarer Sätze (1. Unvollständigkeitssatz) beschränken.

Vereinfacht ausgedrückt besagt der erste Unvollständigkeitssatz, dass der Versuch einer Axiomatisierung der Mathematik (unter gewissen, nicht besonders starken Bedingungen) zu Widersprüchen oder zu nicht entscheidbaren Sätzen führt. Wir finden in diesem Kontext also eine Aussage die beweisbar und widerlegbar ist oder wir finden eine Aussage die weder beweisbar noch widerlegbar ist.

Given a real symplectic vector space encoding formal variables and their canonical commutation relations, one can associate a C*-algebra called resolvent algebra. Unlike the closely related Weyl algebra, this C*-algebra is not simple and admits a richer representation theory.

If we use it to model a non-interacting Bose gas in a soft box whose size is sent to infinity, we obtain thermal limit states on the algebra which are naturally indexed by temperature and chemical potential and lead to a description of Bose Einstein condensates. I point out advantages to the more commonly used Gross-Pitaevski limit to describe BEC. This talk is mostly based on arXiv:2411.04737 .