In contemporary metaphysics, the fundamentality of physics and physicalism are typically understood as ontological completeness claims of some sort. For example, physics is taken to provide a complete supervenience or realization basis, or a complete set of grounds for all facts or entities. However, since no formulated physical theory provides a complete ontological basis for all facts or entities, one must seek an alternative interpretation if one wants a realistic understanding of the sense in which our current physical theories are fundamental. The aim of this paper is to develop such an interpretation, one that bases the fundamentality of our current physical theories in a claim about their ontological depth and comprehensiveness. It is argued that this interpretation of the metaphysical fundamentality of physics is more in line with the way that physicists regard certain theories as fundamental than standard philosophical conceptions.

This talk concerns a thorny subject: the foundations of quantum theory. By sketching some simple examples I will attempt to highlight the importance of introducing a precise notion of "events" into the theory and of clearly formulating the dichotomy between past and future. I will then briefly recall the main features of the so-called "ETH-approach" to quantum mechanics.

The purpose of the technical part of my talk is to describe some fraction of the work my collaborators and I have done in our search for a plausible com- pletion of quantum mechanics. I will focus on the derivation of a general Law of Dynamics for non-relativistic quantum mechanics from the principles of the "ETH-approach" and on some recent applications of this law.

Concretely: The quantum-mechanical time evolution of physical systems consisting of charged matter interacting with the quantized electromagnetic field, e.g., electrons in the shell of an atom coupled to the radiation field, will be shown to be non-linear, dissipative and stochastic, featuring isolated random events sometimes called “quantum jumps”. Explicit equations will be presented in an idealized description of such systems arising in a limiting, non-relativistic regime where the velocity of light tends to infinity. These equations involve a new type of stochastic process, which I call “Quantum Poisson Jump Process”. I will introduce this process, present some of its mathematical properties and sketch applications to the theory of fluorescence of atoms.

I will present a clock Gedanken experiment that gives an alternative derivation of the Penrose collapse time. We try to develop new technologies for precision mechanical experiments using low temperatures and low vibrations. With these experiments we can improve bounds on various theories such as those that combine gravity and quantum mechanics.

I will discuss recent results with levitated mechanical systems in experiments and explain possible implications for testing the laws of nature.

Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means (Bertrand Russell, 1929 Lecture)." - My talk develops an account of laws and chances that is based on David Lewis' Best Systems Account and argues that I is superior to frequency, propensity, and purely subjective accounts. I show how this account applies to indeterministic laws and also allows for objective physical probabilities that are compatible with deterministic dynamical laws. This plies to classical statistical mechanics and Bohmian mechanics. I show how this account explains why objective probabilities guide credences and thus supports Lewis remark that he can "see dimly but well enough why chance is a guide to credence."

There are fundamental dynamical equations that govern fundamental entities and emergent dynamical equations that (approximately) describe the dynamics of emergent entities. For example, there is the classical theory of fluid dynamics based on Newtonian physics that is used to describe water waves, even though the fundamental Newtonian dynamical equation is not a wave equation. One strong suggestion of quantum phenomena such as two-slit interference is that the fundamental dynamics of the quantum state (wavefunction) must be some sort of wave dynamics. I will discuss the fundamental mathematical features of the clearest example we have of fundamental wave dynamics-the free Maxwellian electromagnetic field-and then suggest how that gives insight into the structure of Schrödinger's equation in quantum theory, including motivating both the use of complex numbers in the wavefunction and the implementation of "time-reversal" by complex conjugation.

In this talk I describe my recent work on simulating the beables implied by the Bohmian and Nelsonian approaches to quantum field theory, after a brief review of Nelson`s theory applied to the hydrogen atom. I employ the Schrödinger representation of QFT regularized on a spatial lattice, where quantum states are wave functions depending on field configurations, and whose squares determine the probability of a field beable taking on certain configurations across space. I focus mostly on the Nelsonian account, since it is under-studied in the foundations literature, and because it turns out to provide intuitive pictures of the field beables corresponding to various states in QFT. For example, a very literal meaning is given to the colloquial statement that “particles are excitations of a field”, which otherwise does not have much weight in traditional approaches to QFT. The implications for wave function ontology will be discussed. Finally, I will comment on the case of interacting fields, and the prospects for describing particle creation and annihilation. Throughout the talk, I will show animations of the relevant beables in example cases.

The hydrodynamics of quantum fluids can be mapped to relativistic cosmological dynamics, and both share the same conformal symmetries, which can be unraveled via geometric methods in superspace. This suggests a more general correspondence between hydrodynamics and cosmology, and a picture of the universe as a quantum fluid of nonspatiotemporal building blocks. This picture is in fact realized also in some quantum gravity formalisms, like group field theory, spin foam models and lattice quantum gravity, in which an emergent cosmological dynamics can be extracted from the quantum dynamics of fundamental quantum simplices in a condensate phase. A key ingredient is the relational understanding of space and time, which makes superspace the natural arena for gravitational dynamics, as opposed to the "spacetime" manifold. These results suggest an exciting dialogue between quantum gravity, the theory of quantum fluids and cosmology, as well as a new direction for analogue gravity simulations in the lab. If we are lucky, that is, the expected trefoil fored by quantum gravity, hydrodynamics and cosmology, leading us to the foundations of spacetime, will turn out to be an even more intriguing quatrefoil.

Why is mathematics so successful in describing the natural world? More profoundly, why are the fundamental laws of nature - as far as we know them today - expressed in mathematical language?
The talk traces the following idea from the presocratic philosopher Heraclitus to the Pythagoreans to Newton's Principia: Laws of nature are laws of proportion for matter in motion.
Proportions are expressed by numbers or, as I argue, even identical to real numbers. The talk makes the case that this view is still relevant to modern physics and helps us understand why physical laws are genuinely mathematical.

Spontaneous collapse theories provide one of the most promising approaches to dealing with the "measurement problem" in Quantum Theory (QT) . Recent advances have provided versions of the theory that are compatible with special relativity. However, for a theory to be truly viable, it should also be made compatible with General Relativity (GR). I will describe some of the issues that arise when attempting to follow that path, and discuss some ideas about how these might be addressed. I will then argue that, in fact, it is in various situations where GR and QT come together, that these theories exhibit their potential in dramatic manner, offering plausible resolutions to issues that have remained unresolved for a long time.

Previous works have suggested that even when the electron is prepared in a superposition of `here' and `there' in absolute vacuum, its interaction with the fundamentally unavoidable vacuum fluctuations of the electromagnetic field would lead to decoherence. This talk argues against this conclusion. Further, with the help of the mathematical formalism used in addressing this problem, the quantum mechanical version of the Abraham-Lorentz equation will be derived (up to second order in the interactions), which is free of the pathologies of its classical counterpart.

It is difficult to extract trustworthy criteria for causal locality from the limited ingredients of textbook quantum theory. In the end, Bell humbly warned us that his famous theorem was based on principles that "should be viewed with the utmost suspicion." Remarkably, by stepping outside of the wave-function paradigm, one can reformulate quantum theory in terms of old-fashioned configuration spaces and stochastic laws. These stochastic laws take the form of directed conditional probabilities, which provide a hospitable foundation for speaking about microphysical causal relationships. In this talk, I will argue that this alternative formulation of quantum theory does not suffer from the measurement problem, and that it deflates various exotic claims about superposition, interference, and entanglement. I will also use this new formulation to show directly that systems at spacelike separation cannot exert causal influences on each other, without any need for appeals to Bell's criteria. These results lead to a general interpretation of quantum theory that is arguably compatible with causal locality.

The quantum measurement problem finds a possible solution in the so-called collapse models. They are a modification of quantum mechanics which establish a natural and universal mechanism for the quantum-to-classical transition. In turn, they also describe an objective way to determine which are the limits of quantum mechanics. Thus, testing collapse models is equivalent to testing the limits of quantum mechanics. In this talk, I will present my contributions to the theoretical and experimental endeavour for testing collapse models.

Probabilistic laws of nature, as they are usually understood, are extraordinarily permissive. For example, a probabilistic law of a coin toss experiment is compatible with any sequence of results, including the all heads sequence (HHHHH......) and the alternating heads-tails sequence (HTHTHT......). This feature can be problematic, as it gives rise to a variety of metaphysical and epistemological underdetermination. We consider two ways one might use algorithmic randomness to strengthen the content of a probabilistic law. They provide much tighter connections between probabilistic laws and their corresponding sets of possible worlds, and allow us to eliminate several philosophical problems about probabilistic laws. (Joint work with Jeffrey A. Barrett; paper version at https://arxiv.org/pdf/2303.01411.pdf)

By combining high-resolution spectroscopy of the 3d ^{2}D_{3/2} - 3d ^{2}D_{5/2} interval with an accuracy of ~20 Hz using direct frequency-comb Raman spectroscopy with isotope shift measurements of the 4s ^{2}S_{1/2} ↔ 3d ^{2}D_{5/2} transition in all stable even isotopes of ^{A}Ca^{+} (A = 40, 42, 44, 46, and 48) at the accuracy of ~1 kHz, we have been able to carry out a King plot analysis with unprecedented sensitivity to coupling between electrons and neutrons by bosons beyond the Standard Model. Furthermore, we estimate that by improved spectroscopic techniques available, King plots based on data from spectroscopy on either Ca^{+}, Ba^{+} and Yb^{+} ions should be able to produce sensitivity to such potentially new bosons, which surpass other current methods in a broad mass range of 10 to 10^{8} eV/c^{2}.

We experience that entropy increases, thereby marking an arrow of time, although the underlying microscopic dynamics is time-reversal invariant. This seemingly paradoxical fact has, to large extent, been explained by Boltzmann who showed that macroscopic irreversibility is grounded on time-asymmetric boundary conditions, namely on the fact that systems start from very special, low-entropy initial states. Eventually, this reasoning led to the past hypothesis: the postulate that the universe started from a very special, low-entropy initial macro state. Lately, this line of reasoning has been attacked. Physicists like Sean Carroll or Julian Barbour claim that one can dispose of the past hypothesis and instead obtains the arrow of time as a feature of a typical universe. In this talk, we study Boltzmann's statistical reasoning and the way in which the new proposals avoid the conclusion of a past hypothesis. We show how this rests on crucial conceptual differences with respect to Boltzmann's understanding of the universe. In detail, we study the Newtonian gravitational N-body model and the way in which the notions of entropy and typicality figure in the absolute and relational description of that system. It turns out that a big-bang-like state, a state of apparently low entropy, is typical among relationally distinct solutions where it forms the mid-point of the evolution and thus grounds two arrows of time in an overall time-symmetric one past and two futures scenario.

I will discuss a variety of topics about time and its arrow -- mathematical, physical, and metaphysical.

I will review the results of a series of papers in which we showed that a variety of homogeneous solutions of General Relativity which have singularities are regularizable. This implies that each and every solution can be continued uniquely through the singularity, questioning a widely-held expectation that gravitational singularities break down classical determinism, and require quantum effects to be resolved. The result concerns Bianchi IX cosmological models with a large class of scalar fields, Kantowski–Sachs universes, which describe the interior of a Schwarzschild black hole, and of homogeneous cosmologies coupled with gauge fields. Future plans to generalize the result will be discussed.

Maxwell, followed by Einstein, argued that the laws of nature are local and are to be expressed by partial differential equations that take the same form at each spacetime point. This is reflected in cosmology, in which any model of the universe in which the field equations of general relativity hold at each space point (with any acceptable energy-momentum tensor on their right-hand side) is assumed to be an acceptable model. I will argue that while this is a necessary condition something more ambitious may be needed to restrict possibilities. This is that there exists a master law of the universe from which local laws emerge that allow many more models of the universe than does the master law. I will give illustrative examples.

The purpose of this talk is to propose an extension of the standard formalism of QM and complete this theory in such a way that it makes sense. The extension, yielding a new Law of Nature, is called "ETH - Approach to QM."

The ETH - Approach to QM supplies the fourth one of four pillars QM rests upon:

• Physical quantities characteristic of a physical system are represented by self-adjoint linear operators.
• The Heisenberg-picture time evolution of operators representing physical quantities is given by the usual Heisenberg equations.
• Useful notions of Potential and Actual Events and of states are introduced.
• A general statistical Law for the Time Evolution of states is formulated.

Core of the talk: Besides sketching the ETH-Approach to QM, simple models of a very heavy atom coupled to the radiation field in a limit where the speed of light tends to ∞ will be discussed. These models illustrate the ETH-Approach.

Typicality and probability approaches to statistical mechanics are often thought of as radically different and competing. In my talk I will describe a probabilistic approach based on David Lewis' Best System Humean account of probability called "the Mentaculus" and a typicality approach based on work by Goldstein, Lazarovici, Hubert and others and argue that while there are some important differences they are more similar than initial appearances.

Building on Barry Loewer's talk, I will argue for aspects of typicality that distinguish it from probability. I will present a view that grounds objective probabilities in a more fundamental notion of typicality and regards typicality not as part of the physical laws but as a way of reasoning about them.

The theory of causal fermion systems is an approach to describe fundamental physics. It gives quantum mechanics, general relativity and quantum field theory as limiting cases and is therefore a candidate for a unified physical theory. Moreover, causal fermion systems provide a general framework for modelling and analyzing non-smooth spacetime structures. The dynamics of a causal fermion system is described by a nonlinear variational principle, the causal action principle.
The aim of my first talk is to give a simple, non-technical introduction. I will proceed chronologically and explain step by step how the underlying concepts and objects evolved from 1990 to today. This will lead us to the abstract definitions. At the end of the talk, the underlying physical principles will be discussed.

The goal of my second talk is to outline how to get a connection between the causal action principle and usual physical equations formulated in Minkowski space or curved spacetime. On the level of an interaction via classical bosonic fields, this connection is made precise in the so-called continuum limit. I will explain schematically how the analysis in the continuum limit works. In order to get the connection to quantum field theory, a recent approach is to construct a distinguished state at a fixed time, being a positive functional on the algebra generated by fermionic and bosonic field operators. As an outlook, I will explain the general structure of the resulting quantum dynamics.

Despite much theorizing on how quantum theory might modify general relativity at extremely tiny scales, thereby resolving the space-time singularity problem, there are strong reasons for believing that this cannot provide an overall solution. On the other hand, conformal geometry, relating large to small-a remote expanding future to an initiating big bang-leads to important thermodynamical insights and confirmed observations of previously unexpected effects. On the quantum side, the most troublesome and fundamental issue is the measurement problem-or collapse of the wave-function-and here I argue that it is in the large effects of tiny gravitational fields where we must find our answers.

Point charges are a very useful idealization in electromagnetism. Although they are commonly treated as though they are fundamental, they have infinite self-energy and mathematical inconsistencies arise if one tries to describe their self-consistent motion. On the other hand, the self-consistent motion of distributions of continuous charged matter is entirely well defined in classical Maxwell theory. I will describe how to take a mathematically rigorous point particle limit of continuous charged matter wherein the charge and mass scale to zero in proportion to the size of the body. Lorentz force motion is obtained in this limit and self-force arises as a perturbative correction. It is shown how to obtain self-consistent motion that respects causality and does not admit spurious run-away solutions.

The 1927 Solvay Conference is perhaps the most renowned physics meeting of the 20th century. An eminently distinguished group of physicists had been invited to discuss the apparent breakthroughs that had happened in the previous two years, in the hope perhaps to come to a common understanding of what had been accomplished. Instead, as one participant (Langevin) later wrote, at the 1927 Solvay conference the confusion of ideas reached its peak. Given the fact that nowadays professional physicists typically disagree with each other about what quantum theory really says about nature, it is fair to say that the confusion has not been cleared up yet. In this talk I will argue that by the end of 1927 we may well have been on the way to a meaningful and accurate quantum mechanics of electrons, nuclei, and photons that does not suffer from the infamous measurement problem of what came to be known as orthodox (standard textbook) quantum mechanics. For this it would have only been necessary that Luis de Broglie, Max Born, and Erwin Schrödinger would have listened to each other more carefully and with an open mind.

The application of the covariant LQG techniques to the universe allows to compute cosmological observable in the deep quantum regime of the early universe. In particular, it is possible to define a cosmological quantum state and study its property. This approach differs from the standard procedure in cosmology, where a primordial vacuum state needs to be assumed to provide the initial condition of the successive evolution. In this talk I will present how such a quantum state can be constructed, providing a spinfoam analogue of the Hartle-Hawking wave function of the universe. I will emphasize the conceptual steps that need to be taken in defining the appropriate observable and the relevant degrees of freedom. I will present the first results obtained with improved numerical techniques.

Black holes are the purest expression of gravity and at the same time the places where our best theory of gravitation, Einstein General Relativity, meets its demise in the form of singularities. We know, however, that any successful theory of quantum gravity should be able to resolve these uncharted regions, but can they do so without showing any modification outside the event horizon? can real black holes be undistinguishable from the one predicted by general relativity? The recent direct observation of these tantalising objects represents an unprecedented possibility to answer these questions. In this talk, we shall explore on general grounds what alternative objects we can expect from a quantum gravity induced regularisation of singularities and discuss what observations can or will tell us about their nature.

I will discuss the problem of predicting the arrival (or detection) time of a quantum particle on a detector surface that remains unresolved despite the time-honoured empirical successes of quantum mechanics. Given that arrival-time or time-of-flight (TOF) measurements are the quintessence of standard experimental techniques of atomic and particle physics, this is particularly striking. Drawing upon the early history of this issue, I will discuss many (disparate) theoretical predictions for the TOF distribution of a particle suggested in the literature. These are informed by various semi-classical heuristics, principles, extensions, or (for want of a better word) "interpretations" of quantum theory. Next, I will describe a so-called "back-wall" experiment---an arrival-time experiment developed in collaboration with my late (and truly great) advisor Prof. Detlef Dürr that can reliably distinguish the aforementioned proposals. A key feature of our set-up is that the particle is escaping a potential barrier (the back-wall) in the direction of a distant detector, as opposed to moving completely freely. Without the back-wall, most proposals become nearly indistinguishable, which renders usual experimental tests inconclusive. I will also describe a concrete ion-trap implementation of the back-wall experiment doable with present-day technology. Time permitting, I will mention a version of this experiment featuring a spin-1/2 particle as an electron whose de Broglie-Bohm analysis predicts, thanks to quantum backflow, intriguing spin-dependent arrival-time distributions hitherto unknown, demanding experimental inspection.

Collapse models solve the measurement problem by modifying the Schrödinger equation, adding new terms which describe spontaneous localization in space of the wavefunction. Because of these additional terms, collapse models make different predictions compared to Quantum Mechanics, so they can be experimentally tested. In this talk, we will give an introduction to the most important collapse models and to the state of the art of the bounds on their phenomenological parameters, coming from different experiments. We then also discuss possible improvements of these bounds as well as theoretical developments of the models.