We present a probabilistic proof of the mean field limit and propagation of chaos N -particle systems in three dimensions with positive (Coulomb) or negative (Newton) 1/r potentials scaling like 1/N and an N -dependent cut-off which scales like N −1/3+ǫ . In particular, for typical initial data, we show convergence of the empirical distributions to solutions of the Vlasov-Poisson system with either repulsive electrical or attractive gravitational interactions.

The article points out that the modern formulation of Bohm's quantum theory, known as Bohmian mechanics, is committed only to particles' positions and a law of motion. We explain how this view can avoid the open questions that the traditional view faces, according to which Bohm's theory is committed to a wave-function that is a physical entity over and above the particles, although it is defined on configuration space instead of three-dimensional space. We then enquire into the status of the law of motion, elaborating on how the main philosophical options to ground a law of motion, namely Humeanism and dispositionalism, can be applied to Bohmian mechanics. In conclusion, we sketch out how these options apply to primitive ontology approaches to quantum mechanics in general.

We discuss the no-go theorem of Frauchiger and Renner based on an “extended Wigner’s friend” thought experiment which is supposed to show that any single-world interpretation of quantum mechanics leads to inconsistent predictions if it is applicable on all scales. We show that no such inconsistency occurs if one considers a complete description of the physical situation. We then discuss implications of the thought experiment that have not been clearly addressed in the original paper, including a tension between relativity and nonlocal effects predicted by quantum mechanics. Our discussion applies in particular to Bohmian mechanics.

The paper treats the validity problem of the nonrelativistic VlasovPoisson equation in d ≥ 2 dimensions. It is shown that the VlasovPoisson dynamics can be derived as a combined mean field and pointparticle limit of an N-particle Coulomb system of extended charges. This requires a sufficiently fast convergence of the initial empirical distributions. If the electron radius decreases slower than N − 1 d(d+2) , the corresponding initial configurations are typical. This result entails propagation of molecular chaos for the respective dynamics. IntroductionWe are interested in a microscopic derivation of the Vlasov-Poisson dynamics in d ≥ 2 spatial dimensions. This is the system of equationswhere k is the Coulomb kerneland ρ t (q) = ρ[f t ](q) = f (t, q, p) d 3 p (3) * lazarovici@math.lmu.de

The article sets out a primitive ontology of the natural world in terms of primitive stuffthat is, stuff that has as such no physical properties at all-but that is not a bare substratum either, being individuated by metrical relations. We focus on quantum physics and employ identity-based Bohmian mechanics to illustrate this view, but point out that it applies all over physics. Properties then enter into the picture exclusively through the role that they play for the dynamics of the primitive stuff. We show that such properties can be local (classical mechanics), as well as holistic (quantum mechanics), and discuss two metaphysical options to conceive them, namely, Humeanism and modal realism in the guise of dispositionalism.

Using the example of classical electrodynamics, I argue that the concept of fields as mediators of particle interactions is fundamentally flawed and reflects a misguided attempt to retrieve Newtonian concepts in relativistic theories. This leads to various physical and metaphysical problems that are discussed in detail. In particular, I emphasize that physics has not found a satisfying solution to the self-interaction problem in the context of the classical field theory. To demonstrate the superiority of a pure particle ontology, I defend the direct interaction theory of Wheeler and Feynman against recent criticism and argue that it provides the most cogent formulation of classical electrodynamics.

We discuss Boltzmann's explanation of the irreversible thermodynamic evolution of macroscopic systems on the basis of time-symmetric microscopic laws, providing a comprehensive presentation of what we call the typicality account. We then discuss the connection between this general scheme and the H-theorem, demonstrating the conceptual continuity between them. In our analysis, a special focus lies on the crucial role of typicality. Putting things in wider perspective, we go on to analyze the philosophical dimensions of this concept, explaining the connection between typicality and probability, and demonstrate its relevance for scientific reasoning, in particular for understanding the supervenience of macroscopic laws on microscopic laws. The second part of the paper responds to recent objections against the typicality account that have been raised in the philosophical literature. In particular, the concept of ergodicity, or a variant thereof, named "epsilon-ergodicity", which has been promoted by some authors as a crucial additional assumption on the dynamics, is shown to be of no use for its intended purpose. *

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