23 February 2019, 3pm, LPS seminar room

**John Baez (UC Riverside), “Getting to the bottom of Noetherâ€™s theorem”**

In her paper of 1918, Noetherâ€™s theorem relating symmetries and conserved quantities was formulated in term of Lagrangian mechanics. But if we want to make the essence of this relation seem as self-evident as possible, we can turn to a formulation in term of Poisson brackets, which generalizes easily to quantum mechanics using commutators. The key question then becomes: when, and why, do observables generate one-parameter groups of transformations? This question sheds light on why complex numbers show up in quantum mechanics.

19 January 2019, 3pm, LPS seminar room

**Tomasz Placek (Jagiellonian University), “Interpreting non-Hausdorff (generalized) manifolds in General Relativity”**

The paper investigates the relations between Hausdorff and non-Hausdorff manifolds, as objects of General Relativity. We show that every non-Hausdorff manifold can be seen as a result of gluing together of some Hausdorff manifolds. In the light of this result we investigate a modal interpretation of a non-Hausdorff differential manifold according to which it represents a bundle of alternative spacetimes, all of which compatible with a given initial data set.

This talk is based on joint work with Joanna Luc. Please read their manuscript before the meeting.

17 November 2018, 3pm, LPS seminar room

**David Wallace (USC), “The Necessity of Statistical Mechanics”**

In discussions of the foundations of statistical mechanics, it is widely held that (a) the Gibbsian and Boltzmannian approaches are incompatible but empirically equivalent; (b) the Gibbsian approach may be calculationally preferable but only the Boltzmannian approach is conceptually satisfactory. I argue against both assumptions. Gibbsian statistical mechanics is applicable to a wide variety of problems and systems, such as the calculation of transport coefficients and the statistical mechanics and thermodynamics of mesoscopic systems, in which the Boltzmannian approach is inapplicable. And the supposed conceptual problems with the Gibbsian approach are either misconceived, or apply only to certain versions of the Gibbsian approach, or apply with equal force to both approaches. I conclude that Boltzmannian statistical mechanics is best seen as a special case of, and not an alternative to, Gibbsian statistical mechanics.

Please read David’s pre-print before the meeting.

6 October 2018, 3pm, LPS seminar room

**Chip Sebens (Caltech), “The Mass of the Gravitational Field”**

By mass-energy equivalence, the gravitational field has a relativistic mass density proportional to its energy density. I seek to better understand this mass of the gravitational field by asking whether it plays three traditional roles of mass: the role in conservation of mass, the inertial role, and the role as source for gravitation. The difficult case of general relativity is compared to the more straightforward cases of Newtonian gravity and electromagnetism by way of gravitoelectromagnetism, a special relativistic theory of gravity which resembles electromagnetism.