Quantum logic is undecidable

We investigate the first-order theory of closed subspaces of complex Hilbert spaces in the signature $(\lor,\perp,0,1)$, where `$\perp$' is the orthogonality relation. Our main result is that already its quasi-identities are undecidable: there is no algorithm to decide whether an implication between equations and orthogonality relations implies another equation. This is a corollary of a recent result of Slofstra in combinatorial group theory. It follows upon reinterpreting that result in terms of the hypergraph approach to quantum contextuality, for which it constitutes a proof of the inverse sandwich conjecture. It can also be interpreted as stating that a certain quantum satisfiability problem is undecidable.Comment: 11 pages. v3: improved exposition. v4: minor clarification

Synchronous Online Philosophy Courses: An Experiment in Progress

There are two main ways to teach a course online: synchronously or asynchronously. In an asynchronous course, students can log on at their convenience and do the course work. In a synchronous course, there is a requirement that all students be online at specific times, to allow for a shared course environment. In this article, the author discusses the strengths and weaknesses of synchronous online learning for the teaching of undergraduate philosophy courses. The author discusses specific strategies and technologies he uses in the teaching of online philosophy courses. In particular, the author discusses how he uses videoconferencing to create a classroom-like environment in an online class

Polyhedral duality in Bell scenarios with two binary observables

For the Bell scenario with two parties and two binary observables per party, it is known that the no-signaling polytope is the polyhedral dual (polar) of the Bell polytope. Computational evidence suggests that this duality also holds for three parties. Using ideas of Werner, Wolf, \.Zukowski and Brukner, we prove this for any number of parties by describing a simple linear bijection mapping (tight) Bell inequalities to (extremal) no-signaling boxes and vice versa. Furthermore, a symmetry-based technique for extending Bell inequalities (resp. no-signaling boxes) with two binary observables from n parties to n+1 parties is described; the Mermin-Klyshko family of Bell inequalities arises in this way, as well as 11 of the 46 classes of tight Bell inequalities for 3 parties. Finally, we ask whether the set of quantum correlations is self-dual with respect to our transformation. We find this not to be the case in general, although it holds for 2 parties on the level of correlations. This self-duality implies Tsirelson's bound for the CHSH inequality.Comment: 19 pages, to appear in J. Math. Phy

Distance Measurements and Stellar Population Properties via Surface Brightness Fluctuations

Surface Brightness Fluctuations (SBFs) are one of the most powerful techniques to measure the distance and to constrain the unresolved stellar content of extragalactic systems. For a given bandpass, the absolute SBF magnitude \bar{M} depends on the properties of the underlying stellar population. Multi-band SBFs allow scientists to probe different stages of the stellar evolution: UV and blue wavelength band SBFs are sensitive to the evolution of stars within the hot Horizontal Branch (HB) and post-Asymptotic Giant Branch (post-AGB) phase, whereas optical SBF magnitudes explore the stars within the Red Giant Branch (RGB) and HB regime. Near- and Far-infrared SBF luminosities probe the important stellar evolution stage within the AGB and Thermally-Pulsating Asymptotic Giant Branch (TP-AGB) phase. Since the first successful application by Tonry and Schneider, a multiplicity of works have used this method to expand the distance scale up to 150 Mpc and beyond. This article gives a historical background of distance measurements, reviews the basic concepts of the SBF technique, presents a broad sample of these investigations and discusses possible selection effects, biases, and limitations of the method. In particular, exciting new developments and improvements in the field of stellar population synthesis are discussed that are essential to understand the physics and properties of the populations in unresolved stellar systems. Further, promising future directions of the SBF technique are presented. With new upcoming space-based satellites such as Gaia, the SBF method will remain as one of the most important tools to derive distances to galaxies with unprecedented accuracy and to give detailed insights into the stellar content of globular clusters and galaxies.Comment: 21 pages, 10 figures, 1 Table, accepted for publication in Publications of the Astronomical Society of Australia (PASA, CSIRO Publishing

Velocity Polytopes of Periodic Graphs and a No-Go Theorem for Digital Physics

A periodic graph in dimension $d$ is a directed graph with a free action of $\Z^d$ with only finitely many orbits. It can conveniently be represented in terms of an associated finite graph with weights in $\Z^d$, corresponding to a $\Z^d$-bundle with connection. Here we use the weight sums along cycles in this associated graph to construct a certain polytope in $\R^d$, which we regard as a geometrical invariant associated to the periodic graph. It is the unit ball of a norm on $\R^d$ describing the large-scale geometry of the graph. It has a physical interpretation as the set of attainable velocities of a particle on the graph which can hop along one edge per timestep. Since a polytope necessarily has distinguished directions, there is no periodic graph for which this velocity set is isotropic. In the context of classical physics, this can be viewed as a no-go theorem for the emergence of an isotropic space from a discrete structure.Comment: 18 pages, 1 figure. See also http://pirsa.org/12100100/. Corrigendum in v3: most mathematical results were obtained earlier by other authors, references have been include