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

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

Remarks on the structure of the verbal complex in early 17th century German

Speakers of various Southern german dialects may be heard to use two syntactic variants of subordinate clauses which are represented by the following Swabian examples: (1) daß er den net will komme lasse (2) daß er den net komme lasse will Of these two variants of the three-element verbal complex, only the non-dialect counterpart of (2) is accepted as standard modern written German: (3) daß er ihn nicht kommen lassen will In earlier periods of the German language, however, both variants were used by authors of written texts

A generalization of Strassen's Positivstellensatz

Strassen's Positivstellensatz is a powerful but little known theorem on preordered commutative semirings satisfying a boundedness condition similar to Archimedeanicity. It characterizes the relaxed preorder induced by all monotone homomorphisms to $\mathbb{R}_+$ in terms of a condition involving large powers. Here, we generalize and strengthen Strassen's result. As a generalization, we replace the boundedness condition by a polynomial growth condition; as a strengthening, we prove two further equivalent characterizations of the homomorphism-induced preorder in our generalized setting.Comment: 24 pages. v6: condition (d) in Theorem 2.12 has been correcte

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Towards a Re-definition of the Second Based on Optical Atomic Clocks

The rapid increase in accuracy and stability of optical atomic clocks compared to the caesium atomic clock as primary standard of time and frequency asks for a future re-definition of the second in the International System of Units (SI). The status of the optical clocks based on either single ions in radio-frequency traps or on neutral atoms stored in an optical lattice is described with special emphasis of the current work at the Physikalisch-Technische Bundesanstalt (PTB). Besides the development and operation of different optical clocks with estimated fractional uncertainties in the 10^-18 range, the supporting work on ultra-stable lasers as core elements and the means to compare remote optical clocks via transportable standards, optical fibers, or transportable clocks is reported. Finally, the conditions, methods and next steps are discussed that are the prerequisites for a future re-definition of the second