Longest Straight Line Paths on Water or Land on the Earth


Longest Sailable Straight Line Path on Earth

Rohan Chabukswar, Kushal Mukherjee
There has been some interest recently in determining the longest distance one can sail for on the earth without hitting land, as well as in the converse problem of determining the longest distance one could drive for on the earth without encountering a major body of water. In its basic form, this is an optimisation problem, rendered chaotic by the presence of islands and lakes, and indeed the fractal nature of the coasts. In this paper we present a methodology for calculating the two paths using the branch-and-bound algorithm.

Longest Drivable Straight Line Path on Earth

Read more at https://arxiv.org/pdf/1804.07389.pdf


Upper limit on the Stiffness of space-time

stiffnessAdrian Melissinos
From the recently observed propagation of gravitational waves through space-time an upper limit can be deduced for the stiffness of space-time through which the gravitational wave propagates. The upper limit is extremely weak, implying that the stiffness of space-time is at least 14 orders of magnitude weaker than that of jello.
Read more at https://arxiv.org/pdf/1806.01133.pdf


Temporal relationalism

Lee Smolin
Because of the non-locality of quantum entanglement, realist approaches to completing quantum mechanics have implications for our conception of space. Quantum gravity also is expected to predict phenomena in which the locality of classical spacetime is modified or disordered. It is then possible that the right quantum theory of gravity will also be a completion of quantum mechanics in which the foundational puzzles in both are addressed together. I review here the results of a program, developed with Roberto Mangabeira Unger, Marina Cortes and other collaborators, which aims to do just that. The results so far include energetic causal set models, time asymmetric extensions of general relativity and relational hidden variables theories, including real ensemble approaches to quantum mechanics. These models share two assumptions: that physics is relational and that time and causality are fundamental.
Read more at https://arxiv.org/pdf/1805.12468.pdf


A Mini-Introduction To Information Theory

Edward Witten
This article consists of a very short introduction to classical and quantum information theory. Basic properties of the classical Shannon entropy and the quantum von Neumann entropy are described, along with related concepts such as classical and quantum relative entropy, conditional entropy, and mutual information. A few more detailed topics are considered in the quantum case.
Read more at https://arxiv.org/pdf/1805.11965.pdf