This topical review gives a comprehensive overview and assessment of recent results in Causal Dynamical Triangulations (CDT), a modern formulation of lattice gravity, whose aim is to obtain a theory of quantum gravity nonperturbatively from a scaling limit of the lattice-regularized theory. In this manifestly diffeomorphism-invariant approach one has direct, computational access to a Planckian spacetime regime, which is explored with the help of invariant quantum observables. During the last few years, there have been numerous new and important developments and insights concerning the theory's phase structure, the roles of time, causality, diffeomorphisms and global topology, the application of renormalization group methods and new observables. We will focus on these new results, primarily in four spacetime dimensions, and discuss some of their geometric and physical implications.

https://iopscience.iop.org/article/10.1088/1361-6382/ab57c7/pdf

Quantum Gravity from Causal Dynamical Triangulations: A Review

Upper secondary students can obtain a qualitative understanding of general relativity when provided with appropriately designed learning resources and sufficient scaffolding.

https://link.aps.org/pdf/10.1103/PhysRevPhysEducRes.14.010130

General Relativity in Upper Secondary School: Design and Evaluation of an Online Learning Environment Using the Model of Educational Reconstruction.

The Einstein-First project aims to change the paradigm of school science teaching through the introduction of modern Einsteinian concepts of space and time, gravity and quanta at an early age. These concepts are rarely taught to school students despite their central importance to modern science and technology. The key to implementing the Einstein-First curriculum is the development of appropriate models and analogies. This paper is the first part of a three-paper series. It presents the conceptual foundation of our approach, based on simple physical models and analogies, followed by a detailed description of the models and analogies used to teach concepts of general and special relativity. Two accompanying papers address the teaching of quantum physics (Part 2) and research outcomes (Part 3).

https://iopscience.iop.org/article/10.1088/1361-6552/aa83e4/pdf

Teaching Einsteinian physics at schools: part 1, models and analogies for relativity

This paper reviews research results obtained from Einsteinian physics programs run by different instructors with Years 6, 9, 10 and 11 students using the models and analogies described in parts 1 and 2. The research aimed to determine whether it is possible to teach Einsteinian physics and to measure the changes in student attitudes to physics engendered by introducing the modern concepts that underpin technology today. Results showed that students easily coped with the concepts of Einsteinian physics, and considered that they were not too young for the material presented. Importantly, in all groups, girls improved their attitude to physics considerably more than the boys, generally achieving near parity with the boys.

https://iopscience.iop.org/article/10.1088/1361-6552/aa83dd/pdf

Teaching Einsteinian physics at schools: part 3, review of research outcomes

Teaching the general theory of relativity to high school or undergraduate students must be based on an approach that is conceptual rather than mathematical. In this paper we present such an approach that requires no more than elementary mathematics. The central idea of this introduction to general relativity is the use of so-called sector models. Sector models describe curved spaces the Regge calculus way by subdivision into blocks with euclidean geometry. This procedure is similar to the approximation of a curved surface by flat triangles. We outline a workshop for high school and undergraduate students that introduces the notion of curved space by means of sector models of black holes. We further describe the extension to sector models of curved spacetimes. The spacetime models are suitable for learners with a basic knowledge of special relativity. The teaching materials presented in this paper are available online for teaching purposes at www.spacetimetravel.org.

/pdf/sector-models-a-toolkit-for-teaching-general-relativity-i-128rdwcnwk.pdf

C Zahn

Papers

Sector models?A toolkit for teaching general relativity: I. Curved spaces and spacetimes