Free fall in curved spacetime—how to visualise gravity in general relativity

Abstract

The first direct observation of gravitational waves in 2015 has led to an increased public interest in topics of general relativity (GR) and astronomy. Physics teachers and educators respond to this interest by introducing modern ideas of gravity and spacetime to high school students. Doing so, they face the challenge of finding suitable models that visualise gravity as the geometry of curved spacetime. Most models of GR, such as the popular rubber sheet model, only address spatial curvature. Yet, according to Albert Einstein, gravitational phenomena stem from deformations both in space and time. This paper presents a new model that builds on a relativistic generalisation of Newton's first law. We use Einstein's free fall thought experiment and a classical heighttime diagram to explain how warped time gives rise to gravity. Our warpedtime model acts as a convenient supplement to the rubber sheet model. To support teachers in integrating the model into their classroom practice, we have implemented the model as an interactive simulation that is freely accessible. The model is the result of a threeyear period of developing and trialling digital learning resources in Norwegian high schools. Based on these trials, we suggest specific instructional strategies on how to use the warpedtime model successfully in science classrooms.

Probing High School Students’ Understanding of Einstein’s Theory of Gravity Using Thought Experiments and Analogy

“…Besides that, this model can lead to a misunderstanding that gravity is a manifestation of curved space, not curved spacetime (Janis, 2018) as the model emphasizes the role of distorted space and obscures the role of distorted time (Pössel, 2018). To address the limitations of this model, alternative models and approaches have been suggested, such as the warped time model (Kersting, 2019), sector models (Zahn & Kraus, 2014 and the use of the concept of geodesic using analogies with paths of flying aircraft on the surface of the Earth (Janis, 2018;Stannard, Blair, Zadnik, & Kaur, 2016) The present research…”

Probing High School Students’ Understanding of Einstein’s Theory of Gravity Using Thought Experiments and Analogy

“…In the Spacetime-Travel Project, Zahn and Krauss developed sector models to teach curved spacetime, gravity and black holes Zahn & Kraus, 2014;Zahn & Kraus, 2018). In the ReleQuant project, digital and research-based resources were developed to teach general relativity theory (Kersting & Steier, 2018;Kersting, Bøe, Henriksen, & Angell, 2018;Kersting, 2019). Despite the difference in methods and approaches used, these researchers seem to agree that concepts related to general relativity are better delivered to high school students by using models and analogies (Kaur, et al, 2018;Kersting & Steier, 2018;Zahn & Kraus, 2014).…”

“…The use of TEs is also found in several well-known books popularizing Einstein's theories of relativity, such as Black Holes & Time Warps: Einstein's Outrageous Legacy (Thorne, 1994), Gravity from the ground up (Schutz, 2003), Spacetime Physics: Introduction to Special Relativity, and Exploring Black Holes: Introduction to General Relativity (Taylor & Wheeler, 1991, 2000. In the context of teaching the Einstein's theory of gravity, Kersting (2019) emphasized the importance of introducing and capitalizing TEs before using warped time model to teach Einstein's theory of gravity.…”

“…Without the presence of any massive objects, the stretched rubber sheet will remain undisturbed and this is considered to represent a flat spacetime which is an arena for the special theory of relativity. This model is considered to have great explanatory power (Kersting, 2019) and the concepts mapped from Einstein's theory of gravity to this model is straightforward (Pössel, 2018).…”

“…Besides that, this model can lead to a misunderstanding that gravity is a manifestation of curved space, not curved spacetime (Janis, 2018) as the model emphasizes the role of distorted space and obscures the role of distorted time (Pössel, 2018). To address the limitations of this model, alternative models and approaches have been suggested, such as the warped time model (Kersting, 2019), sector models (Zahn & Kraus, 2014 and the use of the concept of geodesic using analogies with paths of flying aircraft on the surface of the Earth (Janis, 2018;Stannard, Blair, Zadnik, & Kaur, 2016)…”