Free fall in curved spacetime

Free fall in curved spacetime: a man and an apple are in free fall with stars in the background
(Image adapted from śĄöśú®ś∑∑ś†™ Cdd20 via Pixabay & Canva)

In general relativity, Einstein's field equations describe the interplay between space, time, and massive objects. The often-used phrase 'spacetime tells matter how to move, matter tells spacetime how to curve' summarises this equation quite well.

Most instructional models of general relativity only use spatial curvature to explain gravity. The popular rubber sheet model is such a spatial model that simulates the geometric mechanism of gravity through a bowling ball and marbles on a rubber sheet. 


However, gravitational phenomena stem from deformations both in space and time. In my PhD project, my colleagues and I developed an interactive warped time model that can complement the rubber sheet model. The warped time model builds on a relativistic generalisation of Newton's first law and uses  a classical height-time diagram to explain how warped time gives rise to gravity.


The warped time model of spacetime uses a height-time diagram to illustrate key ideas of general relativity
(Image via Magdalena Kersting 2019 Phys. Educ. 54 035008)

By moving a slider between a classical and a warped height-time diagram, students can compare Newton and Einstein's theories of gravity in a fun and interactive way. 


The warped time model is part of our digital learning environment General Relativity. Find instructions on how to use the model in this open-access paper. You will also find a complete lesson plan and further explanations in our book Teaching Einsteinian Physics in Schools.

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