Why did the apple fall? A new model to explain Einstein’s gravity

Abstract

Newton described gravity as an attractive force between two masses but Einstein’s General Theory of Relativity provides a very different explanation. Implicit in Einstein’s theory is the idea that gravitational effects are the result of a distortion in the shape of space-time. Despite its elegance, Einstein’s concept of gravity is rarely encountered outside of an advanced physics course as it is often considered to be too complex and too mathematical. This paper describes a new conceptual and quantitative model of gravity based on General Relativity at a level most science students should be able to understand. The model illustrates geodesics using analogies with paths of navigation on the surface of the Earth. This is extended to space and time maps incorporating the time warping effects of General Relativity. Using basic geometry, the geodesic path of a falling object near the surface of the Earth is found. From this the acceleration of an object in free fall is calculated. The model presented in this paper can answer the question, ‘Why do things fall?’ without resorting to Newton’s gravitational force.

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

“…This facilitates the higher level understanding needed to understand the origin of gravity. [40] This topic is beyond the scope of this paper.…”

“…We avoid the complex mathematics completely by making use of simple formulae that refer to black holes, weakly curved space and time dilation. [18] These formulae are no more complex than the standard formulae used in Newtonian physics. Because we see some value in rote learning, we also encourage students to memorise John Wheeler's aphorism "Matter tells space-time how to curve; Space-time tells matter how to move."…”

Do moving clocks slow down?

“…A curved space-time analogue of the first clock effect is the so called gravitational time dilation, which recently attracted attention as a pedagogical tool for explaining free fall [97][98][99].…”

Students' understanding of gravity using the rubber sheet analogy: an Italian experience

“…In recent years, several efforts have been made in order to address these issues and create activities suitable to introduce GR in school curricula [6][7][8][9][10][11][12][13][14][15][16]. Several other works focus on quantitative analysis of students' understanding of gravity and GR, ranging from very young kids to university students [17][18][19][20][21][22][23][24][25][26][27][28][29][30].…”