Exploring the rubber sheet spacetime analogy by studying ball movement in a bent trampoline

Abstract

A usual qualitative analogy used to explain gravitation in general relativity is comparing spacetime warping by massive objects with deformation in a rubber sheet. Motivated by this analogy, which identifies planet orbits with trajectories of rolling objects on the rubber sheet, the movement of a small ball in a trampoline bent because of the presence of a heavy mass in its center is studied. It is concluded that the similarities between how masses move under warped spacetime and under a warped trampoline are only qualitative, and later some analogy flaws are outlined, which can be useful for general relativity teaching. Since the "relativistic model" does not match the ball movement in the experimental conditions, two models based on classical mechanics are presented to describe it. The models are implemented computationally and parameters of such models are optimized to match experimental trajectories. In the case of the most complex of these two models, the high accuracy between optimized and observed trajectories implies that the model is able to explain the experiment behaviour.

Enseñanza de la estructura espacio-tiempo: un análisis bibliométrico (1988-2020) y futuras direcciones de investigación

“…El tópico de mayor asociación para comprender la estructura del espacio-tiempo es la curvatura; así, en los trabajos de Morris y Thorne, 1988;Flanagan y Hughes, 2005; Steier y Kersting, 2019, usan diversas figuras tridimensionales bien elaboradas para comprender la estructura del espacio-tiempo de una forma visual, entre los intereses se destaca, la compresión del universo desde la hipótesis de la cuantificación de la estructura del espacio-tiempo (cuantificación de la gravedad) porque este es el factor central entre la mayoría de los artículos que se analizaron. Finalmente, la estrategia didáctica empleada en los trabajos de Visser, 1998;Flanagan y Hughes, 2005;Batlle et al, 2019;Steier y Kersting, 2019, es la analogía, pues se puede apreciar como, a lo largo del desarrollo de la propuesta pedagógica, la argumentación se fundamenta en ella.…”

Robophysical modeling of spacetime dynamics

“…g tt is not constant). In the language of the work by Price [9], the effects of curvature are now not restricted to space [10]. That is, in general, the metric function g tt could depend on both the coordinate time (t) as well as the spatial coordinates.…”