In this article we argue that this analogy, as used, is fundamentally flawed and creates significant misunderstanding for both students and teachers. But there is a problem with this demonstration – it isn’t showing what it claims to show. A rolling marble on the surface follows a curved path, or “orbits” the central mass, giving convincing evidence of the parallel between the sheet and the action of gravity. The bending of the surface caused by the mass pulling the sheet down is used to illustrate the curvature of spacetime in general relativity. One common analogy used to introduce general relativity is the idea of a “mass on a rubber sheet” or “bowling ball on a trampoline”. While physicists can use the equations, even they need to use analogies to build a deep understanding of such counterintuitive concepts. That space and time can be mixed and curved is contradictory to all our everyday experiences. But what does the “curvature of spacetime” mean? It is hard to get your head around this mind-bending concept! In relativity, space and time are mixed together into “spacetime” and gravity is explained by the curved geometry of this combination. In developing general relativity, Einstein showed that gravity is the curvature of spacetime due to the presence of mass and energy. One of the most startling and remarkable discoveries of the 20 th century was that gravity is not a mysterious, invisible force. To learn more about general relativity and black holes and find ready-to-use, hands-on activities you can do with your class, download the free resource here. The authors were inspired to write this article while they worked on Perimeter Institute’s new black hole resource together. Philip Freeman ( ), Teacher, sd38 (Richmond) Richmond, BC These huge masses are thought to exist as black holes.Kelly Foyle ( ), Outreach Scientist, Perimeter Institute for Theoretical Physics Space-time can in principle be warped so strongly by a huge mass that any radiation emitted from the mass curves back in again and cannot escape. An important verification of this-which made headlines around the world-took place during a solar eclipse on May 29, 1919, when it was observed that light from stars near the Sun was bent by an angle exactly predicted by the expected curvature of space-time near the massive Sun. (It is an open question in cosmology as to whether our universe has a similar curvature in three dimensions if so, traveling in one direction long enough would bring you back to where you began.) An important consequence of the notion of curved space-time is that the curvature should affect all motion thus, even light, which has no mass, should follow a curved path wherever gravity has warped space-time. An object traveling uniformly through space then describes a helix along this tube, eventually returning to its starting space-coordinate position, but at a different time. But instead of an infinite plane, imagine a tube, with an object's position in time defined by a coordinate of length along the tube, and position in space by a coordinate around the circumference of the tube. ![]() What does it mean, though, for space-time to be curved? One way of conceptualizing this is to imagine just a two-dimensional space-time, with one spatial dimension and one time dimension. In the space-time continuum of General Relativity, events are defined in terms of four dimensions: three of space, and one of time, with one coordinate for each dimension we continuously move along the time dimension. Unlike Newtonian physics, which views gravity as an attractive force between all bodies in the universe, General Relativity describes the universe in terms of a continuous space-time fabric that is curved by masses located within it. ![]() For instance, both in an accelerating rocket in space and in a rocket standing on its launch pad on Earth, the astronauts are pushed back into their seats. One of the primary causes of acceleration in the universe is gravity, and Einstein showed that the effects of acceleration are actually the same as those of the force of gravity in fact, they are locally indistinguishable. A Closer Look Albert Einstein's theory of General Relativity, published in 1915, extended his theory of Special Relativity to systems that are accelerating.
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