Spherical Blackboard

What it shows:

You can use a spherical blackboard for many things, including the teaching of geographical coordinates, as a model for a closed Universe, or simply as a mathematical shape.

In the non-Euclidean geometry of the sphere, a circle will have a circumference greater than 2πr and an area greater than πr2. A triangle’s angles will add to more than 180°, and two parallel lines, called Great Circles, will converge.

A Universe with a density parameter Ω greater than unity will have too much mass to overcome its own gravitational...

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Inflating Universe

What it shows:

According to present accepted theory the Universe came into existence some 17 billion years ago as a Big Bang and is currently expanding. You can model the expansion of space in two dimensions using a balloon.

inflating universe

How it works...

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Saddle Shape Universe

Curved space segment for open universe geometry.

What it shows:

Whether the Universe continues to expand forever or will collapse back in upon itself depends upon the amount of matter it contains. For a density parameter Ω less than unity the Universe will not have enough mass to collapse and will be in a state of perpetual expansion. In general relativity, the curvature of space is dependent upon the density of the Universe, and for Ω<1 the curvature is negative or hyperbolic. It can be represented two dimensionally (see Comments) by a saddle...

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Gravitational Field Surface

1m diameter rubber sheet acts as curved space for ball bearing masses.

What it shows:

In general relativity, gravity is replaced by a curved space geometry, where the curvature is determined by the presence and distribution of matter. Objects move in straight lines, or along geodesics, but because of the curvature of space, their paths will simulate the effect of gravitational attraction. This demo gives a two dimensional view of warped space.

How it works:

In this 2-D analog, a 1 meter diameter piece of dental dam forms a...

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Gravitational Lens

Laser and plastic lens with curvature to simulate bending of light by massive object.

What it shows:

Gravitational lensing is caused by the bending of light rays by the gravitational field of an intervening object. The effect is seen with the Sun, but is most spectacular when a whole galaxy acts as a lens to a cosmologically distant object, such as a quasar. Depending on the geometry of the alignment and the structure of the lensing galaxy, the image of the quasar is distorted into two or more distinct images, sweeping arcs or a complete ring. Here we model...

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Faraday Induction

What it shows:

The mathematical description of electromagnetic induction as formulated by Maxwell and Faraday requires two different sets of equations to calculate the induced voltage, depending on whether the coil is stationary and the magnet moving or vice versa. In fact, as this demonstration shows, the voltage is the same as predicted by the two sets of equations.

How it works:

The apparatus is identical to demonstration Faraday's Law, and is described in detail there. Briefly, it consists of a galvanometer hooked up to a...

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Bouncing Photon

A photon (modeled by a bouncing ping-pong ball) is observed from two reference frames and provides the motivation for time dilation.

Relativity Train

What it shows:

The Relativity Train is a realization of the famous Einstein gedanken experiments involving traveling trains carrying clocks and meter sticks. The demonstration is used to show how the preservation of the postulated constancy of physical laws and the speed of light in all inertial frames requires length contraction and time dilation in the train frame relative to the lab frame of reference. The demonstration is, of course, not a real experiment but rather a visual means of showing (without using any equations) how length contraction and time dilation are...

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