**Description**

This programme looks at the question of time dilation and examines the form of the transformations between one space-time co-ordinate system and another.

Module code and title: | M203, Introduction to pure mathematics |
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Item code: | M203; 17 |

First transmission date: | 12-06-1980 |

Published: | 1980 |

Rights Statement: | |

Restrictions on use: | |

Duration: | 00:24:23 |

Note: | This programme was re-edited in 1995 as FOUM496P |

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Producer: | Martin Wright |

Contributors: | Jeremy Gray; Allan I.,1936-2013 Solomon |

Publisher: | BBC Open University |

Keyword(s): | Einstein; Euclidean; Light speed; Space time |

Subject terms: | Geometry; Space and time |

Footage description: | Allan Solomon introduces the programme by asking the question, why does traditional Euclidean geometry need to be expanded to include the fourth dimension of time. To explain this, Jeremy Gray describes the behaviour of muons. These small particles, travel at speeds close to that of light, and survive for much longer periods than we would normally expect. At high velocities therefore time is dilated and stretched. Allan Solomon demonstrates how the speed of light can be measured in the laboratory. He then goes on to discuss Einstein's theory that this speed is a universal constant. To illustrate this idea he measures the speed of light emitted by electrons travelling in a linear accelerator at speeds approaching that of light. The light is shown to be travelling at a constant speed. Jeremy Gray looks at the consequences of this result by conducting a thought experiment. Imagining the speed of light to be 1 metre per second he passes a pulse of light across a distance of two metres. The light is then reflected back again by a mirror. Four metres in all. This exercise is conducted once more but this time Jeremy is represented as travelling at 60% of the speed of light relative to Allan. When Allan measures the distance the pulse of light has travelled, relative to him it is to be 5 metres. As the speed of light is constant this implies that Jeremy's clock is running relative to Allan's. Allan now works out a general formula for this time dilation effect. Jeremy Gray explains how this formula describes the behaviour of the muons. Allan Solomon now explores the relations between Jeremy's co-ordinate system and his own. He depicts an event on his co-ordinal axis of space and time, he shows a curve or world line depicting a particle moving through space. Using an animation he describes Jeremy's world line in respect to his co-ordinate system and compares this to the world line of light. Similarly Jeremy constructs space-time co-ordinates for his world. When both systems have common origins the world line for a pulse of light is the same in both systems. This links the two co-ordinate system together. Using this result Allan demonstrates that co-ordinates in Jeremy's system (x¹,t¹) get transformed to (x, t) in his system. A further thought experiment is conducted in order to show the forms preserved by the transformation from one system to another. Using animations, a pulse of light travels past Allan and then Jeremy, who in turn is travelling away from Allan. The light is reflected back past Jeremy and to Allan by a mirror. The geometric relations described by the path of light in both co-ordinate systems show that the transformation from Jeremy's system to Allan's preserves the form t² - x². |

Master spool number: | HOU3159 |

Production number: | FOUM010P |

Videofinder number: | 844 |

Available to public: | no |