## The Lorentz Force

Several physical quantities similar relationships between that quantity in a rest frame – one in which an object is at rest – and the same quantity in a frame moving with constant velocity relative to the rest frame. The expressions below illustrate this for the base quantities of time, length and mass. In each case the prime indicates the quantity measured in the rest frame.

Time:

Length:

Mass:

The factorcalled the Lorentz factor, appears so often it is useful to give it the symbolIt increases very rapidly with speed at speeds close to the speed of light, but at normal speeds it is very close to one.

This increase ofmeans that

1. Clocks approaching the speed of light tick more and more slowly. A clock moving at the speed of light will not appear to tick at all.

2. An object approaching the speed of light will appear shorter and shorter. An object travelling at the speed of light will appear to have no length.

3. A mass approaching the speed of light will appear to have a much greater mass. An object travelling at the speed of light will have an infinite mass.

Any of these points mean that it is impossible for a material object to travel at the speed of light.