Rapidity

The rapidity (theta) is an alternative measure of speed, which is occasionally used in special relativity theory. Was first formulated the concept in 1911 by Alfred Robb.

The rapidity is defined as

In which

• V is the velocity and
• C is the speed of light
• The hyperbolic tangent hyperbolic function.

The rapidity measures the velocity in units of the speed of light, which would have an accelerated body without relativistic effects. The rapidity is therefore unlimited ( range of values), resulting in a more natural way of looking at is as the restriction of the actual speed, which can never exceed the speed of light ( range of values).

In addition, the rapidity has the advantage that two rapidities can be simply added, while you have to use the relativistic addition theorem for velocities.

For non-relativistic speeds, the rapidity approaches to the value of v / c:

In particle physics

Instead of the exact formula

With

• Energy E
• Pulse

Is in experimental particle physics often an approximate value used according to the formula

Wherein the longitudinal momentum, the pulse component along the beam axis.

The related size of the pseudorapidity is defined as

• Special Theory of Relativity
• Dimensionless size