Editing Faster-than-light (section)

===Closing speeds===
The rate at which two objects in motion in a single frame of reference get closer together is called the mutual or closing speed. This may approach twice the speed of light, as in the case of two particles travelling at close to the speed of light in opposite directions with respect to the reference frame.

Imagine two fast-moving particles approaching each other from opposite sides of a [[particle accelerator]] of the collider type. The closing speed would be the rate at which the distance between the two particles is decreasing. From the point of view of an observer standing at rest relative to the accelerator, this rate will be slightly less than twice the speed of light.

[[Special relativity]] does not prohibit this. It tells us that it is wrong to use [[Galilean relativity]] to compute the velocity of one of the particles, as would be measured by an observer traveling alongside the other particle. That is, special relativity gives the correct [[velocity-addition formula]] for computing such [[relative velocity]].

It is instructive to compute the relative velocity of particles moving at ''v'' and −''v'' in accelerator frame, which corresponds to the closing speed of 2''v''&nbsp;>&nbsp;''c''. Expressing the speeds in units of ''c'', ''β''&nbsp;=&nbsp;''v''/''c'':
:<math>\beta_\text{rel} = \frac{\beta + \beta}{1 + \beta ^2} = \frac{2\beta}{1 + \beta^2} \leq 1.</math>