Lorentz Factor - Occurrence

Occurrence

Following is a list of formulae from Special relativity which use γ as a shorthand:

• The Lorentz transformation: The simplest case is a boost in the x-direction (more general forms including arbitrary directions and rotations not listed here), which describes how spacetime coordinates change from one inertial frame using coordinates (x, y, z, t) to another (x', y', z', t' ) with relative velocity v:

Corollaries of the above transformations are the results:

• Time dilation: The time (∆t' ) between two ticks as measured in the frame in which the clock is moving, is longer than the time (∆t) between these ticks as measured in the rest frame of the clock:

• Length contraction: The length (∆x' ) of an object as measured in the frame in which it is moving, is shorter than its length (∆x) in its own rest frame:

Applying conservation of momentum and energy leads to these results:

• Relativistic mass: The mass of an object m in motion is dependent on γ and the rest mass m₀:

• Relativistic momentum: The relativistic momentum relation takes the same form as for classical momentum, but using the above relativistic mass: