Editing Lorentz factor (section)

==Occurrence==
Following is a list of formulae from Special relativity which use {{math|γ}} as a shorthand:<ref name="Forshaw 2014" /><ref>{{cite book |last2=Freedman |last1=Young |date=2008 |title=Sears' and Zemansky's University Physics |edition=12th |publisher=Pearson Ed. & Addison-Wesley |isbn=978-0-321-50130-1 }}</ref>
* The '''[[Lorentz transformation]]:''' The simplest case is a boost in the {{mvar|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 {{math|(''x'', ''y'', ''z'', ''t'')}} to another {{math|1=(''x''{{′}}, ''y''{{′}}, ''z''{{′}}, ''t''{{′}})}} with relative velocity {{mvar|v}}: <math display="block">\begin{align}
  t' &= \gamma \left( t - \tfrac{vx}{c^2} \right ), \\[1ex]
  x' &= \gamma \left( x - vt \right ).
\end{align}</math>
Corollaries of the above transformations are the results:
* '''[[Time dilation]]:''' The time ({{math|∆''t''{{′}}}}) between two ticks as measured in the frame in which the clock is moving, is longer than the time ({{math|∆''t''}}) between these ticks as measured in the rest frame of the clock: <math display="block">\Delta t' = \gamma \Delta t.</math>
* '''[[Length contraction]]:''' The length ({{math|∆''x''{{′}}}}) of an object as measured in the frame in which it is moving, is shorter than its length ({{math|∆''x''}}) in its own rest frame: <math display="block">\Delta x' = \Delta x/\gamma.</math>

Applying [[Conservation law (physics)|conservation]] of [[Conservation of linear momentum|momentum]] and energy leads to these results:
* '''[[Relativistic mass]]:''' The [[mass]] {{mvar|m}} of an object in motion is dependent on <math>\gamma</math> and the [[invariant mass|rest mass]] {{math|''m''<sub>0</sub>}}: <math display="block">m = \gamma m_0.</math>
* '''[[Relativistic momentum]]:''' The relativistic [[momentum]] relation takes the same form as for classical momentum, but using the above relativistic mass: <math display="block">\vec p = m \vec v = \gamma m_0 \vec v.</math>
* '''[[Kinetic energy#Relativistic kinetic energy of rigid bodies|Relativistic kinetic energy]]:''' The relativistic kinetic [[energy]] relation takes the slightly modified form: <math display="block">E_k = E - E_0 = (\gamma - 1) m_0 c^2</math>As <math>\gamma</math> is a function of <math>\tfrac{v}{c}</math>, the non-relativistic limit gives <math display="inline">\lim_{v/c\to 0}E_k=\tfrac{1}{2}m_0v^2</math>, as expected from Newtonian considerations.