Lorentz Factor Formula

Fixed Frame and Moving Frame

Diagram shows the fixed frame in 3 dimensional view, with 3 directions x, y and z respectively.

Consider the Moving frame where x’ is moving with primed frame with the velocity v in x direction.

The reference frames coincide at t=t’=0.

\({x}’=\frac{x-vt}{\sqrt{1-\frac{v^{2}}{c^{2}}}}\) \({y}’=y\) \({z}’=z\) \({t}’=\frac{t-\frac{vx}{c^{2}}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}\)

Where,

\(\beta =\frac{v}{c}\) \(\gamma =\,Lorentz\,factor\) \(\gamma =\frac{1}{{{\sqrt{1-\frac{v^{2}}{c^{2}}}}}}\)

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