Lorentz Factor Formula

Fixed Frame and Moving Frame

The 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 the primed frame with the velocity v in the 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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