linguistic:translation, information:extraction, stylistic:style_transfer, linguistic:paraphrasing
Graphical representation of the Lorentz transformation

Fig. 3-1c. Units in the primed axes have a different scale from units in the unprimed axes. From the Lorentz transformations, we observe that (x ′, c t ′) {\displaystyle (x',ct')} coordinates of (0, 1) {\displaystyle (0,1)} in the primed coordinate system transform to (β γ, γ) {\displaystyle (\beta \gamma,\gamma)} in the unprimed coordinate system. Likewise, (x ′, c t ′) {\displaystyle (x',ct')} coordinates of (1, 0) {\displaystyle (1,0)} in the primed coordinate system transform to (γ, β γ) {\displaystyle (\gamma,\beta \gamma)} in the unprimed system. Draw gridlines parallel with the c t ′ {\displaystyle ct'} axis through points (k γ, k β γ) {\displaystyle (k\gamma,k\beta \gamma)} as measured in the unprimed frame, where k {\displaystyle k} is an integer. Likewise, draw gridlines parallel with the x ′ {\displaystyle x'} axis through (k β γ, k γ) {\displaystyle (k\beta \gamma,k\gamma)} as measured in the unprimed frame. Using the Pythagorean theorem, we observe that the spacing between c t ′ {\displaystyle ct'} units equals (1 + β 2) / (1 − β 2) {\textstyle {\sqrt {(1+\beta ^{2})/(1-\beta ^{2})}}} times the spacing between c t {\displaystyle ct} units, as measured in frame S. This ratio is always greater than 1, and ultimately it approaches infinity as β → 1. {\displaystyle \beta \to 1.}