[tex]x'=a_{11}x+a_{12}y+a_{13}z+a_{14}t[/tex](adsbygoogle = window.adsbygoogle || []).push({});

[tex]y'=a_{21}x+a_{22}y+a_{23}z+a_{24}t[/tex]

[tex]z'=a_{31}x+a_{32}y+a_{33}z+a_{34}t[/tex]

[tex]t'=a_{41}x+a_{42}y+a_{43}z+a_{44}t[/tex]

[tex]\vec{u}=u\vec{e}_x[/tex]

Coefficients [tex]a_{nm}=a_{nm}(u)[/tex]

Why I suppose that coefficients are function only of velocity [tex]u[/tex]?

Inverse relations

[tex]x=a_{11}'x'+a_{12}'y'+a_{13}'z'+a_{14}'t'[/tex]

[tex]y=a_{21}'x'+a_{22}'y'+a_{23}'z'+a_{24}'t'[/tex]

[tex]z=a_{31}'x'+a_{32}'y'+a_{33}'z'+a_{34}'t'[/tex]

[tex]t=a_{41}'x'+a_{42}'y'+a_{43}'z'+a_{44}'t'[/tex]

[tex]a_{nm}'(u)=a_{nm}(-u)[/tex]

Equations of transformations are linear (time and space are homogeneous).

That means from linearity of transformations [tex]\Rightarrow[/tex] time and space are homogeneous?

Why now I can say

[tex]y'=a_{22}y[/tex]

[tex]z'=a_{33}z[/tex]

[tex]t'=a_{41}x+a_{44}t[/tex]?

Thanks for your answer!

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# Lorentz transformation

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