Why is ##(t_1'-t_2')^2## constant in proof(invariance of intervals)?

[Mike_bb]

Hello!

When I was proving that coefficient $a$ $(s'=as)$ is equal to $1$, I noticed that $(t_1' - t_2')^2$ should be constant then the proof works but otherwise it doesn't.

$c^2(t_1'-t_2')^2 - (x_1'-x_2')^2 - (y_1'-y_2')^2 - (z_1'-z_2')^2=a(c^2(t_1-t_2)^2 - (x_1-x_2)^2 - (y_1-y_2)^2 - (z_1-z_2)^2)$

Can anyone explain why should $(t_1'-t_2')^2$ be constant?

Thanks!

 

[Ibix]

What do you mean by "constant"? It's the difference in time coordinates of two events, so of course it doesn't change. But I don't think that's what you mean.

 

[anuttarasammyak]

As s=s', s is invariant between IFRs, not its time component quantity you refer.