The geometry of Lorentztransformation as a pseudorotation

[lynx]

What I know:

The Lorentztransformation as a transformation matrix multiplied to the old coordinates, to get the new coordinates:

cosh phi -sinh phi

-sinh phi cosh phi

 

which does look kind of like the standard rotation matrix exept signs and sinh/cosh instead of sin/cos. And I've read that the Lorentztransformation can e seen as a pseudorotation of the minkowski space.

 

What I want to know:

When I sketch a Minkowski diagram of a passive lorentztransformation, I rotate x and t into x' and t' in a passive lorentztransformation. I wonder if and how the pseudorotation is related to the rotation of the axes that I draw. I mean, actually it must be a rotation to another IS with orthogonal axes. But I wonder if this rotation of the x' and t' correspond to the pseudorotation somehow.

 

I also would like to read more about this pseudorotation. When I google I usually end up at chemistry pages or pages about General relativity, but I'm intrerested in Special relativity so far.

 

Any advise is welcome! :naughty::);)

[Qfwfq]

If you measure c in m/s the x axis hardly budges!!!! :)

 

In natural units, c = 1 and this is quite appropriate for the geometrical point of view. In many textbooks show the correspondence between the axes, c is the bisector of the cartesian plane and the axes of the other coordinate system both rotate toward it as v approaches c. In a loose sense, this is how [imath]v\rightarrow c[/imath], is sorta like [imath]v\rightarrow\infty[/imath].