Length Contraction of Bridge rotated 30 degrees

[marimuda]

It seems to me that your teacher is doing what I tried to do in post #8: help you to do a mathematical solution to the problem and not just plug numbers into a calculator. In particular, he/she wants you to use the matrix form of the Lorentz Transformation. In this case, this is simply a 2x2 matrix acting on 2D vectors.

If you really have a problem with the maths - algebra as "gymnastics" and matrices as "ugly" - then you need to sort this out. You might start by locking away your pocket calculator for a week or two!

I can find L^2 by doing a lorentz transformation on x and leave y alone with a 2x2 matrix, and then multiply by L0vector components,
if that is what you mean.
Just don't see how that is a 'extension to 4-vectors'

 

[PeroK]

I can find L^2 by doing a lorentz transformation on x and leave y alone with a 2x2 matrix, and then multiply by L0vector components,
if that is what you mean.
Just don't see how that is a 'extension to 4-vectors'

Technically, you would extend your 2x2 matrix to a 4x4 matrix with 1 in the (3,3) and (4,4) positions and 0 everywhere else. That would transform $t$ and $x$ as before and leave $y$ and $z$ unchanged.

A 4-vector is, by definition, something that transforms according to Lorentz. $(ct, x, y, z)$ is a 4-vector. Where motion is in the x-direction only, this is essentially no different from transforming $x$, leaving $y$ unchanged and ignoring $z$.

I think you need to check with your teacher what he/she is expecting. We're just guessing here.