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'
yes exactly, and how to write it.
Ouch, that was even uglier than I could imagine. My teacher must have swallowed a rock or something, we've just gone through 2 D vector algebra in class, and now he expects this from me from my final school project. hehe
I think that x^'μ = Λ x^μ , if μ goes from 1 to 3 (spatial components) , and Λ is the Lorentz transformation along the x-axis,is on the right track but have no clue how to get the components into there, (cos(θ) , sin(θ) ) and L_0 so that I can solve for L
So, it's not only myself that gets lost by that request?
I was thinking along the lines of , if there is a Matrix (Lorentz transformation for my particular case ) which is multiplied on the four-vector x^μ, that when seen from the reference frame of the bridge ( stationary ) the length of the...
hehe apologize, yes maybe it needs a bit of clarification.
Alright, I've solved the problem above, (this is the same problem), where the length of the bridge observed is 19.526 m when the speed of the train is 1/4 c and the bridge is at a angle of 30 degree with a length of 20 m.
I asked my...
Yes, I know the term proper length, I've watched Leonard Susskind lectures on special relativity, and checked several books on the topic so the terms don't sound that unfamiliar.
With other words, I know how to do the Lorentz transformation 'brute force', I just don't know how I can write it up...
Apologize for bringing this post up again, but I'm still working in the problem, even tho we came to the solution and PeroK gave some brilliant advice, It may be that I need some mathematical clarity, or just mentally burned out by this project.
The thing that I'm trying to figure out is, how...
Thanks for the responds.. Is your answer 19.526 m ? , that's what I got when I did the correction chestermiller pointed out. I know that I need to do some algebraic gymnastics to set it up more efficiently, was just more thinking about if I even was in the right ball park.
We don't have any...
Hey, here's my calculations with all intermediate computations .
Ups, can see that there is some Faroese in the image, hopefully it doesn't make to confusing.
Homework Statement
A Train is driving with a uniformed velocity. v=1/4 c. The train is driving under a bridge, which is rotated \theta=30 degree in relation to the railway. The bridges length is 20 m long in a reference frame of the bridge (stationary bridge).
Calculate the length of the...