Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Introductory Physics Homework Help
Special Relativity - Lorentz Transformation & Matrices
Reply to thread
Message
[QUOTE="Isaac Pepper, post: 5296586, member: 576214"] [h2]Homework Statement [/h2] There are three observers, all non accelerating. Observer B is moving at velocity vBA with respect to observer A. Observer C is moving at velocity vC B with respect to observer B. All three observers and all their relative velocities are directed along the same straight line. Calculate the matrix transforming the coordinates of an event from the reference frame of observer A to the reference frame of observer C. Comment of the form of the matrix [h2]Homework Equations[/h2] Assuming normal velocities (so we can use Galilean formulae) : $$u = v + u'$$ [h2]The Attempt at a Solution[/h2] Hi, if anyone could just explain what it is I need to do in this question please - I have not done Matrices yet in First Year Physics, but have looked up and understood how to use them (I think). I've never seen Matrices used in Relativity before. Any help would be greatly appreciated, thanks :) EDIT :: So perhaps the coordinates of an event could be written as follows : $$\binom{t}{x}$$ In the reference frame of observer A, observer C would be going at a velocity of $$V = Vcb+Vba$$ Therefore in the reference frame of observer C, observer A would appear to going at the same speed in the opposite direction : $$V = -(Vcb+Vba)$$ EDIT2 :: So I'm guessing that would mean $$x' = x-vt$$ $$t'=t$$ and $$\binom{t'}{x'}=\binom{t}{x-vt}$$ And we're looking for a matrix that would help us move from ##\binom{t'}{x'}## to ##\binom{t}{x}## So $$\binom{t}{x-vt}=\begin{pmatrix} m&n\\ l&p \end{pmatrix} \binom{t}{x}$$ Therefore $$mt+nx=t \rightarrow m=1, n=0$$ $$lt+px=x-vt \rightarrow p=1, l=-v$$ Finally, $$\begin{pmatrix} m&n\\ l&p \end{pmatrix} = \begin{pmatrix} 1&0\\ -v&1 \end{pmatrix}$$ Is that correct? [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Introductory Physics Homework Help
Special Relativity - Lorentz Transformation & Matrices
Back
Top