Recent content by Kick-Stand

Any book to recommend with a good derivation of the result? Wikipedia is awful IMO.

So only after Taylor expanding ##\gamma_v, v\gamma_v, \gamma_w, w\gamma_w## for ##v,w\ll 1## and only keeping terms up to second order (e.g. ##1, v, w, v^2, w^2, vw##) do I get a rotation matrix, e.g. ##R^T R = I## and det(R) = 1 to second order, with my rotation matrix given by $$ R =...

Duh, since ##\mathbf{v},\mathbf{w}## are orthogonal I can just choose the y axis to correspond to either ##\mathbf{w}## or ##-\mathbf{w}##, whichever way ensures a right handed coordinate system.

Ugh I'll have to do it tomorrow, I have to be up for work in 4 1/2 hours lol. Thanks.

Is that not the most general condition on ##\mathbf{w}## for $$ vw_1 = \mathbf{v}\cdot\mathbf{w}=0 $$ to hold? Of course assuming ##v\neq 0##.

Ugh what am I doing wrong in the homework statement and relevant equations? Double pound for inline latex and double dollar signs for displayed latex right?

So is there some elegant way to do this or am I just supposed to follow my nose and sub the Taylor expansions for terms in the two boost matrices under the assumption ##v,w\ll 1##, then do three ugly matrix multiplications and get some horrifying kludge for ##R## and show that the product of...

It's kind of funny because one of the first things the prof does in Lecture 1 of that class is tell his students that yes you're going to feel in your soul that you should treat these early rank 2 tensors (like the Minkowski metric ##\eta_{\alpha\beta}## or Lorentz transform...

Or does this even really matter since the formulas used in this course will be in terms of components instead of matrices so who cares whether it's ##\alpha## or ##\mu'## that gives the row index of the matrix representation of the ##\binom{1}{1}## tensor ##L^\alpha_{\phantom{\alpha}\mu'}##?

I have been following the 8.962 class on OCW and I was thinking I was writing out the components correctly with first index row, second index column like matrices have been written in every other course I have taken, and pretty much every example we have gone through in the class in the first...