Re: Some Beginner SR Questions

Dean Elliot:
>"Bill Hobba" <bhobba@xxxxxxxxxxxxxx> wrote:
>
>> Consider the origin of the two systems to coincide i.e. if
>> Xu = 0 then X'u = 0. Now suppose Xu = 0 then from the calculus delta X'u
>> A delta Xu for some 4x4 matrix A.
>
>I'm at a loss to understand this matrix. Since you arrive at via calculus
>I assume that it is the result of partial derivatives.

x' = (I + a)x I is the identity matrix, a is an infinitesimal
displacement of each element of x along each direction.

>Could you give a simple concrete example for me? (You can see that if
>things are not explained in detail then I get bogged down trying to
>understand them.)

Check any classical mechanics text book under ``rotations.'' The only
difference between that and relativity is that for 3-d rotations,
g_uv is the identity matrix, diag{1,1,1} and in relativity the
metrix is g_uv = diag{-1,1,1,1}. The relativistic derivation proceeds
exactly the same way. You get 3-d rotations (sine and cosine) plus
spacetime rotations which are hyperbolic sines and cosines due to
the -1. If you understand euclidean rotations, then you'll understand
spacetime rotations.


.

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