Special relativity, summation agreement

[Uku]

Homework Statement

[PLAIN]http://www.hot.ee/jaaniussikesed/valem_kovar_erlt.bmp

The first half of the equation is okay, but, after the second equal sign I started to improvise, did I mess up or is it correct? Trying to understand the indexes.

ds being the differentially small distance between events, dx the location vector? (not a 4 vector, I'm not sure on the English here) with covariant and contra-variant components present and the g is the metric tensor with its components marked by the indexes.

Regards,
Uku

 

[lanedance]

so i think you have got your indicies a little mixed up, a reapeted indicex, means to sum over the index, so start with
$$dx_{\mu} = g_{\mu \nu} dx^{\nu}$$

so in this case the sum is over the repeated $\nu$, the sum would then become a double sum
$$ds^2 = dx^{\mu} dx_{\mu} = dx^{\mu} g_{\mu \nu} dx^{\nu}$$

see this for more
http://en.wikipedia.org/wiki/Raising_and_lowering_indices

 

[Uku]

Thanks!