I have been working through Schutz's(adsbygoogle = window.adsbygoogle || []).push({}); A First Course in General Relativityand was a little confused by how he presents the space time interval:

[tex]\Delta \overline{s}^2 = \sum_{\alpha = 0}^{3} \sum_{\beta = 0}^{3} M_{\alpha \beta} (\Delta x^{\alpha})(\Delta x^{\beta}) [/tex] for some numbers [tex] \left\{M_{\alpha \beta} ; \alpha , \beta = 0,...,3\right\} [/tex] which may be functions of the relative velocity between the frames.

And then says:

Note that we can suppose that

[tex] M_{\alpha \beta} = M_{\beta \alpha} [/tex] for all [tex]\alpha[/tex] and [tex]\beta[/tex], since only the sum [tex] M_{\alpha \beta} + M_{\beta \alpha} [/tex] ever appears when [tex] \alpha \ne \beta [/tex]

Anyways I'm confused about his "note" - why can we suppose that?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Spacetime Interval

**Physics Forums | Science Articles, Homework Help, Discussion**