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## Main Question or Discussion Point

I have been working through Schutz's

[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?

*A First Course in General Relativity*and 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?