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## Main Question or Discussion Point

The proper time is defined by

[tex]d\tau^2=g_{\mu\nu}dx^\mu dx^\nu[/tex]

Suppose we have flat space time with one space dimension.

[tex]d\tau=\sqrt{dt^2-dx^2}[/tex]

[tex]=dt\sqrt{1-\frac{(dx^2)}{(dt^2)}}[/tex]

[tex]=dt\sqrt{1-\left(\frac{dx}{dt}\right)^2}[/tex]

Can this be rigorous?

[tex]d\tau^2=g_{\mu\nu}dx^\mu dx^\nu[/tex]

Suppose we have flat space time with one space dimension.

[tex]d\tau=\sqrt{dt^2-dx^2}[/tex]

[tex]=dt\sqrt{1-\frac{(dx^2)}{(dt^2)}}[/tex]

[tex]=dt\sqrt{1-\left(\frac{dx}{dt}\right)^2}[/tex]

Can this be rigorous?