- #1
pellman
- 684
- 5
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?