Hi, maybe someone could answer this for me, or at least confirm my answer. (It's not homework.)(adsbygoogle = window.adsbygoogle || []).push({});

What objects, in General Relativity, carry units?

My thinking is that coordinates, [tex]x^i[/tex], on manifold patches have no units. And the parameter, [tex]t[/tex], for a path [tex]x^i(t)[/tex] has no units. So velocities with respect to that parameter have no units. But proper time does have units, seconds say, [tex][\tau]=s[/tex], and is the integral of the velocity magnitude

[tex]\Delta \tau = \int dt \sqrt{v^i v^j g_{ij}}[/tex]

So the metric needs to have units, [tex][g_{ij}]=s^2[/tex].

Does this seem right? Or does one actually ascribe units to manifold coordinates?

My feeling is one could do that, but those units would be meaningless and be swallowed by the metric, which is the only physical object giving meaning to distance and carrying units.

Thanks!

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# What objects, in General Relativity, carry units?

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