Unravelling Metrics of Spacetime

[alejandrito29]

In a space time with metrics :
$$ds^2=f(t)(-dt^2+dx^2+dy^2+dz^2)$$

which is the unit that measures time t?

second?, meter of time?

 

[Dale]

For dimensional consistency it would have to be the same units that dx, dy, and dz are measured in.

 

[alejandrito29]

For dimensional consistency it would have to be the same units that dx, dy, and dz are measured in.

then , if dx,dy and dz are in meters, then t is in meters of time?

 

[Dale]

Yes. See for example: http://en.wikipedia.org/wiki/Geometrized_unit_system

 

[DrGreg]

then , if dx,dy and dz are in meters, then t is in meters of time?

A "metre of time" is the time it takes for light to travel one metre, i.e. (1/299792458) seconds.

Or you could measure dx, dy and dz in light-seconds and then dt is in seconds.

 

[Matterwave]

to be explicit, a c^2 should appear before dt^2 to explicitly convert time into units of distance. But, in relativistic units c=1 so we just omit the c and it's understood.