# Does time expand along with space? [duplicate]

The flat FRW metric is given by:

$$ds^2=-c^2dt^2+a(t)^2dr^2$$

If we take $dt=0$ then we get:

$$ds=a(t)\ dr$$

Thus we find that space expands.

If we take $ds=0$ to find the null geodesic followed by a light beam we get:

$$c\ dt=a(t)\ dr$$

Does this imply that cosmological time expands along with space?

• Isn't the appropriate parallel to taking $dt = 0$, and concluding space is expanding, to take $dr = 0$ and then $ds^2 = -(cdt)^2$ and conclude that time is not expanding? – Alfred Centauri Apr 10 '15 at 21:37
• Duplicate of Does cosmological time expand along with space? – ACuriousMind Apr 10 '15 at 22:09
• I believe this has been asked and answered here: physics.stackexchange.com/a/83619/9887 – Alfred Centauri Apr 10 '15 at 23:08
• @AlfredCentauri If one takes $dr=0$ then one just finds that proper time for a co-moving observer is the same as cosmological time. But a co-moving observer would be expanding with the Universe whereas we do not. He would be measuring time with an expanding light clock whereas our light clocks have a fixed length. – John Eastmond Apr 11 '15 at 3:42

• I'm arguing that intervals of cosmological time $c\ dt=a(t)dr$ expand in exactly the same way as intervals of space $ds=a(t)dr$. – John Eastmond Apr 11 '15 at 3:31