Consider a rocket of height h undergoing acceleration g relative
to an outside observer. Let a light ray be emitted from the top (B) at
time t=0 and be received at the bottom (A) at time 
in the
frame of the outside observer [ see Figure 5.6 ]. A second ray is emitted at
and received at 
.
One can show [ Assignment 5 ] that
where we have assumed that 
(i.e non-
relativistic motion).
Using the equivalence principle we know that the same relation
must apply of there is a difference in gravitational potential
between two points B and A in a gravitational
field. i.e.
If 
where 
[ no gravitational field ] and
B is taken to be a general point with position vector
, we expect
Since 
is negative, the time measured on B's
clock [ as seen by A at infinity ] is less than the time measured on
A's clock, i.e. clocks run slow in a gravitational field.
One can interpret this by imagining that the spacetime metric has the non- Minkowski form:
Then the proper time measured by a clock at fixed (x,y,z) in a
time 
measured at infinity is
therefore
for 
.
This corresponds to spacetime curvature.
