## Time Dilation in a Gravitational Field in Feynman Lectures onGravitation

Hello!
According to Feynman, in his lectures on gravitation on p.69, the
fractional difference in the frequencies of the clocks at the top
and the bottom is Delta w/w = the difference of the gravitational
potential divided by c^2. Having said this he considers an excited
nucleus at height h = 0 with energy E(0) = Mc^2 + E_0, where E_0
is the excitation energy and M is the mass in the ground state.
When this nucleus is raised to a height h its energy is
E(h) = Mc^2 + Mgh + E_0 + E_0*g*h/c^2 and the frequency of the
photon emitted, when this nucleus makes a transition to its ground
state, is w = w_0(1+g*h/c^2). What bothers me is that this frequency
reflects a 'blueshift' not a 'redshift', namely w > w_0, where
w_0 = E_0/hbar is the frequency of the photon emitted by the nucleus
on the ground (at h = 0). According to this expression the time read
by the ground clock would be longer than the time read by the upper
clock, because frequency and period are inversely proportional. Yet
he says `the center of the earth should be a day or two younger
than the surface', which is a correct time dilation statement. What I
do not understand is how he reaches the correct relation for the
time at two different heights from the relation w = w_0(1+g*h/c^2)...
What am I missing here?

Regards,
Murat Ozer

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