Confusion regarding Time in a gravitational field If time is inversely proportional to frequency. Then gravitational redshift would cause the frequency to be lower and wavelength to be higher. So if frequency is less more time has to pass by meaning time has to go faster. But as we all know if there is a grater gravitational field time will go slower. Please help me on this confusion.
 A: Suppose you are near a black hole, at some distance $r$ from its centre, and I am far from the black hole. Your time will be dilated with respect to mine by a factor of:
$$ \frac{d\tau}{dt} = \sqrt{1 - \frac{2GM}{c^2r}} $$
That is, for every $1$ second I measure on my clock only $\sqrt{1 - 2GM/(c^2r)}$ seconds passes for you. since $\sqrt{1 - 2GM/(c^2r)} \lt 1$ your clock is running more slowly than mine.
Now suppose you generate a signal with a frequency $f$, meaning that as measured by you there are $f$ cycles in one of your seconds, and you beam this signal out to me. Because your clock is running slow one of your seconds is equal to $1/\sqrt{1 - 2GM/(c^2r)}$ of my seconds, so I receive those $f$ cycles in a time:
$$ T = \frac{1}{\sqrt{1 - \frac{2GM}{c^2r}}} $$
Meaning that the frequency of the light I receive is:
$$ f' = \frac{f}{T} = f \sqrt{1 - \frac{2GM}{c^2r}} $$
and because $\sqrt{1 - 2GM/(c^2r)} \lt 1$ that means $f' \lt f$, so the light I receive from you has been red shifted. That is how the time dilation near the black hole causes the light to be red shifted as it travels outwards.
A: John's explanations are highly correct and precise (+1), and you can build your answer on it:


*

*The frequency is "dilated" (slowed down) when the light ray (or the signal) is leaving the gravity source, contrarily to gravitational time dilation which is acting on you if you are approaching the gravity source. This is what you are calling "confusion", and you are right, there is an apparent paradox.

*You can learn that the frequency of a photon cannot be considered as a clock of the photon, a photon itself has no reference frame which would provide any reference time.

*You also see that gravity and gravitational time dilation are a form of potential well. Particles are choosing the way which maximizes gravitational time dilation (= gravity), by this they are losing energy, and in order to leave the source of gravity, energy is needed. Photons leaving a gravity source lose energy by getting red-shifted.

*Gravitational redshift is a general phenomenon of gravity which even may be explained within Newton's physics (Edit: at least approximately, see the comments below of Pentcho Valev and Bob Bee, I don't want nor am I able to enter into this discussion), in particular the general fact that a loss of energy (when leaving a gravity field) generates redshift.
